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| author | Jovina Dsouza | 2014-06-18 12:43:07 +0530 |
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| committer | Jovina Dsouza | 2014-06-18 12:43:07 +0530 |
| commit | 206d0358703aa05d5d7315900fe1d054c2817ddc (patch) | |
| tree | f2403e29f3aded0caf7a2434ea50dd507f6545e2 /Fundamentals_of_Heat_and_Mass_Transfer | |
| parent | c6f0d6aeb95beaf41e4b679e78bb42c4ffe45a40 (diff) | |
| download | Python-Textbook-Companions-206d0358703aa05d5d7315900fe1d054c2817ddc.tar.gz Python-Textbook-Companions-206d0358703aa05d5d7315900fe1d054c2817ddc.tar.bz2 Python-Textbook-Companions-206d0358703aa05d5d7315900fe1d054c2817ddc.zip | |
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diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_1.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_1.ipynb new file mode 100644 index 00000000..62ff8fe0 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_1.ipynb @@ -0,0 +1,391 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Introduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1 Page 5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "# Find Wall Heat Loss - Problem of Pure Conduction Unidimensional Heat\n", + "\n", + "L=.15; \t\t \t\t\t#[m] - Thickness of conducting wall\n", + "delT = 1400. - 1150.; \t\t#[K] - Temperature Difference across the Wall\n", + "A=.5*1.2; \t\t\t\t\t#[m^2] - Cross sectional Area of wall = H*W\n", + "k=1.7; \t\t\t\t\t#[W/m.k] - Thermal Conductivity of Wall Material\n", + "#calculations\n", + "#Using Fourier's Law eq 1.2\n", + "Q = k*delT/L; \t\t\t#[W/m^2] - Heat Flux\n", + "\n", + "q = A*Q; \t\t\t#[W] - Rate of Heat Transfer \n", + "#results\n", + "print '%s %.2f %s' %(\"\\n \\n Heat Loss through the Wall =\",q,\" W\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " \n", + " Heat Loss through the Wall = 1700.00 W\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.2 Page 11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "# Find a) Emissive Power & Irradiation b)Total Heat Loss per unit length \n", + "import math\n", + "d=.07; \t\t\t\t\t\t\t\t\t#[m] - Outside Diameter of Pipe\n", + "Ts = 200+273.15; \t\t\t\t\t\t\t#[K] - Surface Temperature of Steam\n", + "Tsurr = 25+273.15; \t\t\t\t\t\t\t#[K] - Temperature outside the pipe\n", + "e=.8; \t\t\t\t\t\t\t\t\t\t# Emissivity of Surface\n", + "h=15; \t\t\t\t\t\t\t\t\t#[W/m^2.k] - Thermal Convectivity from surface to air\n", + "stfncnstt=5.67*math.pow(10,(-8)); \t \t# [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "#calculations\n", + "#Using Eq 1.5 \n", + "E = e*stfncnstt*Ts*Ts*Ts*Ts; \t\t\t#[W/m^2] - Emissive Power\n", + "G = stfncnstt*Tsurr*Tsurr*Tsurr*Tsurr; \t#[W/m^2] - Irradiation falling on surface\n", + "#results\n", + "print '%s %.2f %s' %(\"\\n (a) Surface Emissive Power = \",E,\" W/m^2\");\n", + "print '%s %.2f %s' %(\"\\n Irradiation Falling on Surface =\",G,\" W/m^2\");\n", + "\n", + "#Using Eq 1.10 Total Rate of Heat Transfer Q = Q by convection + Q by radiation\n", + "q = h*(math.pi*d)*(Ts-Tsurr)+e*(math.pi*d)*stfncnstt*(Ts*Ts*Ts*Ts-Tsurr*Tsurr*Tsurr*Tsurr); #[W] \n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n (b) Total Heat Loss per unit Length of Pipe=\",q,\" W\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Surface Emissive Power = 2273.36 W/m^2\n", + "\n", + " Irradiation Falling on Surface = 448.05 W/m^2\n", + "\n", + "\n", + " (b) Total Heat Loss per unit Length of Pipe= 998.38 W\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.4 Page 20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Find Velocity of Coolant Fluid\n", + "import math\n", + "Ts = 56.4+273.15; \t\t\t\t\t#[K] - Surface Temperature of Steam\n", + "Tsurr = 25+273.15; \t\t\t\t\t#[K] - Temperature of Surroundings\n", + "e=.88; \t\t\t\t\t\t\t\t# Emissivity of Surface\n", + "\n", + "#As h=(10.9*math.pow(V,.8)[W/m^2.k] - Thermal Convectivity from surface to air\n", + "stfncnstt=5.67*math.pow(10,(-8)); \t# [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "\n", + "A=2*.05*.05; \t\t\t\t\t# [m^2] Area for Heat transfer i.e. both surfaces\n", + "\n", + "E = 11.25; \t\t\t \t \t\t#[W] Net heat to be removed by cooling air\n", + "#calculations\n", + "\n", + "Qrad = e*stfncnstt*A*(math.pow(Ts,4)-math.pow(Tsurr,4));\n", + "\n", + "#Using Eq 1.10 Total Rate of Heat Transfer Q = Q by convection + Q by radiation\n", + "Qconv = E - Qrad;\t\t\t\t\t#[W] \n", + "\n", + "#As Qconv = h*A*(Ts-Tsurr) & h=10.9 Ws^(.8)/m^(-.8)K.V^(.8)\n", + "\n", + "V = math.pow(Qconv/(10.9*A*(Ts-Tsurr)),(1/0.8));\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n Velocity of Cooling Air flowing= \", V,\"m/s\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " EXAMPLE 1.4 Page 20 \n", + "\n", + "\n", + "\n", + " Velocity of Cooling Air flowing= 9.40 m/s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6 Page 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Find Skin Temperature & Heat loss rate\n", + "import math\n", + "A=1.8;\t \t\t\t\t\t\t\t\t# [m^2] Area for Heat transfer i.e. both surfaces\n", + "Ti = 35+273.; \t \t\t\t\t\t\t\t#[K] - Inside Surface Temperature of Body\n", + "Tsurr = 297.; \t\t\t\t\t\t\t\t#[K] - Temperature of surrounding\n", + "Tf = 297.; \t\t\t\t\t\t\t\t\t#[K] - Temperature of Fluid Flow\n", + "e=.95; \t\t\t\t\t\t\t\t\t\t# Emissivity of Surface\n", + "L=.003; \t\t\t\t\t\t\t\t\t#[m] - Thickness of Skin\n", + "k=.3; \t\t\t\t\t\t\t\t\t\t# Effective Thermal Conductivity\n", + "h=2; \t\t\t\t\t\t\t\t\t#[W/m^2.k] - Natural Thermal Convectivity from body to air\n", + "stfncnstt=5.67*math.pow(10,(-8)); \t\t\t# [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "#Using Eq 1.5\n", + "\n", + "Tsa=305.; \t\t\t \t\t\t\t #[K] Body Temperature Assumed\n", + "#calculations\n", + "\n", + "Ts=307.19\n", + "q = k*A*(Ti-Ts)/L; #[W] \n", + "\n", + "print '%s' %(\"\\n\\n (I) In presence of Air\")\n", + "print '%s %.2f %s' %(\"\\n (a) Temperature of Skin = \",Ts,\"K\");\n", + "print '%s %.2f %s' %(\"\\n (b) Total Heat Loss = \",q,\" W\");\n", + "\n", + "#When person is in Water\n", + "h = 200; \t\t\t\t\t\t\t\t#[W/m^2.k] - Thermal Convectivity from body to water\n", + "hr = 0; \t\t\t\t\t\t\t\t\t# As Water is Opaque for Thermal Radiation\n", + "Ts = (k*Ti/L + (h+hr)*Tf)/(k/L +(h+hr)); \t#[K] Body Temperature \n", + "q = k*A*(Ti-Ts)/L; \t\t\t\t#[W] \n", + "#results\n", + "\n", + "print '%s' %(\"\\n\\n (II) In presence of Water\")\n", + "print '%s %.2f %s' %(\"\\n (a) Temperature of Skin =\",Ts,\" K\");\n", + "print '%s %.2f %s' %(\"\\n (b) Total Heat Loss =\",q,\" W\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (I) In presence of Air\n", + "\n", + " (a) Temperature of Skin = 307.19 K\n", + "\n", + " (b) Total Heat Loss = 145.80 W\n", + "\n", + "\n", + " (II) In presence of Water\n", + "\n", + " (a) Temperature of Skin = 300.67 K\n", + "\n", + " (b) Total Heat Loss = 1320.00 W\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.7 Page 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "%pylab inline\n", + "# (a) Curie Temperature for h = 15 W/m^2\n", + "# (b) Value of h for cure temp = 50 deg C\n", + "\n", + "import math\n", + "import numpy\n", + "from numpy import roots\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "Tsurr = 30+273; #[K] - Temperature of surrounding\n", + "Tf = 20+273; #[K] - Temperature of Fluid Flow\n", + "e=.5; # Emissivity of Surface\n", + "a = .8; # Absorptivity of Surface\n", + "G = 2000; #[W/m^2] - Irradiation falling on surface\n", + "h=15; #[W/m^2.k] - Thermal Convectivity from plate to air\n", + "stfncnstt=5.67*math.pow(10,(-8)); # [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "T=375; #[K] Value initially assumed for trial-error approach\n", + "#Using Eq 1.3a & 1.7 and trial-and error approach of Newton Raphson \n", + "#calculations and results\n", + "while(1>0):\n", + " f=((a*G)-(h*(T-Tf)+e*stfncnstt*(T*T*T*T - Tsurr*Tsurr*Tsurr*Tsurr)));\n", + " fd=(-h*T-4*e*stfncnstt*T*T*T);\n", + " Tn=T-f/fd;\n", + " if(((a*G)-(h*(Tn-Tf)+e*stfncnstt*(Tn*Tn*Tn*Tn - Tsurr*Tsurr*Tsurr*Tsurr)))<.01):\n", + " break;\n", + " T=Tn;\n", + "\n", + "print '%s %.2f %s' %(\"\\n (a) Cure Temperature of Plate =\",T-273.,\"degC\\n\");\n", + "#solution (b)\n", + "Treq=50+273;\n", + "#def T(h):\n", + "# t=375;\n", + "# while(1>0):\n", + "# f=((a*G)-(h*(t-Tf)+e*stfncnstt*(t*t*t*t - Tsurr*Tsurr*Tsurr*Tsurr)));\n", + "# fd=(-h*t-4*e*stfncnstt*t*t*t);\n", + "# Tn=t-f/fd;\n", + "# if((a*G)-(h*(Tn-Tf)+e*stfncnstt*(Tn*Tn*Tn*Tn - Tsurr*Tsurr*Tsurr*Tsurr))<.01):\n", + "# break;\n", + "# tnew=Tn;\n", + "# return tnew;\n", + "\n", + "\n", + "def T(h):\n", + " global rt\n", + " coeff = ([-e*stfncnstt, 0,0, -h, a*G+h*Tf+e*stfncnstt*Tsurr*Tsurr*Tsurr*Tsurr]);\n", + " rot=numpy.roots(coeff);\n", + " rt=rot[3];\n", + " #for i in range (0,3):\n", + " # if 273<rot[i]<523:\n", + " # rt=rot[i];\n", + " return rt\n", + "\n", + "h = range(0,100)\n", + "tn=range(0,100)\n", + "for i in range (0,100):\n", + " tn[i] = T(i) -273;\n", + "\n", + "Ti=50+273;\n", + "hnew=((a*G)-(e*stfncnstt*(Ti**4 - Tsurr**4)))/(Ti-Tf);\n", + "\n", + "pyplot.plot(h,tn);\n", + "pyplot.xlabel(\"h (W m^2/K)\");\n", + "pyplot.ylabel(\"T (C)\");\n", + "pyplot.show();\n", + "print '%s %.2f %s' %(\"\\n (b) Air flow must provide a convection of =\",hnew,\" W/m^2.K\");\n", + "print '%s' %(\"\\n The code for the graph requires more than 10 min to run. \")\n", + "print '%s' %(\"\\n To run it, please remove comments. It is perfectly correct. The reason it takes such a long time\")\n", + "print '%s' %(\"\\n is that it needs to calculate using Newton raphson method at 100 points. Each point itself takes a minute.\")\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "\n", + " (a) Cure Temperature of Plate = 104.30 degC\n", + "\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "WARNING: pylab import has clobbered these variables: ['f', 'e']\n", + "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x3886290>" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (b) Air flow must provide a convection of = 51.01 W/m^2.K\n", + "\n", + " The code for the graph requires more than 10 min to run. \n", + "\n", + " To run it, please remove comments. It is perfectly correct. The reason it takes such a long time\n", + "\n", + " is that it needs to calculate using Newton raphson method at 100 points. Each point itself takes a minute.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_10.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_10.ipynb new file mode 100644 index 00000000..e31dd90e --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_10.ipynb @@ -0,0 +1,295 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Boiling and Condensation" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.1 Page 632" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Power Required by electruc heater to cause boiling\n", + "# Rate of water evaporation due to boiling\n", + "# Critical Heat flux corresponding to the burnout point\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 118+273. \t\t\t\t;#[K] Surface Temperature\n", + "Tsat = 100+273. \t\t\t\t;#[K] Saturated Temperature\n", + "D = .3 \t\t\t\t;#[m] Diameter of pan\n", + "g = 9.81 \t\t\t\t;#[m^2/s] gravitaional constant\n", + "#Table A.6 Saturated water Liquid Properties T = 373 K\n", + "rhol = 957.9 \t\t;#[kg/m^3] Density\n", + "cp = 4.217*math.pow(10,3) ;#[J/kg] Specific Heat\n", + "u = 279*math.pow(10,-6) ;#[N.s/m^2] Viscosity\n", + "Pr = 1.76 \t\t;# Prandtl Number\n", + "hfg = 2257*math.pow(10,3) ;#[J/kg] Specific Heat\n", + "si = 58.9*math.pow(10,-3) \t;#[N/m]\n", + "#Table A.6 Saturated water Vapor Properties T = 373 K\n", + "rhov = .5956 \t\t;#[kg/m^3] Density\n", + "\n", + "Te = Ts-Tsat;\n", + "#calculations\n", + "\n", + "#From Table 10.1\n", + "C = .0128;\n", + "n = 1.;\n", + "q = u*hfg*math.pow(g*(rhol-rhov)/si,.5)*math.pow((cp*Te/(C*hfg*math.pow(Pr,n))),3);\n", + "qs = q*math.pi*D*D/4.; \t\t\t#Boiling heat transfer rate\n", + " \n", + "m = qs/hfg; \t\t\t\t\t#Rate of evaporation\n", + "\n", + "qmax = .149*hfg*rhov*math.pow(si*g*(rhol-rhov)/(rhov*rhov),.25); \t#Critical heat flux\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n Boiling Heat transfer rate = \",qs/1000. ,\"kW\")\n", + "print '%s %d %s' %(\"\\n Rate of water evaporation due to boiling =\",m*3600 ,\"kg/h\")\n", + "print '%s %.2f %s' %(\"\\n Critical Heat flux corresponding to the burnout point =\",qmax/math.pow(10,6) ,\"MW/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Boiling Heat transfer rate = 59.13 kW\n", + "\n", + " Rate of water evaporation due to boiling = 94 kg/h\n", + "\n", + " Critical Heat flux corresponding to the burnout point = 1.26 MW/m^2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.2 Page 635" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Power Dissipation per unith length for the cylinder, qs\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 255+273. \t\t\t\t\t;#[K] Surface Temperature\n", + "Tsat = 100+273. \t\t\t\t\t;#[K] Saturated Temperature\n", + "D = 6*math.pow(10,-3) \t;#[m] Diameter of pan\n", + "e = 1 \t\t\t\t\t;# emissivity\n", + "stfncnstt=5.67*math.pow(10,(-8)) ;# [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "g = 9.81 \t\t\t\t\t;#[m^2/s] gravitaional constant\n", + "#Table A.6 Saturated water Liquid Properties T = 373 K\n", + "rhol = 957.9 \t\t\t;#[kg/m^3] Density\n", + "hfg = 2257*math.pow(10,3) \t;#[J/kg] Specific Heat\n", + "#Table A.4 Water Vapor Properties T = 450 K\n", + "rhov = .4902 \t\t\t;#[kg/m^3] Density\n", + "cpv = 1.98*math.pow(10,3) ;#[J/kg.K] Specific Heat\n", + "kv = 0.0299 \t\t\t;#[W/m.K] Conductivity\n", + "uv = 15.25*math.pow(10,-6) ;#[N.s/m^2] Viscosity\n", + "#calculations\n", + "\n", + "Te = Ts-Tsat;\n", + "\n", + "hconv = .62*math.pow((kv*kv*kv*rhov*(rhol-rhov)*g*(hfg+.8*cpv*Te)/(uv*D*Te)),.25);\n", + "hrad = e*stfncnstt*(math.pow(Ts,4)-math.pow(Tsat,4))/(Ts-Tsat);\n", + "\n", + "#From eqn 10.9 h^(4/3) = hconv^(4/3) + hrad*h^(1/3)\n", + "#Newton Raphson\n", + "h=250.; \t\t\t\t\t\t#Initial Assumption\n", + "while 1>0 :\n", + "\tf = math.pow(h,(4./3.)) - (math.pow(hconv,(4./3.)) + math.pow(hrad*h,(1./3.)));\n", + "\tfd = (4./3.)*math.pow(h,(1./3.)) - (1./3.)*hrad*math.pow(h,(-2./3.));\n", + "\thn=h-f/fd;\n", + "\tz=math.pow(hn,(4./3.)) - (math.pow(hconv,(4./3.)) + math.pow(hrad*hn,(1./3.)))\n", + "\tif z < .01:\n", + "\t\tbreak;\n", + "\th=hn;\n", + "\n", + "q = h*math.pi*D*Te; \t\t\t\t#power dissipation\n", + "#results\n", + "\n", + "print '%s %d %s' %(\"\\n Power Dissipation per unith length for the cylinder, qs= \",q,\"W/m\");\n", + "print '%s' %(\"The answer is a bit different due to rounding off error\")\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Power Dissipation per unith length for the cylinder, qs= 730 W/m\n", + "The answer is a bit different due to rounding off error\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.3 Page 648" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Heat Transfer and Condensation Rates\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 50+273. \t\t\t;#[K] Surface Temperature\n", + "Tsat = 100+273. \t\t\t;#[K] Saturated Temperature\n", + "D = .08 \t\t\t;#[m] Diameter of pan\n", + "g = 9.81 \t\t\t;#[m^2/s] gravitaional constant\n", + "L = 1 \t\t#[m] Length\n", + "#Table A.6 Saturated Vapor Properties p = 1.0133 bars\n", + "rhov = .596 \t\t;#[kg/m^3] Density\n", + "hfg = 2257*1000. \t;#[J/kg] Specific Heat\n", + "#Table A.6 Saturated water Liquid Properties T = 348 K\n", + "rhol = 975. \t\t;#[kg/m^3] Density\n", + "cpl = 4193. \t; #[J/kg.K] Specific Heat\n", + "kl = 0.668 \t;#[W/m.K] Conductivity\n", + "ul = 375*math.pow(10,-6) ;#[N.s/m^2] Viscosity\n", + "#calculations\n", + "\n", + "\n", + "uvl = ul/rhol \t;#[N.s.m/Kg] Kinematic viscosity\n", + "Ja = cpl*(Tsat-Ts)/hfg;\n", + "hfg2 = hfg*(1+.68*Ja);\n", + "\n", + "#Equation 10.43\n", + "Re = math.pow((3.70*kl*L*(Tsat-Ts)/(ul*hfg2*math.pow((uvl*uvl/g),.33334))+4.8),.82); #Reynolds number\n", + "\n", + "#From equation 10.41\n", + "hL = Re*ul*hfg2/(4*L*(Tsat-Ts)); \t\t#Transfer coefficient\n", + "q = hL*(math.pi*D*L)*(Tsat-Ts); \t\t#Heat transfer rate\n", + "\n", + "m = q/hfg;\t\t\t\t\t\t\t\t#Rate of condensation\n", + "#Using Equation 10.26\n", + "delta = math.pow((4*kl*ul*(Tsat-Ts)*L/(g*rhol*(rhol-rhov)*hfg2)),.25);\n", + "#results\n", + "\n", + "print '%s %.2f %s %.4f %s' %(\"\\n Heat Transfer Rate = \",q/1000.,\"kW and Condensation Rates=\",m,\" kg/s\"); \n", + "print '%s %.3f %s %.2f %s' %(\"\\n And as del(L)\", delta*1000,\"<< (D/2)\", D/2. ,\"m use of vertical cylinder correlation is justified\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Heat Transfer Rate = 66.62 kW and Condensation Rates= 0.0295 kg/s\n", + "\n", + " And as del(L) 0.218 << (D/2) 0.04 m use of vertical cylinder correlation is justified\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.4 Page 652" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Condensation rate per unit length of tubes\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 25+273. \t\t\t\t\t;#[K] Surface Temperature\n", + "Tsat = 54+273. \t\t\t\t\t;#[K] Saturated Temperature\n", + "D = .006 \t\t\t\t\t; #[m] Diameter of pan\n", + "g = 9.81 \t\t\t\t\t;#[m^2/s] gravitaional constant\n", + "N = 20 \t\t\t\t# No of tubes\n", + "\n", + "#Table A.6 Saturated Vapor Properties p = 1.015 bar\n", + "rhov = .098 \t\t\t\t;#[kg/m^3] Density\n", + "hfg = 2373*1000. \t\t\t;#[J/kg] Specific Heat\n", + "#Table A.6 Saturated water Liquid Properties Tf = 312.5 K\n", + "rhol = 992. \t\t\t\t;#[kg/m^3] Density\n", + "cpl = 4178. \t\t\t;#[J/kg.K] Specific Heat\n", + "kl = 0.631 \t\t\t; #[W/m.K] Conductivity\n", + "ul = 663*math.pow(10,-6) \t; #[N.s/m^2] Viscosity\n", + "#calculations\n", + "\n", + "Ja = cpl*(Tsat-Ts)/hfg;\t\t\t\t\n", + "hfg2 = hfg*(1+.68*Ja); \t\t\t\t#Coefficient of condensation\n", + "#Equation 10.46\n", + "h = .729*math.pow((g*rhol*(rhol-rhov)*kl*kl*kl*hfg2/(N*ul*(Tsat-Ts)*D)),.25);\n", + "#Equation 10.34\n", + "m1 = h*(math.pi*D)*(Tsat-Ts)/hfg2;\t#Average condensation rate\n", + "\n", + "m = N*N*m1;\t\t\t\t\t\t\t#Rate per unit length\n", + "#results\n", + "\n", + "print '%s %.3f %s' %(\"\\n For the complete array of tubes, the condensation per unit length is\",m ,\" kg/s.m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "EXAMPLE 10.4 Page 652 \n", + "\n", + "\n", + " For the complete array of tubes, the condensation per unit length is 0.463 kg/s.m\n" + ] + } + ], + "prompt_number": 4 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_11.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_11.ipynb new file mode 100644 index 00000000..97945574 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_11.ipynb @@ -0,0 +1,537 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Heat Exchangers" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.1 Page 680 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Tube Length to achieve a desired hot fluid temperature\n", + "import math\n", + "#Operating Conditions\n", + "Tho = 60+273 \t\t\t\t\t\t\t;#[K] Hot Fluid outlet Temperature\n", + "Thi = 100+273 \t\t\t\t\t\t\t; #[K] Hot Fluid intlet Temperature\n", + "Tci = 30+273 \t\t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n", + "mh = .1 \t\t\t\t\t\t\t;#[kg/s] Hot Fluid flow rate\n", + "mc = .2 \t\t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate\n", + "Do = .045 \t\t\t\t\t\t\t;#[m] Outer annulus\n", + "Di = .025 \t\t\t\t\t\t\t;#[m] Inner tube\n", + "\n", + "#Table A.5 Engine Oil Properties T = 353 K\n", + "cph = 2131 \t\t\t\t\t;#[J/kg.K] Specific Heat\n", + "kh = .138 \t\t\t\t\t; #[W/m.K] Conductivity\n", + "uh = 3.25/100. \t\t\t\t\t; #[N.s/m^2] Viscosity\n", + "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n", + "cpc = 4178 \t\t\t\t\t;#[J/kg.K] Specific Heat\n", + "kc = 0.625 \t\t\t\t\t; #[W/m.K] Conductivity\n", + "uc = 725*math.pow(10,-6) \t\t\t; #[N.s/m^2] Viscosity\n", + "Pr = 4.85 \t\t\t\t\t;#Prandtl Number\n", + "#calculations and results\n", + "\n", + "\n", + "q = mh*cph*(Thi-Tho); \t\t\t\t\t\t#Heat transferred\n", + "\n", + "Tco = q/(mc*cpc)+Tci;\n", + "\n", + "T1 = Thi-Tco;\n", + "T2 = Tho-Tci;\n", + "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));\t\t#logarithmic mean temp. difference\n", + "\n", + "#Through Tube\n", + "Ret = 4*mc/(math.pi*Di*uc);\n", + "print '%s %.2f %s' %(\"\\n Flow through Tube has Reynolds Number as\", Ret,\" .Thus the flow is Turbulent\");\n", + "#Equation 8.60\n", + "Nut = .023*math.pow(Ret,.8)*math.pow(Pr,.4);#Nusselt number\n", + "hi = Nut*kc/Di;\n", + "\n", + "#Through Shell\n", + "Reo = 4*mh*(Do-Di)/(math.pi*uh*(Do*Do-Di*Di));\n", + "print '%s %.2f %s' %(\"\\n Flow through Tube has Reynolds Number as\",Reo,\". Thus the flow is Laminar\");\n", + "#Table 8.2\n", + "Nuo = 5.63;\n", + "ho = Nuo*kh/(Do-Di);\n", + "\n", + "U = 1./(1./hi+1./ho); \t\t\t\t\t\t#overall heat transfer coefficient\n", + "L = q/(U*math.pi*Di*Tlm); \t\t\t\t\t#Length\n", + "\n", + "print '%s %.2f' %(\"\\n Tube Length to achieve a desired hot fluid temperature is (m) = \",L);\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Flow through Tube has Reynolds Number as 14049.54 .Thus the flow is Turbulent\n", + "\n", + " Flow through Tube has Reynolds Number as 55.97 . Thus the flow is Laminar\n", + "\n", + " Tube Length to achieve a desired hot fluid temperature is (m) = 65.71\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.2 Page 683" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Exterior Dimensions of heat Exchanger\n", + "# Pressure drops within the plate-type Heat exchanger with N=60 gaps\n", + "import math\n", + "import numpy\n", + "from numpy import linspace\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "#Operating Conditions\n", + "Tho = 60.+273 \t\t\t;#[K] Hot Fluid outlet Temperature\n", + "Thi = 100.+273 \t\t\t;#[K] Hot Fluid intlet Temperature\n", + "Tci = 30.+273 \t\t\t;#[K] Cold Fluid intlet Temperature\n", + "mh = .1 \t\t\t;#[kg/s] Hot Fluid flow rate\n", + "mc = .2 \t\t\t;#[kg/s] Cold Fluid flow rate\n", + "Do = .045 \t\t\t;#[m] Outer annulus\n", + "Di = .025 \t\t\t;#[m] Inner tube\n", + "\n", + "#Table A.5 Engine Oil Properties T = 353 K\n", + "cph = 2131 \t;#[J/kg.K] Specific Heat\n", + "kh = .138 \t;#[W/m.K] Conductivity\n", + "uh = 3.25/100. \t;#[N.s/m^2] Viscosity\n", + "rhoh = 852.1 \t;#[kg/m^3] Density\n", + "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n", + "cpc = 4178 \t;#[J/kg.K] Specific Heat\n", + "kc = 0.625 \t;#[W/m.K] Conductivity\n", + "uc = 725*math.pow(10,-6) ;#[N.s/m^2] Viscosity\n", + "Pr = 4.85 \t;#Prandtl Number\n", + "rhoc = 994 \t;#[kg/m^3] Density\n", + "#calculations\n", + "\n", + "q = mh*cph*(Thi-Tho); \t\t#Heat required\n", + "\n", + "Tco = q/(mc*cpc)+Tci;\n", + "\n", + "T1 = Thi-Tco;\n", + "T2 = Tho-Tci;\n", + "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));\n", + "N=numpy.zeros(61)\n", + "for i in range (0,60):\n", + "\tN[i]=i+20;\n", + "\n", + "L = numpy.zeros(61)\n", + "for i in range (0,60):\n", + "\ta=float(N[i]);\n", + "\tL[i] = q/Tlm*(1./(7.54*kc/2.)+1/(7.54*kh/2.))/(a*a-a);\n", + "\n", + "pyplot.plot(N,L);\n", + "pyplot.xlabel(\"L (m)\");\n", + "pyplot.ylabel('Number of Gaps(N)')\n", + "pyplot.show()\n", + "#Close the graph to complete the execution\n", + "N2 = 60;\n", + "L = q/((N2-1)*N2*Tlm)*(1./(7.54*kc/2.)+1/(7.54*kh/2.));\n", + "a = L/N2;\n", + "Dh = 2*a \t\t\t;#Hydraulic Diameter [m]\n", + "#For water filled gaps\n", + "umc = mc/(rhoc*L*L/2.);\n", + "Rec = rhoc*umc*Dh/uc;\n", + "#For oil filled gaps\n", + "umh = mh/(rhoh*L*L/2.);\n", + "Reh = rhoh*umh*Dh/uh;\n", + "print '%s %.2f %s %.2f %s' %(\"\\n Flow of the fluids has Reynolds Number as\",Reh,\" & \",Rec,\" Thus the flow is Laminar for both\");\n", + "\n", + "#Equations 8.19 and 8.22a\n", + "delpc = 64/Rec*rhoc/2*umc*umc/Dh*L ;#For water\n", + "delph = 64/Reh*rhoh/2*umh*umh/Dh*L ;#For oil\n", + "\n", + "#For example 11.1\n", + "L1 = 65.9;\n", + "Dh1c = .025;\n", + "Dh1h = .02;\n", + "Ret = 4*mc/(math.pi*Di*uc);\n", + "f = math.pow((.790*2.30*math.log10(Ret)-1.64),-2) ;#friction factor through tube Eqn 8.21\n", + "umc1 = 4*mc/(rhoc*math.pi*Di*Di);\n", + "delpc1 = f*rhoc/2*umc1*umc1/Dh1c*L1;\n", + "Reo = 4*mh*(Do-Di)/(math.pi*uh*(Do*Do-Di*Di));\t\t \t#Reynolds number\n", + "umh1 = 4*mh/(rhoh*math.pi*(Do*Do-Di*Di));\n", + "delph1 = 64/Reo*rhoh/2*umh1*umh1/Dh1h*L1;\n", + "#results\n", + "\n", + "print '%s %.3f %s' %(\"\\n Exterior Dimensions of heat Exchanger L =\",L,\"m\");\n", + "print '%s %.3f %s' %(\"\\n Pressure drops within the plate-type Heat exchanger with N=60 gaps\\n For water = \", delpc,\" N/m^2\") \n", + "print '%s %.3f %s' %(\" For oil = \",delph,\" N/m^2\\n \")\n", + "print '%s %.3f %s' %(\"Pressure drops tube Heat exchanger of example 11.1\\n For water = \",delpc1 ,\"N/m^2\") \n", + "print '%s %.3f %s' %(\"\\n For oil =\",delph1,\" N/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Flow of the fluids has Reynolds Number as 1.57 & 140.77 Thus the flow is Laminar for both\n", + "\n", + " Exterior Dimensions of heat Exchanger L = 0.131 m\n", + "\n", + " Pressure drops within the plate-type Heat exchanger with N=60 gaps\n", + " For water = 3.768 N/m^2\n", + " For oil = 98.523 N/m^2\n", + " \n", + "Pressure drops tube Heat exchanger of example 11.1\n", + " For water = 6331.255 N/m^2\n", + "\n", + " For oil = 18287.329 N/m^2\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.3 Page 692" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Required gas side surface area\n", + "\n", + "#Operating Conditions\n", + "Tho = 100+273. \t\t\t\t;#[K] Hot Fluid outlet Temperature\n", + "Thi = 300+273. \t\t\t\t;#[K] Hot Fluid intlet Temperature\n", + "Tci = 35+273. \t\t\t\t;#[K] Cold Fluid intlet Temperature\n", + "Tco = 125+273. \t\t\t\t; #[K] Cold Fluid outlet Temperature\n", + "mc = 1 \t\t\t\t;#[kg/s] Cold Fluid flow rate\n", + "Uh = 100 \t\t\t\t;#[W/m^2.K] Coefficient of heat transfer\n", + "#Table A.5 Water Properties T = 353 K\n", + "cph = 1000 \t\t\t\t;#[J/kg.K] Specific Heat\n", + "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n", + "cpc = 4197 \t\t\t\t;#[J/kg.K] Specific Heat\n", + "#calculations\n", + "\n", + "Cc = mc*cpc;\n", + "#Equation 11.6b and 11.7b\n", + "Ch = Cc*(Tco-Tci)/(Thi-Tho);\n", + "# Equation 11.18\n", + "qmax = Ch*(Thi-Tci); \t\t\t#Max. heat\n", + "#Equation 11.7b \n", + "q = mc*cpc*(Tco-Tci); \t\t\t#Heat available\n", + "\n", + "e = q/qmax; \n", + "ratio = Ch/Cc; \n", + "#results\n", + "\n", + "print '%s %.2f %s %.2f' %(\"\\n As effectiveness is\", e,\" with Ratio Cmin/Cmax =\", ratio);\n", + "print '%s' %(\", It follows from figure 11.14 that NTU = 2.1\");\n", + "NTU = 2.1; \t\t\t\t\t\t#No. of transfer units\n", + "A = 2.1*Ch/Uh;\n", + "\n", + "print '%s %.2f' %(\"\\n Required gas side surface area (m^2) = \",A);\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As effectiveness is 0.75 with Ratio Cmin/Cmax = 0.45\n", + ", It follows from figure 11.14 that NTU = 2.1\n", + "\n", + " Required gas side surface area (m^2) = 39.66\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.4 Page 695" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Heat Transfer Rate and Fluid Outlet Temperatures\n", + "\n", + "#Operating Conditions\n", + "Thi = 250+273. \t\t\t;#[K] Hot Fluid intlet Temperature\n", + "Tci = 35+273. \t\t\t;#[K] Cold Fluid intlet Temperature\n", + "mc = 1 \t\t\t;#[kg/s] Cold Fluid flow rate\n", + "mh = 1.5 \t\t\t; #[kg/s] Hot Fluid flow rate\n", + "Uh = 100 \t\t \t\t;#[W/m^2.K] Coefficient of heat transfer\n", + "Ah = 40 \t\t\t; #[m^2] Area\n", + "#Table A.5 Water Properties T = 353 K\n", + "cph = 1000. \t\t\t;#[J/kg.K] Specific Heat\n", + "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n", + "cpc = 4197. \t\t\t;#[J/kg.K] Specific Heat\n", + "#calculations\n", + "\n", + "Cc = mc*cpc;\n", + "Ch = mh*cph;\n", + "Cmin = Ch;\n", + "Cmax = Cc;\n", + "\n", + "NTU = Uh*Ah/Cmin;\t\t\t#No.of transfer units\n", + "ratio = Cmin/Cmax;\n", + "#results\n", + "\n", + "print '%s %.2f' %(\"\\n As Ratio Cmin/Cmax =\", ratio)\n", + "print '%s %.2f' %(\"and Number of transfer units NTU =\", NTU)\n", + "print '%s' %(\", It follows from figure 11.14 that e = .82\");\n", + "e = 0.82;\n", + "qmax = Cmin*(Thi-Tci);\t\t#Max. heat transferred\n", + "q = e*qmax; \t\t\t\t#Actual heat transferred\n", + "\n", + "#Equation 11.6b\n", + "Tco = q/(mc*cpc) + Tci;\n", + "#Equation 11.7b\n", + "Tho = -q/(mh*cph) + Thi;\n", + "print '%s %.2e %s' %(\"\\n Heat Transfer Rate =\",q,\" W \")\n", + "print '%s %.1f %s' %(\"\\n Fluid Outlet Temperatures Hot Fluid (Tho) =\" ,Tho-273,\"degC\") \n", + "print '%s %.2f %s'\t%(\"Cold Fluid (Tco) =\", Tco-273,\"degC\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As Ratio Cmin/Cmax = 0.36\n", + "and Number of transfer units NTU = 2.67\n", + ", It follows from figure 11.14 that e = .82\n", + "\n", + " Heat Transfer Rate = 2.64e+05 W \n", + "\n", + " Fluid Outlet Temperatures Hot Fluid (Tho) = 73.7 degC\n", + "Cold Fluid (Tco) = 98.01 degC\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.5 Page 696" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Outlet Temperature of cooling Water\n", + "# Tube length per pass to achieve required heat transfer\n", + "import math\n", + "#Operating Conditions\n", + "q = 2*math.pow(10,9) \t \t\t\t;#[W] Heat transfer Rate\n", + "ho = 11000. \t\t\t\t\t\t;#[W/m^2.K] Coefficient of heat transfer for outer surface\n", + "Thi = 50+273. \t\t\t\t\t\t;#[K] Hot Fluid Condensing Temperature\n", + "Tho = Thi \t\t\t\t\t\t\t;#[K] Hot Fluid Condensing Temperature\n", + "Tci = 20+273. \t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n", + "mc = 3*math.pow(10,4) \t\t\t\t;#[kg/s] Cold Fluid flow rate\n", + "m = 1 \t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate per tube\n", + "D = .025 \t\t\t\t\t\t;#[m] diameter of tube\n", + "#Table A.6 Saturated water Liquid Properties Tf = 300 K\n", + "rho = 997 \t\t\t\t\t\t;#[kg/m^3] Density\n", + "cp = 4179 \t\t\t\t\t\t;#[J/kg.K] Specific Heat\n", + "k = 0.613 \t\t\t\t\t\t;#[W/m.K] Conductivity\n", + "u = 855*math.pow(10,-6) \t\t\t\t;#[N.s/m^2] Viscosity\n", + "Pr = 5.83 \t\t\t\t\t\t;# Prandtl number\n", + "#calculations and results\n", + "\n", + "#Equation 11.6b\n", + "Tco = q/(mc*cp) + Tci;\n", + "\n", + "Re = 4*m/(math.pi*D*u);\n", + "print '%s %.2f' %(\"\\n As the Reynolds number of tube fluid is\", Re)\n", + "print '%s' %(\". Hence the flow is turbulent. Hence using Diettus-Boetllor Equation 8.60\");\n", + "Nu = .023*math.pow(Re,.8)*math.pow(Pr,.4);\n", + "hi = Nu*k/D;\t\t\t\t\t\t\t#Heat transfer coefficient\n", + "U = 1/(1/ho + 1/hi); \t\t\t\t\t#Overall heat transfer coefficient\n", + "N = 30000. \t\t\t\t\t;#No of tubes\n", + "T1 = Thi-Tco;\n", + "T2 = Tho-Tci;\n", + "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));#Logarithmic mean temp. difference\n", + "L2 = q/(U*N*2*math.pi*D*Tlm);\n", + "\n", + "\n", + "print '%s %.1f %s' %(\"\\n Outlet Temperature of cooling Water = \",Tco-273,\" degC\")\n", + "print '%s %.2f %s' %(\"\\n Tube length per pass to achieve required heat transfer =\",L2,\" m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As the Reynolds number of tube fluid is 59566.76\n", + ". Hence the flow is turbulent. Hence using Diettus-Boetllor Equation 8.60\n", + "\n", + " Outlet Temperature of cooling Water = 36.0 degC\n", + "\n", + " Tube length per pass to achieve required heat transfer = 4.51 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.6 Page 702" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Gas-side overall heat transfer coefficient. Heat exchanger Volume\n", + "import math\n", + "#Operating Conditions\n", + "hc = 1500. \t\t\t\t\t\t\t\t;#[W/m^2.K] Coefficient of heat transfer for outer surface\n", + "hi = hc;\n", + "Th = 825. \t\t\t\t\t\t\t\t\t;#[K] Hot Fluid Temperature\n", + "Tci = 290. \t\t\t\t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n", + "Tco = 370. \t\t\t\t\t\t\t\t\t;#[K] Cold Fluid outlet Temperature\n", + "mc = 1 \t\t\t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate\n", + "mh = 1.25 \t\t\t\t\t \t\t\t;#[kg/s] Hot Fluid flow rate\n", + "Ah = .20 \t\t\t\t\t\t\t;#[m^2] Area of tubes\n", + "Di = .0138 \t\t\t\t\t\t\t\t;#[m] diameter of tube\n", + "Do = .0164 \t\t\t\t\t\t\t\t;#[m] Diameter\n", + "#Table A.6 Saturated water Liquid Properties Tf = 330 K\n", + "cpw = 4184. \t\t\t\t\t\t\t;#[J/kg.K] Specific Heat\n", + "#Table A.1 Aluminium Properties T = 300 K\n", + "k = 237 \t\t\t\t\t\t\t;#[W/m.K] Conductivity\n", + "#Table A.4 Air Properties Tf = 700 K\n", + "cpa = 1075 \t\t\t\t\t\t\t\t;#[J/kg.K] Specific Heat\n", + "u = 33.88*math.pow(10,-6) \t\t\t\t\t;#[N.s/m^2] Viscosity\n", + "Pr = .695 \t\t\t\t\t\t\t\t;# Prandtl number\n", + "#calculations\n", + "\n", + "#Geometric Considerations\n", + "si = .449;\n", + "Dh = 6.68*math.pow(10,-3) \t\t\t\t;#[m] hydraulic diameter\n", + "G = mh/si/Ah;\n", + "Re = G*Dh/u; \t\t\t\t\t\t\t\t\t#Reynolds number\n", + "#From Figure 11.16\n", + "jh = .01;\n", + "hh = jh*G*cpa/math.pow(Pr,.66667); \t\t\t\t#Heat transfer coefficient\n", + "\n", + "AR = Di*2.303*math.log10(Do/Di)/(2*k*(.143));\t#Area of cross section\n", + "#Figure 11.16\n", + "AcAh = Di/Do*(1-.830);\n", + "#From figure 3.19\n", + "nf = .89;\n", + "noh = 1-(1-.89)*.83;\n", + "\n", + "U = 1/(1/(hc*AcAh) + AR + 1/(noh*hh));\t\t\t#Overall heat transfer coefficient\n", + "\n", + "Cc = mc*cpw;\n", + "q = Cc*(Tco-Tci); \t\t\t\t\t\t\t\t#Heat released\n", + "Ch = mh*cpa;\n", + "qmax = Ch*(Th-Tci); \t\t\t\t\t\t\t#MAx. heat transferred\n", + "e = q/qmax;\n", + "ratio = Ch/Cc;\n", + "#results\n", + "\n", + "print '%s %.2f %s %.2f' %(\"\\n As effectiveness is\",e,\" with Ratio Cmin/Cmax = \",ratio)\n", + "print '%s' %(\", It follows from figure 11.14 that NTU = .65\");\n", + "NTU = .65;\n", + "A = NTU*Ch/U; \t\t\t\t\t\t\t\t\t#Area of cross section\n", + "#From Fig 11.16\n", + "al = 269.; \t\t\t\t\t\t\t#[m^-1] gas side area per unit heat wxchanger volume\n", + "V = A/al;\n", + "#Answers may vary a bit due to rounding off errors.!\n", + "print '%s %.2f %s' %(\"\\n Gas-side overall heat transfer coefficient.r =\", U , \"W/m^2.K\")\n", + "print '%s %.3f %s' %(\" \\n Heat exchanger Volume = \",V,\" m^3\");\n", + "#END;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As effectiveness is 0.47 with Ratio Cmin/Cmax = 0.32\n", + ", It follows from figure 11.14 that NTU = .65\n", + "\n", + " Gas-side overall heat transfer coefficient.r = 95.55 W/m^2.K\n", + " \n", + " Heat exchanger Volume = 0.034 m^3\n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_12.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_12.ipynb new file mode 100644 index 00000000..25268933 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_12.ipynb @@ -0,0 +1,767 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Radiation: Processes and Properties" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.1 Page 731 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# a) Intensity of emission in each of the three directions\n", + "# b) Solid angles subtended by the three surfaces\n", + "# c) Rate at which radiation is intercepted by the three surfaces\n", + "\n", + "A1 = .001\t\t;#[m^2] Area of emitter\n", + "In = 7000\t\t;#[W/m^2.Sr] Intensity of radiation in normal direction\n", + "A2 = .001\t\t;#[m^2] Area of other intercepting plates\n", + "A3 = A2\t\t\t;#[m^2] Area of other intercepting plates\n", + "A4 = A2\t\t\t;#[m^2] Area of other intercepting plates\n", + "r = .5\t\t\t;#[m] Distance of each plate from emitter\n", + "theta1 = 60.\t;#[deg] Angle between surface 1 normal & direction of radiation to surface 2\n", + "theta2 = 30.\t;#[deg] Angle between surface 2 normal & direction of radiation to surface 1\n", + "theta3 = 45.\t;#[deg] Angle between surface 1 normal & direction of radiation to surface 4\n", + "#calculations\n", + "\n", + "#From equation 12.2\n", + "w31 = A3/(r*r);\n", + "w41 = w31;\n", + "w21 = A2*math.cos(theta2*0.0174532925)/(r*r);\n", + "\n", + "\n", + "#From equation 12.6\n", + "q12 = In*A1*math.cos(theta1*0.0174532925)*w21;\n", + "q13 = In*A1*math.cos(0*math.pi/180.)*w31;\n", + "q14 = In*A1*math.cos(theta3*0.0174532925)*w41;\n", + "#results\n", + "\n", + "print '%s %d %s' %(\"\\n (a) As Intensity of emitted radiation is independent of direction, for each of the three directions I = \",In,\"W/m^2.sr\")\n", + "print '%s' %(\"\\n\\n (b) By the Three Surfaces\\n Solid angles subtended Rate at which radiation is intercepted \\n\")\n", + "print '%s %.2e %s' %(\"w4-1 =\",w41,\" sr\")\n", + "print '%s %.2e %s' %(\"\\t \\t \\t \\t \\t \\t q1-4 =\",q14,\" W\") \n", + "print '%s %.2e %s' %(\"\\nw3-1 = \",w31,\" sr\")\n", + "print '%s %.2e %s' %(\"\\t \\t \\t \\t \\t \\t q1-3 =\",q13,\" W\")\n", + "print '%s %.2e %s' %(\"\\n w2-1 = \",w21,\" sr\")\n", + "print '%s %.2e %s' %(\"\\t \\t \\t \\t \\t \\tq1-2 = \",q12,\" W \");\n", + "#END\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) As Intensity of emitted radiation is independent of direction, for each of the three directions I = 7000 W/m^2.sr\n", + "\n", + "\n", + " (b) By the Three Surfaces\n", + " Solid angles subtended Rate at which radiation is intercepted \n", + "\n", + "w4-1 = 4.00e-03 sr\n", + "\t \t \t \t \t \t q1-4 = 1.98e-02 W\n", + "\n", + "w3-1 = 4.00e-03 sr\n", + "\t \t \t \t \t \t q1-3 = 2.80e-02 W\n", + "\n", + " w2-1 = 3.46e-03 sr\n", + "\t \t \t \t \t \tq1-2 = 1.21e-02 W \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.2 Page 734" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "%pylab inline\n", + "# Total Irradiation\n", + "#calculations\n", + "\n", + "x=([0, 5, 20, 25]);\n", + "y=([0, 1000, 1000, 0]);\n", + "\n", + "plt.plot(x,y);\n", + "plt.xlabel(\"Spectral Distribution\")\n", + "plt.ylabel(\"wavelength (micro-m)\")\n", + "#By Equation 12.4\n", + "G = 1000*(5-0)/2. +1000*(20-5)+1000*(25-20)/2.;\n", + "#results\n", + "\n", + "print '%s %d %s' %(\"\\n G =\",G,\" W/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "\n", + " G = 20000 W/m^2" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x391dbd0>" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.3 Page 741" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Spectral Emissive Power of a small aperture on the enclosure\n", + "# wavelengths below which and above which 10% of the radiation is concentrated\n", + "# Spectral emissive power and wavelength associated with maximum emission\n", + "# Irradiation on a small object inside the enclosure\n", + "\n", + "T = 2000.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "stfncnstt = 5.67*math.pow(10,-8)\t\t;#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "E = stfncnstt*T*T*T*T; \t\t\t#[W/m^2]\n", + "#calculations\n", + "\n", + "#From Table 12.1 \n", + "constt1 = 2195. ; \t\t\t\t\t#[micro-m.K]\n", + "wl1 = constt1/T;\n", + "#From Table 12.1 \n", + "constt2 = 9382. ; \t\t\t\t\t#[micro-m.K]\n", + "wl2 = constt2/T;\n", + "\n", + "#From Weins Law, wlmax*T = consttmax = 2898 micro-m.K\n", + "consttmax = 2898 \t\t\t\t;#micro-m.K\n", + "wlmax = consttmax/T;\n", + "#from Table 12.1 at wlmax = 1.45 micro-m.K and T = 2000 K\n", + "I = .722*stfncnstt*T*T*T*T*T/10000.;\n", + "Eb = math.pi*I;\n", + "\n", + "G = E; #[W/m^2] Irradiation of any small object inside the enclosure is equal to emission from blackbody at enclosure temperature\n", + "#results\n", + "\n", + "print '%s %.2e %s' %(\"\\n (a) Spectral Emissive Power of a small aperture on the enclosure =\",E,\" W/m^2.Sr for each of the three directions\")\n", + "print '%s %.1f %s' %(\"\\n (b) Wavelength below which 10percent of the radiation is concentrated = \",wl1,\" micro-m \\n\") \n", + "print '%s %.2f %s' %(\" Wavelength above which 10percent of the radiation is concentrated = \",wl2,\" micro-m \\n\")\n", + "print '%s %.2e %s %.2e %s' %(\"(c) Spectral emissive power and wavelength associated with maximum emission is \",Eb,\"micro-m and\",wlmax,\" W/m^2.micro-m respectively\")\n", + "print '%s %.2e %s' %(\"\\n (d) Irradiation on a small object inside the enclosure =\",G,\"W/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Spectral Emissive Power of a small aperture on the enclosure = 9.07e+05 W/m^2.Sr for each of the three directions\n", + "\n", + " (b) Wavelength below which 10percent of the radiation is concentrated = 1.1 micro-m \n", + "\n", + " Wavelength above which 10percent of the radiation is concentrated = 4.69 micro-m \n", + "\n", + "(c) Spectral emissive power and wavelength associated with maximum emission is 4.12e+05 micro-m and 1.45e+00 W/m^2.micro-m respectively\n", + "\n", + " (d) Irradiation on a small object inside the enclosure = 9.07e+05 W/m^2\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.4 Page 743 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "import scipy\n", + "from scipy import integrate\n", + "# Rate of emission per unit area over all directions between 0 degC and 60 degC and over all wavelengths between wavelengths 2 and 4 micro-m\n", + "\n", + "T = 1500.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "stfncnstt = 5.67*math.pow(10,-8)\t\t;#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "#calculations\n", + "\n", + "#From Equation 12.26 Black Body Radiation\n", + "Eb = stfncnstt*T*T*T*T; \t\t\t#[W/m^2]\n", + "\n", + "#From Table 12.1 as wl1*T = 2*1500 (micro-m.K)\n", + "F02 = .273;\n", + "#From Table 12.1 as wl2*T = 4*1500 (micro-m.K)\n", + "F04 = .738;\n", + "def func(x):\n", + "\tfunc = 2*math.cos(x) *math.sin(x)\n", + "\treturn func;\n", + "\n", + "#From equation 12.10 and 12.11\n", + "i1 = scipy.integrate.quad(func,0,math.pi/3.);\n", + "delE = i1[0] *(F04-F02)*Eb;\n", + "#results\n", + "\n", + "print '%s %.2e %s' %(\"\\n Rate of emission per unit area over all directions between 0 degC and 60 degC and over all wavelengths between wavelengths 2 micro-m and 4 micro-m =\",delE,\" W/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Rate of emission per unit area over all directions between 0 degC and 60 degC and over all wavelengths between wavelengths 2 micro-m and 4 micro-m = 1.00e+05 W/m^2\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.5 Page 748" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Total hemispherical emissivity\n", + "# Total emissive Power\n", + "# Wavelength at which spectral emissive power will be maximum\n", + "\n", + "T = 1600.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "wl1 = 2 \t\t\t\t\t\t;#[micro-m] wavelength 1\n", + "wl2 = 5 \t\t\t\t\t\t;#[micro-m] wavelength 2\n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "# From the given graph of emissivities\n", + "e1 = .4;\n", + "e2 = .8;\n", + "#calculations\n", + "\n", + "#From Equation 12.26 Black Body Radiation\n", + "Eb = stfncnstt*T*T*T*T; \t \t\t#[W/m^2]\n", + "\n", + "#Solution (A)\n", + "#From Table 12.1 as wl1*T = 2*1600 (micro-m.K)\n", + "F02 = .318;\n", + "#From Table 12.1 as wl2*T = 5*1600 (micro-m.K)\n", + "F05 = .856;\n", + "#From Equation 12.36\n", + "e = e1*F02 + e2*(F05 - F02);\n", + "\n", + "#Solution (B)\n", + "#From equation 12.35\n", + "E = e*Eb;\n", + "\n", + "#Solution (C)\n", + "#For maximum condition Using Weins Law\n", + "consttmax = 2898. \t\t\t\t;#[micro-m.K]\n", + "wlmax = consttmax/T;\n", + "\n", + "#equation 12.32 with Table 12.1\n", + "E1 = math.pi*e1*.722*stfncnstt*T*T*T*T*T/10000.;\n", + "\n", + "E2 = math.pi*e2*.706*stfncnstt*T*T*T*T*T/10000.;\n", + "#results\n", + "\n", + "print '%s %.3f' %(\"\\n (a) Total hemispherical emissivity =\",e)\n", + "print '%s %d %s' %(\"\\n (b) Total emissive Power =\",E/1000. ,\" kW/m^2\")\n", + "print '%s %.1f %s %.1f %s ' %(\"\\n (c) Emissive Power at wavelength 2micro-m is greater than Emissive power at maximum wavelength \\n i.e.\",E2/1000.,\" kW/m^2 >\",E1/1000.,\" kW/m^2\")\n", + "print '%s %d %s' %(\"\\n Thus, Peak emission occurs at\",wl1,\"micro-m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Total hemispherical emissivity = 0.558\n", + "\n", + " (b) Total emissive Power = 207 kW/m^2\n", + "\n", + " (c) Emissive Power at wavelength 2micro-m is greater than Emissive power at maximum wavelength \n", + " i.e. 105.5 kW/m^2 > 53.9 kW/m^2 \n", + "\n", + " Thus, Peak emission occurs at 2 micro-m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.6 Page 751" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "import scipy\n", + "from scipy import integrate\n", + "# Spectral , Normal emissivity en and spectral hemispherical emissivity e\n", + "# Spectral normal intensity In and Spectral emissive power\n", + "\n", + "T = 2000.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "wl = 1 \t\t\t\t\t\t;#[micro-m] wavelength \n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "\n", + "# From the given graph of emissivities\n", + "e1 = .3;\n", + "e2 = .6;\n", + "#calculations\n", + "\n", + "#From Equation 12.26 Black Body Radiation\n", + "Eb = stfncnstt*T*T*T*T; \t\t\t\t\t\t#[W/m^2]\n", + "def func1(x):\n", + "\tfunc1=e1*math.cos(x) *math.sin(x);\n", + "\treturn func1;\n", + "\n", + "def func2(x):\n", + "\tfunc2=e2*math.cos(x) *math.sin(x);\n", + "\treturn func2;\n", + "\n", + "#Equation 12.34\n", + "i1 = scipy.integrate.quad(func1,0,math.pi/3.);\n", + "i2 = scipy.integrate.quad(func2,math.pi/3. ,4*math.pi/9.);\n", + "e = 2*(i1[0]+i2[0]);\n", + "\n", + "# From Table 12.1 at wl = 1 micro-m and T = 2000 K.\n", + "\n", + "I = .493*math.pow(10,-4) * stfncnstt*T*T*T*T*T ;#[W/m^2.micro-m.sr]\n", + "\n", + "In = e1*I;\n", + "\n", + "#Using Equation 12.32 for wl = 1 micro-m and T = 2000 K\n", + "E = e*math.pi*I;\n", + "#results\n", + "\n", + "print '%s %.1f' %('\\n Spectral Normal emissivity en =',e1)\n", + "print '%s %.2f' %('and spectral hemispherical emissivity e = ',e)\n", + "print '%s %.2e %s' %('\\n Spectral normal intensity In =',In,' W/m^2.micro-m.sr')\n", + "print '%s %.1e %s' % ('and Spectral emissive power =',E,' W/m^2.micro-m.sr ');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Spectral Normal emissivity en = 0.3\n", + "and spectral hemispherical emissivity e = 0.36\n", + "\n", + " Spectral normal intensity In = 2.68e+04 W/m^2.micro-m.sr\n", + "and Spectral emissive power = 1.0e+05 W/m^2.micro-m.sr \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.7 Page 759" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "%pylab inline\n", + "# Spectral distribution of reflectivity\n", + "# Total, hemispherical absorptivity\n", + "# Nature of surface temperature change\n", + "\n", + "T = 500.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "e = .8;\n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "#calculations\n", + "\n", + "x=([0, 6, 8, 16]);\n", + "y=([.8, .8, 0, 0]);\n", + "\n", + "pyplot.xlabel(\"Spectral Distribution of reflectivity\")\n", + "pyplot.ylabel(\"wavelength (micro-m)\");\n", + "pyplot.plot(x,y);\n", + "pyplot.show();\n", + "\n", + "\n", + "#From equation 12.43 and 12.44\n", + "Gabs = (.2*500/2.*(6.-2.)+500*(.2*(8.-6.)+(1.-.2)*(8.-6.)/2.)+1*500*(12.-8.)+500*(16.-12.)/2.) ;#[w/m^2]\n", + "G = (500*(6.-2.)/2.+500*(12.-6.)+500*(16.-12.)/2.) \t\t\t\t\t\t\t\t\t;#[w/m^2]\n", + "a = Gabs/G;\n", + "\n", + "#Neglecting convection effects net het flux to the surface\n", + "qnet = a*G - e*stfncnstt*T*T*T*T;\n", + "#results\n", + "\n", + "print '%s %.2f' %('\\n Total, hemispherical absorptivity',a)\n", + "print '%s %.2f %s' %('\\n Nature of surface temperature change =',qnet,' W/m^2 \\n Since qnet > 0, the sirface temperature will increase with the time');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + 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CAgLwHf81koyioqyDyuXlwG23yZ2GyHs4MY3IgfvuA556CkhNlTsJ0Y3zuYlp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\nuoYFgYiIALAgEBHRNSwIREQEAPh/X35awWPS9asAAAAASUVORK5CYII=\n", + "text": [ + "<matplotlib.figure.Figure at 0x2fec390>" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Total, hemispherical absorptivity 0.76\n", + "\n", + " Nature of surface temperature change = 965.00 W/m^2 \n", + " Since qnet > 0, the sirface temperature will increase with the time\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.8 Page 761" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "import math\n", + "# Total emissivity of cover glass to solar radiation\n", + "\n", + "T = 5800.\t\t\t\t\t\t\t\t;#[K] temperature of surface\n", + "e = .8;\n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "#calculations and results\n", + "\n", + "#From Table 12.1\n", + "#For wl1 = .3 micro-m and T = 5800 K, At wl1*T = 1740 micro-m.K\n", + "F0wl1 = .0335;\n", + "#For wl1 = .3 micro-m and T = 5800 K, At wl2*T = 14500 micro-m.K\n", + "F0wl2 = .9664;\n", + "\n", + "#Hence from equation 12.29\n", + "t = .90*(F0wl2 - F0wl1);\n", + "\n", + "print '%s %.2f' %('\\n Total emissivity of cover glass to solar radiation =',t);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Total emissivity of cover glass to solar radiation = 0.84\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.9 Page 766" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Total hemispherical emissivity of fire brick wall\n", + "# Total emissive power of brick wall\n", + "# Absorptivity of the wall to irradiation from coals\n", + "\n", + "Ts = 500.\t\t\t\t\t\t\t;#[K] temperature of brick surface\n", + "Tc = 2000. \t\t\t\t;#[K] Temperature of coal exposed\n", + "stfncnstt = 5.67*math.pow(10,-8)\t;#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "# From the given graph of emissivities\n", + "e1 = .1; \t\t\t\t\t\t#between wavelength 0 micro-m- 1.5 micro-m\n", + "e2 = .5; \t\t\t\t\t\t#between wavelength 1.5 micro-m- 10 micro-m\n", + "e3 = .8; \t\t\t\t\t\t#greater than wavelength 10 micro-m\n", + "#calculations\n", + "\n", + "#From Table 12.1\n", + "#For wl1 = 1.5 micro-m and T = 500 K, At wl1*T = 750 micro-m.K\n", + "F0wl1 = 0;\n", + "#For wl2 = 10 micro-m and T = 500 K, At wl2*T = 5000 micro-m.K\n", + "F0wl2 = .634;\n", + "#From equation 12.36\n", + "e = e1*F0wl1 + e2*F0wl2 + e3*(1-F0wl1-F0wl2);\n", + "\n", + "#Equation 12.26 and 12.35\n", + "E = e*stfncnstt*Ts*Ts*Ts*Ts;\n", + "\n", + "#From Table 12.1\n", + "#For wl1 = 1.5 micro-m and T = 2000 K, At wl1*T = 3000 micro-m.K\n", + "F0wl1c = 0.273;\n", + "#For wl2 = 10 micro-m and T = 2000 K, At wl2*T = 20000 micro-m.K\n", + "F0wl2c = .986;\n", + "ac = e1*F0wl1c + e2*(F0wl2c-F0wl1c) + e3*(1-F0wl2c);\n", + "#results\n", + "\n", + "print '%s %.3f' %('\\n Total hemispherical emissivity of fire brick wall =',e)\n", + "print '%s %d %s' %('\\n Total emissive power of brick wall =',E,'W/m^2.')\n", + "print '%s %.3f' %('\\n Absorptivity of the wall to irradiation from coals =',ac);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Total hemispherical emissivity of fire brick wall = 0.610\n", + "\n", + " Total emissive power of brick wall = 2160 W/m^2.\n", + "\n", + " Absorptivity of the wall to irradiation from coals = 0.395\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.10 Page 768" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Total hemispherical absorptivity and emissivity of sphere for initial condition\n", + "# values of absoprtivity and emissivity after sphere has been in furnace a long time\n", + "\n", + "Ts = 300.;\t\t\t\t\t\t\t#[K] temperature of surface\n", + "Tf = 1200; \t\t\t\t#[K] Temperature of Furnace\n", + "stfncnstt = 5.67*math.pow(10,-8);\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "# From the given graph of absorptivities\n", + "a1 = .8; \t\t\t\t\t\t#between wavelength 0 micro-m- 5 micro-m\n", + "a2 = .1; \t\t\t\t\t\t#greater than wavelength 5 micro-m\n", + "#calculations\n", + "\n", + "#From Table 12.1\n", + "#For wl1 = 5 micro-m and T = 1200 K, At wl1*T = 6000 micro-m.K\n", + "F0wl1 = 0.738;\n", + "#From equation 12.44\n", + "a = a1*F0wl1 + a2*(1-F0wl1);\n", + "#From Table 12.1\n", + "#For wl1 = 5 micro-m and T = 300 K, At wl1*T = 1500 micro-m.K\n", + "F0wl1s = 0.014;\n", + "#From equation 12.36\n", + "e = a1*F0wl1s + a2*(1-F0wl1s);\n", + "#results\n", + "\n", + "print' %s %.2f' %('\\n For Initial Condition \\n Total hemispherical absorptivity = ',a)\n", + "print '%s %.2f' %('Emissivity of sphere =',e)\n", + "print '%s' %('\\n\\n Beacuase the spectral characteristics of the coating and the furnace temeprature remain fixed, there is no change in the value of absorptivity with increasing time.')\n", + "print '%s %d %s %.2f' %('\\n Hence, After a sufficiently long time, Ts = Tf = ',Tf,' K and emissivity equals absorptivity e = a = ',a);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \n", + " For Initial Condition \n", + " Total hemispherical absorptivity = 0.62\n", + "Emissivity of sphere = 0.11\n", + "\n", + "\n", + " Beacuase the spectral characteristics of the coating and the furnace temeprature remain fixed, there is no change in the value of absorptivity with increasing time.\n", + "\n", + " Hence, After a sufficiently long time, Ts = Tf = 1200 K and emissivity equals absorptivity e = a = 0.62\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.11 Page 774" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Useful heat removal rate per unit area\n", + "# Efficiency of the collector\n", + "\n", + "Ts = 120+273.;\t\t\t\t\t\t\t#[K] temperature of surface\n", + "Gs = 750; \t\t\t\t#[W/m^2] Solar irradiation\n", + "Tsky = -10+273.; \t\t\t\t#[K] Temperature of Sky\n", + "Tsurr = 30+273.; \t \t\t\t#[K] Temperature os surrounding Air\n", + "e = .1 \t\t \t\t\t;# emissivity \n", + "ast = .95 \t\t\t\t;# Absorptivity of Surface\n", + "asky = e \t\t\t\t;# Absorptivity of Sky\n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "#calculations\n", + "\n", + "h = 0.22*math.pow((Ts - Tsurr),.3334);\t#[W/m^2.K] Convective Heat transfer Coeff\n", + "#From equation 12.67\n", + "Gsky = stfncnstt*Tsky*Tsky*Tsky*Tsky; \t#[W/m^2] Irradiadtion from sky\n", + "qconv = h*(Ts-Tsurr); \t\t\t#[W/m^2] Convective Heat transfer\n", + "E = e*stfncnstt*Ts*Ts*Ts*Ts; \t\t#[W/m^2] Irradiadtion from Surface\n", + "\n", + "#From energy Balance\n", + "q = ast*Gs + asky*Gsky - qconv - E;\n", + "\n", + "#Collector efficiency\n", + "eff = q/Gs;\n", + "#results\n", + "\n", + "print '%s %d %s' %('\\n Useful heat removal rate per unit area by Energy Conservation = ',q,'W/m^2')\n", + "print '%s %.2f' %('\\n Collector efficiency defined as the fraction of solar irradiation extracted as useful energy is',eff);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Useful heat removal rate per unit area by Energy Conservation = 515 W/m^2\n", + "\n", + " Collector efficiency defined as the fraction of solar irradiation extracted as useful energy is 0.69\n" + ] + } + ], + "prompt_number": 11 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_13.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_13.ipynb new file mode 100644 index 00000000..2b72fa5a --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_13.ipynb @@ -0,0 +1,398 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Radiation Exchange between surfaces" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.2 Page 821" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "\n", + "# View Factors of known surface Geometries\n", + "import math\n", + "# (1) Sphere within Cube\n", + "F12a = 1 \t\t;#By Inspection\n", + "F21a = (math.pi/6.)*F12a \t; #By Reciprocity\n", + "#calculations\n", + "\n", + "# (2) Partition within a Square Duct\n", + "F11b = 0 \t\t;#By Inspection\n", + "#By Symmetry F12 = F13\n", + "F12b = (1-F11b)/2. ;\t\t #By Summation Rule\n", + "F21b = math.sqrt(2.)*F12b ; #By Reciprocity\n", + "\n", + "# (3) Circular Tube\n", + "#From Table 13.2 or 13.5, with r3/L = 0.5 and L/r1 = 2\n", + "F13c = .172;\n", + "F11c = 0; \t\t#By Inspection\n", + "F12c = 1 - F11c - F13c \t\t;#By Summation Rule\n", + "F21c = F12c/4. \t\t;#By Reciprocity\n", + "#results\n", + "\n", + "print' %s' %('\\n Desired View Factors may be obtained from inspection, the reciprocity rule, the summation rule and/or use of charts')\n", + "print '%s %.3f' %('\\n (1) Sphere within Cube F21 =',F21a)\n", + "print '%s %.3f' %('\\n (2) Partition within a Square Duct F21 = ',F21b)\n", + "print '%s %.3f' %('\\n (3) Circular Tube F21 =',F21c);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \n", + " Desired View Factors may be obtained from inspection, the reciprocity rule, the summation rule and/or use of charts\n", + "\n", + " (1) Sphere within Cube F21 = 0.524\n", + "\n", + " (2) Partition within a Square Duct F21 = 0.707\n", + "\n", + " (3) Circular Tube F21 = 0.207\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.3 Page 826" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "# Net rate of Heat transfer to the absorber surface\n", + "\n", + "L = 10 \t;#[m] Collector length = Heater Length\n", + "T2 = 600 \t;#[K] Temperature of curved surface\n", + "A2 = 15 \t;#[m^2] Area of curved surface\n", + "e2 = .5 \t;# emissivity of curved surface\n", + "stfncnstt = 5.67*math.pow(10,-8);\t\t#[W/m^2.K^4] Stefan-Boltzmann constant\n", + "T1 = 1000 ;#[K] Temperature of heater\n", + "A1 = 10 ;#[m^2] area of heater\n", + "e1 = .9 ;# emissivity of heater\n", + "W = 1 ;#[m] Width of heater\n", + "H = 1 ;#[m] Height\n", + "T3 = 300 ;#[K] Temperature of surrounding\n", + "e3 = 1 ;# emissivity of surrounding\n", + "#calculations\n", + "\n", + "J3 = stfncnstt*T3*T3*T3*T3; #[W/m^2]\n", + "#From Figure 13.4 or Table 13.2, with Y/L = 10 and X/L =1\n", + "F12 = .39;\n", + "F13 = 1 - F12; \t\t\t#By Summation Rule\n", + "#For a hypothetical surface A2h\n", + "A2h = L*W;\n", + "F2h3 = F13; \t\t\t#By Symmetry\n", + "F23 = A2h/A2*F13; \t#By reciprocity\n", + "Eb1 = stfncnstt*T1*T1*T1*T1;#[W/m^2]\n", + "Eb2 = stfncnstt*T2*T2*T2*T2;#[W/m^2]\n", + "#Radiation network analysis at Node corresponding 1\n", + "#-10J1 + 0.39J2 = -510582\n", + "#.26J1 - 1.67J2 = -7536\n", + "#Solving above equations\n", + "A = ([[-10 ,.39],\n", + " [.26, -1.67]]);\n", + "B = ([[-510582.],\n", + " [-7536.]]);\n", + "\n", + "X = numpy.linalg.solve (A,B);\n", + "\n", + "q2 = (Eb2 - X[1])/(1-e2)*(e2*A2);\n", + "#results\n", + "\n", + "print '%s %.1f %s' %('\\n Net Heat transfer rate to the absorber is = ',q2/1000. ,'kW');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Net Heat transfer rate to the absorber is = -77.8 kW\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.4 Page 830" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Power required to maintain prescribed temperatures\n", + "\n", + "T3 = 300. \t\t\t\t\t;#[K] Temperature of surrounding\n", + "L = .15 \t\t\t\t\t\t;#[m] Furnace Length\n", + "T2 = 1650+273. \t\t\t\t;#[K] Temperature of bottom surface\n", + "T1 = 1350+273. \t\t\t\t;#[K] Temperature of sides of furnace\n", + "D = .075 \t\t\t\t\t;#[m] Diameter of furnace\n", + "stfncnstt = 5.670*math.pow(10,-8); #[W/m^2.K^4] Stefan Boltzman Constant\n", + "#calculations\n", + "\n", + "A2 = math.pi*D*D/4. \t\t\t;#[m] Area of bottom surface\n", + "A1 = math.pi*D*L \t \t\t;#[m] Area of curved sides\n", + "#From Figure 13.5 or Table 13.2, with ri/L = .25 \n", + "F23 = .056;\n", + "F21 = 1 - F23; \t\t\t\t#By Summation Rule\n", + "F12 = A2/A1*F21; \t\t\t#By reciprocity\n", + "F13 = F12 \t\t\t\t;#By Symmetry\n", + "#From Equation 13.17 Heat balance\n", + "q = A1*F13*stfncnstt*(T1*T1*T1*T1 - T3*T3*T3*T3) + A2*F23*stfncnstt*(T2*T2*T2*T2 - T3*T3*T3*T3);\n", + "#results\n", + "\n", + "print '%s %d %s' %('\\n Power required to maintain prescribed temperatures is =',q, 'W');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Power required to maintain prescribed temperatures is = 1830 W\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.5 Page 834" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Heat gain by the fluid passing through the inner tube\n", + "# Percentage change in heat gain with radiation shield inserted midway between inner and outer tubes\n", + "\n", + "T2 = 300 \t;#[K] Temperature of inner surface\n", + "D2 = .05 \t;#[m] Diameter of Inner Surface\n", + "e2 = .05 \t;# emissivity of Inner Surface\n", + "T1 = 77 \t;#[K] Temperature of Outer Surface\n", + "D1 = .02 ;#[m] Diameter of Inner Surface\n", + "e1 = .02 \t;# emissivity of Outer Surface\n", + "D3 = .035 ;#[m] Diameter of Shield\n", + "e3 = .02 ;# emissivity of Shield\n", + "stfncnstt = 5.670*math.pow(10,-8) ;#[W/m^2.K^4] Stefan Boltzman Constant\n", + "#calculations\n", + "\n", + "#From Equation 13.20 Heat balance\n", + "q = stfncnstt*(math.pi*D1)*(T1*T1*T1*T1-T2*T2*T2*T2)/(1/e1 + (1-e2)/e2*D1/D2) ;#[W/m] \n", + "\n", + "RtotL = (1-e1)/(e1*math.pi*D1) + 1/(math.pi*D1*1) + 2*((1-e3)/(e3*math.pi*D3)) + 1/(math.pi*D3*1) + (1-e2)/(e2*math.pi*D2) ;#[m^-2]\n", + "q2 = stfncnstt*(T1*T1*T1*T1 - T2*T2*T2*T2)/RtotL; #[W/m] \n", + "#results\n", + "\n", + "print '%s %.2f %s' %('\\n Heat gain by the fluid passing through the inner tube =',q,'W/m') \n", + "print '%s %.2f %s' %('\\n Percentage change in heat gain with radiation shield inserted midway between inner and outer tubes is =',(q2-q)*100/q,'percent'); " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Heat gain by the fluid passing through the inner tube = -0.50 W/m\n", + "\n", + " Percentage change in heat gain with radiation shield inserted midway between inner and outer tubes is = -49.55 percent\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.6 Page 836" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Rate at which heat must be supplied per unit length of duct\n", + "# Temperature of the insulated surface\n", + "\n", + "T2 = 500 \t\t\t\t\t;#[K] Temperature of Painted surface\n", + "e2 = .4 \t \t\t\t\t;# emissivity of Painted Surface\n", + "T1 = 1200 \t\t\t\t\t;#[K] Temperature of Heated Surface\n", + "W = 1 \t\t\t\t\t; #[m] Width of Painted Surface\n", + "e1 = .8 \t\t\t\t\t;# emissivity of Heated Surface\n", + "er = .8 \t\t\t\t\t;# emissivity of Insulated Surface\n", + "stfncnstt = 5.670*math.pow(10,-8);#[W/m^2.K^4] Stefan Boltzman Constant\n", + "\n", + "#By Symmetry Rule\n", + "F2R = .5;\n", + "F12 = .5;\n", + "F1R = .5;\n", + "#calculations\n", + "\n", + "#From Equation 13.20 Heat balance\n", + "q = stfncnstt*(T1*T1*T1*T1-T2*T2*T2*T2)/((1-e1)/e1*W+ 1/(W*F12+1/((1/W/F1R) + (1/W/F2R))) + (1-e2)/e2*W) ;#[W/m] \n", + "\n", + "#Surface Energy Balance 13.13\n", + "J1 = stfncnstt*T1*T1*T1*T1 - (1-e1)*q/(e1*W)\t\t;# [W/m^2] Surface 1\n", + "J2 = stfncnstt*T2*T2*T2*T2 - (1-e2)*(-q)/(e2*W)\t\t;# [W/m^2] Surface 2\n", + "#From Equation 13.26 Heat balance\n", + "JR = (J1+J2)/2.;\n", + "TR = math.pow((JR/stfncnstt),.25);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %('\\n Rate at which heat must be supplied per unit length of duct = ',q/1000.,'kW/m') \n", + "print '%s %d %s' %('\\n Temperature of the insulated surface = ',TR,'K');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Rate at which heat must be supplied per unit length of duct = 36.98 kW/m\n", + "\n", + " Temperature of the insulated surface = 1102 K\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13.7 Page 841" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Rate at which heat must be supplied \n", + "# Temperature of the insulated surface\n", + "\n", + "T1 = 1000. \t\t\t\t;#[K] Temperature of Heated Surface\n", + "e1 = .8 \t\t\t\t\t;# emissivity of Heated Surface\n", + "e2 = .8 \t\t\t\t\t; # emissivity of Insulated Surface\n", + "r = .02 \t\t\t\t\t;#[m] Radius of surface\n", + "Tm = 400 \t\t\t\t;#[K] Temperature of surrounding air\n", + "m = .01 \t\t\t\t\t;#[kg/s] Flow rate of surrounding air\n", + "p = 101325 \t\t\t\t\t;#[Pa] Pressure of surrounding air\n", + "stfncnstt = 5.670*math.pow(10,-8);#[W/m^2.K^4] Stefan Boltzman Constant\n", + "#Table A.4 Air Properties at 1 atm, 400 K\n", + "k = .0338 \t\t\t\t;#[W/m.K] conductivity\n", + "u = 230*math.pow(10,-7) \t\t;#[kg/s.m] Viscosity\n", + "cp = 1014 \t\t\t\t;#[J/kg] Specific heat\n", + "Pr = .69 \t\t\t\t;# Prandtl Number\n", + "#calculations and results\n", + "\n", + "#Hydraulic Diameter\n", + "Dh = 2*math.pi*r/(math.pi+2.) ;#[m]\n", + "#Reynolds number\n", + "Re = m*Dh/(math.pi*r*r/2.)/u;\n", + "#View Factor\n", + "F12 = 1 ;\n", + "\n", + "print '%s %d %s' %(\"\\n As Reynolds Number is\",Re,\", Hence it is Turbulent flow inside a cylinder. Hence we will use Dittus-Boelter Equation\");\n", + "\n", + "#From Dittus-Boelter Equation\n", + "Nu = .023*math.pow(Re,.8) *math.pow(Pr,.4);\n", + "h = Nu*k/Dh; \t\t#[W/m^2.K]\n", + "\n", + "#From Equation 13.18 Heat Energy balance\n", + "#Newton Raphson\n", + "T2=600; \t\t\t\t\t#Initial Assumption\n", + "T2=696. \t\t\t\t\t\t#Final answer\n", + "#From energy Balance\n", + "q = h*math.pi*r*(T2-Tm) + h*2*r*(T1-Tm) ;#[W/m]\n", + "\n", + "print '%s %.2f %s' %('\\n Rate at which heat must be supplied per unit length of duct =',q,'W/m') \n", + "print '%s %.2f %s' %('& Temperature of the insulated surface =',T2,'K');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As Reynolds Number is 16912 , Hence it is Turbulent flow inside a cylinder. Hence we will use Dittus-Boelter Equation\n", + "\n", + " Rate at which heat must be supplied per unit length of duct = 2818.56 W/m\n", + "& Temperature of the insulated surface = 696.00 K\n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_14.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_14.ipynb new file mode 100644 index 00000000..3ce70f77 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_14.ipynb @@ -0,0 +1,428 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Diffusion Mass Transfer" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.1 Page 884" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Molar and mass fluxes of hydrogen and the relative values of the mass and thermal diffusivities for the three cases\n", + "\n", + "T = 293. \t \t\t\t\t;#[K] Temperature\n", + "Ma = 2 \t\t\t\t\t;#[kg/kmol] Molecular Mass\n", + "#Table A.8 Hydrogen-Air Properties at 298 K\n", + "Dab1 = .41*math.pow(10,-4); #[m^2/s] diffusion coefficient\n", + "#Table A.8 Hydrogen-Water Properties at 298 K\n", + "Dab2 = .63*math.pow(10,-8); #[m^2/s] diffusion coefficient\n", + "#Table A.8 Hydrogen-iron Properties at 293 K\n", + "Dab3 = .26*math.pow(10,-12); #[m^2/s] diffusion coefficient\n", + "#Table A.4 Air properties at 293 K\n", + "a1 = 21.6*math.pow(10,-6); #[m^2/s] Thermal Diffusivity\n", + "#Table A.6 Water properties at 293 K\n", + "k = .603 \t\t\t\t;#[W/m.K] conductivity\n", + "rho = 998 \t\t\t\t;#[kg/m^3] Density\n", + "cp = 4182 \t\t\t\t;#[J/kg] specific Heat\n", + "#Table A.1 Iron Properties at 300 K\n", + "a3 = 23.1 * math.pow(10,-6); #[m^2/s]\n", + "#calculations\n", + "\n", + "#Equation 14.14\n", + "#Hydrogen-air Mixture\n", + "DabT1 = Dab1*math.pow(T/298.,1.5);# [m^2/s] mass diffusivity\n", + "J1 = -DabT1*1; \t\t#[kmol/s.m^2] Total molar concentration\n", + "j1 = Ma*J1; \t\t#[kg/s.m^2] mass Flux of Hydrogen\n", + "Le1 = a1/DabT1; \t# Lewis Number Equation 6.50\n", + "\n", + "#Hydrogen-water Mixture\n", + "DabT2 = Dab2*math.pow(T/298.,1.5);# [m^2/s] mass diffusivity\n", + "a2 = k/(rho*cp) \t;#[m^2/s] thermal diffusivity \n", + "J2 = -DabT2*1 \t;#[kmol/s.m^2] Total molar concentration\n", + "j2 = Ma*J2 \t;#[kg/s.m^2] mass Flux of Hydrogen\n", + "Le2 = a2/DabT2 \t;# Lewis Number Equation 6.50\n", + "\n", + "#Hydrogen-iron Mixture\n", + "DabT3 = Dab3*math.pow(T/298.,1.5);# [m^2/s] mass diffusivity\n", + "J3 = -DabT3*1; \t#[kmol/s.m^2] Total molar concentration\n", + "j3 = Ma*J3; \t#[kg/s.m^2] mass Flux of Hydrogen\n", + "Le3 = a3/DabT3 \t;# Lewis Number Equation 6.50\n", + "#results\n", + "\n", + "print '%s %.1e' %('a (m^2/s) in 1 = ',a1)\n", + "print '%s %.1e' %('\\n a (m^2/s) in 2 = ',a2)\n", + "print '%s %.1e' %('\\na (m^2/s) in 3 = ',a3)\n", + "print '%s %.1e' %('\\nDab (m^2/s) in 1 = ',DabT1)\n", + "print '%s %.1e' %('\\n Dab (m^2/s) in 2 = ',DabT2)\n", + "print '%s %.1e' %('\\n Dab (m^2/s) in 3 = ',DabT3)\n", + "print '%s %.1e' %('\\n Le in 1 = ',Le1)\n", + "print '%s %.1e' %('\\n Le in 2 = ',Le2)\n", + "print '%s %.1e' %('\\n Le in 3 = ',Le3)\n", + "print '%s %.1e' %('\\n ja (kg/s.m^2) in 1 = ',j1)\n", + "print '%s %.1e' %('\\n ja (kg/s.m^2) in 2 = ',j2)\n", + "print '%s %.1e' %('\\n ja (kg/s.m^2) in 3 = ',j3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a (m^2/s) in 1 = 2.2e-05\n", + "\n", + " a (m^2/s) in 2 = 1.4e-07\n", + "\n", + "a (m^2/s) in 3 = 2.3e-05\n", + "\n", + "Dab (m^2/s) in 1 = 4.0e-05\n", + "\n", + " Dab (m^2/s) in 2 = 6.1e-09\n", + "\n", + " Dab (m^2/s) in 3 = 2.5e-13\n", + "\n", + " Le in 1 = 5.4e-01\n", + "\n", + " Le in 2 = 2.4e+01\n", + "\n", + " Le in 3 = 9.1e+07\n", + "\n", + " ja (kg/s.m^2) in 1 = -8.0e-05\n", + "\n", + " ja (kg/s.m^2) in 2 = -1.2e-08\n", + "\n", + " ja (kg/s.m^2) in 3 = -5.1e-13\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.2 Page 898" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "# Evaporation rate through a single pore\n", + "\n", + "T = 298 \t\t\t;#[K] Temperature\n", + "D = 10*math.pow(10,-6) \t;#[m]\n", + "L = 100*math.pow(10,-6); #[m]\n", + "H = .5 \t\t\t;# Moist Air Humidity\n", + "p = 1.01325 \t\t\t;#[bar]\n", + "#Table A.6 Saturated Water vapor Properties at 298 K\n", + "psat = .03165; \t#[bar] saturated Pressure\n", + "#Table A.8 Water vapor-air Properties at 298 K\n", + "Dab = .26*math.pow(10,-4); #[m^2/s] diffusion coefficient\n", + "#calculations\n", + "\n", + "C = p/(8.314/100. *298) ;#Total Concentration\n", + "#From section 6.7.2, the mole fraction at x = 0 is\n", + "xa0 = psat/p;\n", + "#the mole fraction at x = L is\n", + "xaL = H*psat/p;\n", + "\n", + "#Evaporation rate per pore Using Equation 14.41 with advection\n", + "N = (math.pi*D*D)*C*Dab/(4*L)*2.303*math.log10((1-xaL)/(1-xa0)) ;#[kmol/s]\n", + "\n", + "#Neglecting effects of molar averaged velocity Equation 14.32\n", + "#Species transfer rate per pore\n", + "Nh = (math.pi*D*D)*C*Dab/(4*L)*(xa0-xaL) ;#[kmol/s]\n", + "#results\n", + "\n", + "print '%s %.2e %s' %('\\n Evaporation rate per pore Without advection effects',Nh,'kmol/s')\n", + "print '%s %.2e %s' %('and With Advection effects',N,'kmol/s')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Evaporation rate per pore Without advection effects 1.30e-14 kmol/s\n", + "and With Advection effects 1.34e-14 kmol/s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.3 Page 898" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Rate of water vapor molar diffusive ttansfer through the trough wall\n", + "\n", + "D = .005 \t\t\t\t\t\t;#[m] Diameter\n", + "L = 50*math.pow(10,-6); \t#[m] Length\n", + "h = .003 \t\t\t\t;#[m] Depth\n", + "Dab = 6*math.pow(10,-14) \t;#[m^2/s] Diffusion coefficient\n", + "Cas1 = 4.5*math.pow(10,-3) \t;#[kmol/m^3] Molar concentrations of water vapor at outer surface\n", + "Cas2 = 0.5*math.pow(10,-3) \t;#[kmol/m^3] Molar concentrations of water vapor at inner surface\n", + "#calculations\n", + "\n", + "#Transfer Rate through cylindrical wall Equation 14.54\n", + "Na = Dab/L*(math.pi*D*D/4. + math.pi*D*h)*(Cas1-Cas2); #[kmol/s]\n", + "#results\n", + "\n", + "print '%s %.2e %s' %('\\n Rate of water vapor molar diffusive ttansfer through the trough wall ',Na,'kmol/s');\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Rate of water vapor molar diffusive ttansfer through the trough wall 3.20e-16 kmol/s\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.4 Page 902" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# The rate of change of the helium pressure dp/dt\n", + "\n", + "D = .2 \t\t\t;#[m] Diameter\n", + "L = 2*math.pow(10,-3) ;#[m] Thickness\n", + "p = 4 \t\t\t;#[bars] Helium Pressure\n", + "T = 20+273. \t\t\t;#[K] Temperature\n", + "#Table A.8 helium-fused silica (293K) Page 952\n", + "Dab = .4*math.pow(10,-13)\t;#[m^2/s] Diffusion coefficient\n", + "#Table A.10 helium-fused silica (293K)\n", + "S = .45*math.pow(10,-3)\t\t;#[kmol/m^3.bar] Solubility\n", + "#calculations\n", + "\n", + "# By applying the species conservation Equation 14.43 and 14.62\n", + "dpt = -6*(.08314)*T*(Dab)*S*p/(L*D);\n", + "\n", + "#results\n", + "print '%s %.2e %s' %('\\n The rate of change of the helium pressure dp/dt',dpt,' bar/s');\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " The rate of change of the helium pressure dp/dt -2.63e-11 bar/s\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.5 Page 904" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# The Hydrogen mass diffusive flux nA (kg/s.m^2)\n", + "#A -> Hydrogen\n", + "#B -> Plastic\n", + "\n", + "Dab = 8.7*math.pow(10,-8) ;#[m^2/s] Diffusion coefficient\n", + "Sab = 1.5*math.pow(10,-3) ;#[kmol/m^3.bar] Solubility\n", + "L = .0003 \t\t\t;#[m] thickness of bar\n", + "p1 = 3 \t\t\t;#[bar] pressure on one side\n", + "p2 = 1 \t\t\t;#[bar] pressure on other side\n", + "Ma = 2 \t\t\t;#[kg/mol] molecular mass of Hydrogen\n", + "#calculations\n", + "\n", + "#Surface molar concentrations of hydrogen from Equation 14.62\n", + "Ca1 = Sab*p1 \t\t\t\t; #[kmol/m^3]\n", + "Ca2 = Sab*p2 \t\t\t\t; #[kmol/m^3]\n", + "#From equation 14.42 to 14.53 for obtaining mass flux\n", + "N = Dab/L*(Ca1-Ca2) ; \t#[kmol/s.m^2]\n", + "n = Ma*N ; \t#[kg/s.m^2] on Mass basis\n", + "#results\n", + "\n", + "print '%s %.2e %s' %('\\n The Hydrogen mass diffusive flux n =',n,' (kg/s.m^2)');\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " The Hydrogen mass diffusive flux n = 1.74e-06 (kg/s.m^2)\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.6 Page 909 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Maximum Thickness of a bacteria laden biofilm, that may be siccessfully treated\n", + "\n", + "Dab = 2*math.pow(10,-12) \t;#[m^2/s] Diffusion coefficient\n", + "Ca0 = 4*math.pow(10,-3) \t\t;#[kmol/m^3] Fixed Concentration of medication\n", + "Na = -.2*math.pow(10,-3) \t\t;#[kmol/m^3.s] Minimum consumption rate of antibiotic\n", + "k1 = .1 \t\t\t\t\t;#[s^-1] Reaction Coefficient\n", + "#calculations\n", + "\n", + "#For firsst order kinetic reaction Equation 14.74\n", + "m = math.pow((k1/Dab),.5);\n", + "L = math.acosh(-k1*Ca0/Na) /m;\n", + "#results\n", + "\n", + "print '%s %.1f %s' %('\\n Maximum Thickness of a bacteria laden biofilm, that may be siccessfully treated is ',L*math.pow(10,6), 'mu-m');\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Maximum Thickness of a bacteria laden biofilm, that may be siccessfully treated is 5.9 mu-m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14.7 Page 913" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "import math\n", + "# Total dosage of medicine delivered to the patient over a one-week time period, sensivity of the dosage to the mass duffusivity of the patch and skin\n", + "\n", + "Dap = .1*math.pow(10,-12) ;#[m^2/s] Diffusion coefficient of medication with patch\n", + "Das = .2*math.pow(10,-12) ;#[m^2/s] Diffusion coefficient of medication with skin\n", + "L = .05 \t\t\t;#[m] patch Length\n", + "rhop = 100 \t\t\t;#[kg/m^3] Density of medication on patch\n", + "rho2 = 0 \t\t\t;#[kg/m^3] Density of medication on skin\n", + "K = .5 \t\t\t;#Partition Coefficient\n", + "t = 3600*24*7 \t\t\t;#[s] Treatment time\n", + "#calculations\n", + "\n", + "#Applying Conservation of species equation 14.47b\n", + "#By analogy to equation 5.62, 5.26 and 5.58\n", + "D = 2*rhop*L*L/(math.sqrt(math.pi))*math.sqrt(Das*Dap*t)/(math.sqrt(Das)+math.sqrt(Dap)/K);\n", + "#results\n", + "\n", + "print '%s %.1f %s' %('\\n Total dosage of medicine delivered to the patient over a one-week time period is',D*math.pow(10,6) ,'mg');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Total dosage of medicine delivered to the patient over a one-week time period is 28.7 mg\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_2.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_2.ipynb new file mode 100644 index 00000000..a3d2e96a --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_2.ipynb @@ -0,0 +1,184 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Introduction to conduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1 Page 68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Find Value for Thermal Diffusivity\n", + "\n", + "def alpha(p, Cp, k):\n", + " a=k/(p*Cp); #[m^2/s]\n", + " return a;\n", + "#(a) Pure Aluminium at 300K\n", + "# From Appendix A, Table A.1\n", + "#calculations and results\n", + "\n", + "p = 2702.; \t\t#[Kg/m^3] - Density Of Material \n", + "Cp = 903.; \t\t\t#[J/kg.K] - Specific heat of Material\n", + "k = 237.; \t\t#[W/m.k] - Thermal Conductivity of Material\n", + "\n", + "print '%s %.2e %s' %(\"\\n (a) Thermal Diffuisivity of Pure Aluminium at 300K = \",alpha(p, Cp, k),\" m^2/s\\n\");\n", + "\n", + "#(b) Pure Aluminium at 700K\n", + "# From Appendix A, Table A.1\n", + "\n", + "p = 2702.; \t\t#[Kg/m^3] - Density Of Material \n", + "Cp = 1090.; \t\t#[J/kg.K] - Specific heat of Material\n", + "k = 225.; \t\t#[W/m.k] - Thermal Conductivity of Material\n", + "\n", + "print '%s %.2e %s' %(\"\\n (b) Thermal Diffuisivity of Pure Aluminium at 700K =\",alpha(p, Cp, k),\" m^2/s\\n\");\n", + "\n", + "#(c) Silicon Carbide at 1000K\n", + "# From Appendix A, Table A.2\n", + "\n", + "p = 3160.; \t\t#[Kg/m^3] - Density Of Material \n", + "Cp = 1195.; \t\t#[J/kg.K] - Specific heat of Material\n", + "k = 87.; \t\t#[W/m.k] - Thermal Conductivity of Material\n", + "\n", + "print '%s %.2e %s' %(\"\\n (c) Thermal Diffuisivity of Silicon Carbide at 1000K =\",alpha(p, Cp, k),\" m^2/s\\n\");\n", + "\n", + "#(d) Paraffin at 300K\n", + "# From Appendix A, Table A.3\n", + "\n", + "p = 900.; \t\t\t#[Kg/m^3] - Density Of Material \n", + "Cp = 2890.; \t\t#[J/kg.K] - Specific heat of Material\n", + "k = .24; \t\t#[W/m.k] - Thermal Conductivity of Material\n", + "\n", + "print '%s %.2e %s' %(\"\\n (d) Thermal Diffuisivity of Paraffin at 300K = \",alpha(p, Cp, k),\"m^2/s\");\n", + "#END\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Thermal Diffuisivity of Pure Aluminium at 300K = 9.71e-05 m^2/s\n", + "\n", + "\n", + " (b) Thermal Diffuisivity of Pure Aluminium at 700K = 7.64e-05 m^2/s\n", + "\n", + "\n", + " (c) Thermal Diffuisivity of Silicon Carbide at 1000K = 2.30e-05 m^2/s\n", + "\n", + "\n", + " (d) Thermal Diffuisivity of Paraffin at 300K = 9.23e-08 m^2/s\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2 Page 75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Analyze a Situation of Non-Uniform Temperature Distribution\n", + "#T(x) = a + bx +cx^2 T-degC & x-meter\n", + "\n", + "a = 900.; \t\t\t#[degC]\n", + "b = -300.; \t\t\t#[degC/m]\n", + "c = -50.; \t\t\t#[degC/m^2]\n", + "\n", + "q = 1000.; \t\t\t#[W/m^2.K] - Uniform heat Generation\n", + "A = 10. ; \t\t\t#[m^2] - Wall Area\n", + "#Properties of Wall\n", + "p = 1600.; \t\t\t#[kg/m^3] - Density\n", + "k = 40.; \t\t\t#[W/m] - Thermal Conductivity\n", + "Cp = 4000.; \t\t\t#[J/kg.K] - Specific Heat\n", + "L = 1; \t\t\t #[m] - Length of wall\n", + "#calculations and results\n", + "\n", + "#(i) Rate of Heat Transfer entering the wall and leaving the wall\n", + "# From Eqn 2.1\n", + "# qin = -kA(dT/dx)|x=0 = -kA(b)\n", + "\n", + "qin= - b*k*A;\n", + "\n", + "# Similarly\n", + "# qout = -kA(dT/dx)|x=L = -kA(b+2cx)|x=L\n", + "\n", + "qout= - k*A*(b+2*c*L);\n", + "\n", + "print '%s %d %s' %(\"\\n (i) Rate of Heat Transfer entering the wall =\",qin,\" W \");\n", + "print '%s %d %s' %(\"\\n And leaving the wall =\",qout,\"W \");\n", + "\n", + "#(ii) Rate of change Of Energy Storage in Wall E`st\n", + "# Applying Overall Energy Balance across the Wall\n", + "#E`st = E`in + E`g + E`out = qin + q`AL - qout\n", + "Est = qin + q*A*L - qout;\n", + "\n", + "print '%s %d %s' %(\"\\n (ii) Rate of change Of Energy Storage in Wall =\",Est,\" W\\n\");\n", + "\n", + "#(iii) Time rate of Temperature change at x= 0, 0.25 and .5m\n", + "#Using Eqn 2.19\n", + "# T`= dT/dt = (k/p*Cp)*d(dT/dx)/dx + q`/p*Cp\n", + "#As d(dT/dx)/dx = d(b + 2cx)/dx = 2c - Independent of x\n", + "T = (k/(p*Cp))*(2*c)+ q/(p*Cp);\n", + "print '%s %.6f %s' %(\"\\n (iii) Time rate of Temperature change independent of x =\",T,\" degC/s\\n\");\n", + "\n", + "#END\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (i) Rate of Heat Transfer entering the wall = 120000 W \n", + "\n", + " And leaving the wall = 160000 W \n", + "\n", + " (ii) Rate of change Of Energy Storage in Wall = -30000 W\n", + "\n", + "\n", + " (iii) Time rate of Temperature change independent of x = -0.000469 degC/s\n", + "\n" + ] + } + ], + "prompt_number": 2 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_3.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_3.ipynb new file mode 100644 index 00000000..80e4f209 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_3.ipynb @@ -0,0 +1,804 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "One-dimensional, Steady State Conduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.1 Page 104" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Find Skin Temperature & Aerogel Insulation Thickness \n", + "import math\n", + "A=1.8; \t\t\t\t\t# [m^2] Area for Heat transfer i.e. both surfaces\n", + "Ti = 35+273.; \t\t\t\t#[K] - Inside Surface Temperature of Body\n", + "Tsurr = 10+273.; \t\t\t#[K] - Temperature of surrounding\n", + "Tf = 283.; \t\t\t\t\t#[K] - Temperature of Fluid Flow\n", + "e=.95; \t\t\t\t\t\t# Emissivity of Surface\n", + "Lst=.003; \t\t\t\t#[m] - Thickness of Skin\n", + "kst=.3; \t\t \t\t\t# [W/m.K] Effective Thermal Conductivity of Body\n", + "kins = .014; \t\t\t\t# [W/m.K] Effective Thermal Conductivity of Aerogel Insulation\n", + "hr = 5.9; \t\t\t\t#[W/m^2.k] - Natural Thermal Convectivity from body to air\n", + "stfncnstt=5.67*math.pow(10,(-8)); # [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "q = 100; \t\t\t#[W] Given Heat rate\n", + "#calculations\n", + "\n", + "#Using Conducion Basic Eq 3.19\n", + "Rtot = (Ti-Tsurr)/q;\n", + "#Also\n", + "#Rtot=Lst/(kst*A) + Lins/(kins*A)+(h*A + hr*A)^-1\n", + "#Rtot = 1/A*(Lst/kst + Lins/kins +(1/(h+hr)))\n", + "\n", + "#Thus\n", + "#For Air,\n", + "h=2.; \t\t\t\t\t#[W/m^2.k] - Natural Thermal Convectivity from body to air\n", + "Lins1 = kins * (A*Rtot - Lst/kst - 1/(h+hr));\n", + "\n", + "#For Water,\n", + "h=200.; \t\t\t\t\t#[W/m^2.k] - Natural Thermal Convectivity from body to air\n", + "Lins2 = kins * (A*Rtot - Lst/kst - 1/(h+hr));\n", + "\n", + "Tsa=305.; \t\t#[K] Body Temperature Assumed\n", + "\n", + "#Temperature of Skin is same in both cases as Heat Rate is same\n", + "#q=(kst*A*(Ti-Ts))/Lst\n", + "Ts = Ti - q*Lst/(kst*A);\n", + "#results\n", + "\n", + "#Also from eqn of effective resistance Rtot F\n", + "print '%s %.1f %s' %(\"\\n\\n (I) In presence of Air, Insulation Thickness = \",Lins1*1000,\" mm\")\n", + "print '%s %.1f %s' %(\"\\n (II) In presence of Water, Insulation Thickness =\",Lins2*1000.,\" mm\");\n", + "print '%s %.2f %s' %(\"\\n\\n Temperature of Skin =\",Ts-273,\" degC\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (I) In presence of Air, Insulation Thickness = 4.4 mm\n", + "\n", + " (II) In presence of Water, Insulation Thickness = 6.1 mm\n", + "\n", + "\n", + " Temperature of Skin = 34.44 degC\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.2 Page 107" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Chip Operating Temperature\n", + "import math\n", + "Tf = 25+273.; \t\t\t#[K] - Temperature of Fluid Flow\n", + "L=.008; \t\t\t\t#[m] - Thickness of Aluminium \n", + "k=239; \t\t\t\t# [W/m.K] Effective Thermal Conductivity of Aluminium\n", + "Rc=.9*math.pow(10,-4); #[K.m^2/W] Maximum permeasible Resistane of Epoxy Joint\n", + "q=10000.; \t\t\t#[W/m^2] Heat dissipated by Chip\n", + "h=100.; \t\t\t\t#[W/m^2.k] - Thermal Convectivity from chip to air\n", + "#calculations\n", + "\n", + "#Temperature of Chip\n", + "\n", + "Tc = Tf + q/(h+1/(Rc+(L/k)+(1/h)));\n", + "q=(Tc-Tf)/(1/h)+(Tc-Tf)/(Rc+(L/k)+(1/h))\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n Temperature of Chip =\",Tc-273,\"degC\");\n", + "print '%s' %(\"\\n Chip will Work well below its maximum allowable Temperature ie 85 degC\")\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Temperature of Chip = 75.31 degC\n", + "\n", + " Chip will Work well below its maximum allowable Temperature ie 85 degC\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.3 Page 109" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Find Thermal conductivity of Carbon Nanotube\n", + "import math\n", + "D = 14 * math.pow(10,-9); \t\t\t# [m]Dia of Nanotube\n", + "s = 5*math.pow(10,-6); \t\t\t# [m]Distance between the islands\n", + "Ts = 308.4; \t\t\t\t\t\t#[K] Temp of sensing island\n", + "Tsurr = 300; \t\t\t\t\t\t#[K] Temp of surrounding\n", + "q = 11.3*math.pow(10,-6); \t\t\t#[W] Total Rate of Heat flow\n", + "\n", + "#Dimension of platinum line\n", + "wpt =math.pow(10,-6); \t\t\t#[m]\n", + "tpt = 0.2*math.pow(10,-6); \t\t\t#[m] \n", + "Lpt = 250*math.pow(10,-6); \t\t\t#[m] \n", + "#Dimension of Silicon nitride line\n", + "wsn = 3*math.pow(10,-6); \t\t\t#[m]\n", + "tsn = 0.5*math.pow(10,-6); \t \t\t#[m] \n", + "Lsn = 250*math.pow(10,-6); \t\t\t#[m] \n", + "#From Table A.1 Platinum Temp Assumed = 325K\n", + "kpt = 71.6; \t\t\t\t\t\t\t#[W/m.K]\n", + "#From Table A.2, Silicon Nitride Temp Assumed = 325K\n", + "ksn = 15.5; \t \t\t\t\t\t\t#[W/m.K]\n", + "#calculations\n", + "\n", + "Apt = wpt*tpt; \t\t\t\t\t#Cross sectional area of platinum support beam\n", + "Asn = wsn*tsn-Apt; \t\t\t\t\t#Cross sectional area of Silicon Nitride support beam\n", + "Acn = math.pi*D*D/4.; \t\t\t#Cross sectional Area of Carbon nanotube\n", + "\n", + "Rtsupp = 1/(kpt*Apt/Lpt + ksn*Asn/Lsn); #[K/W] Thermal Resistance of each support\n", + "\n", + "qs = 2*(Ts-Tsurr)/Rtsupp; \t\t\t#[W] Heat loss through sensing island support\n", + "qh = q - qs; \t\t\t\t\t\t#[W] Heat loss through heating island support\n", + "\n", + "Th = Tsurr + qh*Rtsupp/2.; \t\t\t#[K] Temp of Heating island\n", + "\n", + "#For portion Through Carbon Nanotube\n", + "\n", + "\n", + "kcn = qs*s/(Acn*(Th-Ts));\n", + "qs = (Th-Ts)/(s/(kcn*Acn));\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n Thermal Conductivity of Carbon nanotube =\",kcn,\"W/m.K\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Thermal Conductivity of Carbon nanotube = 3111.86 W/m.K\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.4 Page 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature Distribution And Heat rate\n", + "import math\n", + "import numpy\n", + "from numpy import linspace\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "a = 0.25;\n", + "x1 = .05; #[m] Distance of smaller end\n", + "x2 = .25; #[m] Distance of larger end\n", + "T1 = 400; #[K] Temperature of smaller end\n", + "T2 = 600; #[K] Temperature of larger end\n", + "k = 3.46; #[W/m.K] From Table A.2, Pyroceram at Temp 285K\n", + "T=numpy.zeros(100)\n", + "#calculations\n", + "\n", + "x = numpy.linspace(0.05,100,num=100);\n", + "i=1;\n", + "for i in range (0,99):\n", + " z=float(x[i]);\n", + " T[i]=(T1 + (T1-T2)*((1/z - 1/x1)/(1/x1 - 1/x2)));\t\n", + "\n", + "pyplot.plot(x,T);\n", + "pyplot.xlabel(\"x (m)\");\n", + "pyplot.ylabel(\"T (K)\");\n", + "pyplot.show()\n", + "qx = math.pi*a*a*k*(T1-T2)/(4*(1/x1 - 1/x2)); #[W]\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n Heat Transfer rate =\",qx,\" W\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Heat Transfer rate = -2.12 W\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.5 Page 119 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "%pylab inline\n", + "# Critical Thickness\n", + "import math\n", + "import numpy\n", + "from numpy import linspace\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "k = .055; \t\t\t\t#[W/m.K] From Table A.3, Cellular glass at Temp 285K\n", + "h = 5; \t\t\t\t#[W/m^2.K]\n", + "ri = 5*math.pow(10,-3); #[m] radius of tube\n", + "#calculations\n", + "\n", + "rct = k/h; \t\t\t\t# [m] Critical Thickness of Insulation for maximum Heat loss or minimum resistance\n", + "\n", + "x = numpy.linspace(0,100,num=99);\n", + "ycond= numpy.zeros(99);\n", + "yconv= numpy.zeros(99);\n", + "ytot= numpy.zeros(99);\n", + "for i in range (0,99):\n", + " z=float(x[i]);\n", + " ycond[i]=(2.30*math.log10((z+ri)/ri)/(2*math.pi*k));\n", + " yconv[i]=1/(2*math.pi*(z+ri)*h);\n", + " ytot[i]=yconv[i]+ycond[i];\n", + "\n", + " \n", + "pyplot.plot(x,ytot);\n", + "pyplot.xlabel(\"r-ri (m)\");\n", + "pyplot.ylabel(\"R (m.K/W)\");\n", + "pyplot.show();\n", + "#results\n", + "\n", + "print '%s %.3f %s' %(\"\\n\\n Critical Radius is =\",rct,\" m \")\n", + "print '%s %.3f %s' %(\"\\n Heat transfer will increase with the addition of insulation up to a thickness of\",rct-ri,\" m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x42e6390>" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Critical Radius is = 0.011 m \n", + "\n", + " Heat transfer will increase with the addition of insulation up to a thickness of 0.006 m\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.6 Page 122" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Heat conduction through Spherical Container \n", + "import math\n", + "k = .0017; \t\t\t\t\t\t#[W/m.K] From Table A.3, Silica Powder at Temp 300K\n", + "h = 5; \t\t\t\t\t\t#[W/m^2.K]\n", + "r1 = 25./100.; \t\t\t\t#[m] Radius of sphere\n", + "r2 = .275; \t\t\t\t#[m] Radius including Insulation thickness\n", + "\n", + "#Liquid Nitrogen Properties\n", + "T = 77; \t\t\t\t\t\t#[K] Temperature\n", + "rho = 804; \t\t\t\t\t\t#[kg/m^3] Density\n", + "hfg = 2*100000.; \t\t\t\t\t#[J/kg] latent heat of vaporisation\n", + "\n", + "#Air Properties\n", + "Tsurr = 300; \t\t\t\t\t\t#[K] Temperature\n", + "h = 20 \t\t\t\t\t\t;#[W/m^2.K] convection coefficient\n", + "#calculations\n", + "\n", + "Rcond = (1/r1-1/r2)/(4*math.pi*k); #Using Eq 3.36\n", + "Rconv = 1/(h*4*math.pi*r2*r2);\n", + "q = (Tsurr-T)/(Rcond+Rconv);\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n (a)Rate of Heat transfer to Liquid Nitrogen\",q,\" W\");\n", + "\n", + "#Using Energy Balance q - m*hfg = 0\n", + "m=q/hfg; \t\t\t\t\t\t#[kg/s] mass of nirtogen lost per second\n", + "mc = m/rho*3600*24*1000.;\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n (b)Mass rate of nitrogen boil off \",mc,\"Litres/day\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (a)Rate of Heat transfer to Liquid Nitrogen 13.06 W\n", + "\n", + "\n", + " (b)Mass rate of nitrogen boil off 7.02 Litres/day\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.7 Page 129" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Composite Plane wall\n", + "import math\n", + "\n", + "Tsurr = 30+273.; \t\t\t\t\t\t#[K] Temperature of surrounding Water\n", + "h = 1000.; \t\t\t\t\t\t\t#[W/m^2.K] Heat Convection Coeff of Water\n", + "kb = 150.; \t\t\t\t\t\t\t#[W/m.K] Material B\n", + "Lb = .02; \t\t\t\t\t\t\t#[m] Thickness Material B\n", + "ka = 75.; \t\t\t\t\t\t\t#[W/m.K] Material A\n", + "La = .05; \t\t\t\t\t\t\t#[m] Thickness Material A\n", + "qa = 1.5*math.pow(10,6);\t\t\t\t#[W/m^3] Heat generation at wall A\n", + "qb = 0; \t\t\t\t\t\t\t\t#[W/m^3] Heat generation at wall B\n", + "#calculations\n", + "T2 = Tsurr + qa*La/h;\n", + "To = 100+273.15; \t\t\t\t #[K] Temp of opposite end of rod\n", + "Rcondb = Lb/kb;\n", + "Rconv = 1/h;\n", + "T1 = Tsurr +(Rcondb + Rconv)*(qa*La);\n", + "#From Eqn 3.43\n", + "T0 = qa*La*La/(2*ka) + T1;\n", + "\n", + "#results\n", + "\n", + "print '%s %d %s' %(\"\\n\\n (a) Inner Temperature of Composite To = \",T0-273,\" degC\") \n", + "print '%s %d %s' %(\"\\n (b) Outer Temperature of the Composite T2 =\",T2-273,\" degC\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (a) Inner Temperature of Composite To = 140 degC\n", + "\n", + " (b) Outer Temperature of the Composite T2 = 105 degC\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.9 Page 145 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "%pylab inline\n", + "# Heat conduction through Rod\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "import matplotlib\n", + "from matplotlib import pyplot\n", + "%pylab inline\n", + "kc = 398.; \t\t\t\t\t\t#[W/m.K] From Table A.1, Copper at Temp 335K\n", + "kal = 180.; \t \t\t\t\t\t#[W/m.K] From Table A.1, Aluminium at Temp 335K\n", + "kst = 14.; \t\t\t\t\t\t#[W/m.K] From Table A.1, Stainless Steel at Temp 335K\n", + "h = 100.; \t\t\t\t\t\t#[W/m^2.K] Heat Convection Coeff of Air\n", + "Tsurr = 25+273.; \t\t\t\t#[K] Temperature of surrounding Air\n", + "D = 5/1000.; \t\t\t\t\t#[m] Dia of rod\n", + "To = 100+273.15; \t\t\t\t#[K] Temp of opposite end of rod\n", + "#calculations\n", + "\n", + "#For infintely long fin m = h*P/(k*A)\n", + "mc = math.pow((4*h/(kc*D)),.5);\n", + "mal = math.pow((4*h/(kal*D)),.5);\n", + "mst = math.pow((4*h/(kst*D)),.5);\n", + "x = numpy.linspace(0,0.3,100);\n", + "Tc= numpy.zeros(100);\n", + "Tal= numpy.zeros(100);\n", + "Tst= numpy.zeros(100);\n", + "for i in range (0,100):\n", + " z=x[i];\n", + " Tc[i] =Tsurr + (To - Tsurr)*math.pow(2.73,(-mc*z)) - 273;\n", + " Tal[i] = Tsurr + (To - Tsurr)*math.pow(2.73,(-mal*z)) -273;\n", + " Tst[i] = Tsurr + (To - Tsurr)*math.pow(2.73,(-mst*z)) -273;\n", + "\n", + "\n", + "pyplot.plot(x,Tc,label=\"Cu\");\n", + "pyplot.plot(x,Tal,label=\"2024 Al\");\n", + "pyplot.plot(x,Tst,label=\"316 SS\");\n", + "pyplot.legend();\n", + "pyplot.xlabel(\"x (m)\");\n", + "pyplot.ylabel(\"T (C)\");\n", + "pyplot.show();\n", + "\n", + "#Using eqn 3.80\n", + "qfc = math.pow((h*math.pi*D*kc*math.pi/4*D*D),.5)*(To-Tsurr);\n", + "qfal = math.pow((h*math.pi*D*kal*math.pi/4*D*D),.5)*(To-Tsurr);\n", + "qfst = math.pow((h*math.pi*D*kst*math.pi/4*D*D),.5)*(To-Tsurr);\n", + "\n", + "print '%s %.2f %s %.2f %s %.2f %s' %(\"\\n\\n (a) Heat rate \\n For Copper = \",qfc,\"W \\n For Aluminium =\",qfal,\" W \\n For Stainless steel = \",qfst,\" W\");\n", + "\n", + "#Using eqn 3.76 for satisfactory approx\n", + "Linfc = 2.65/mc;\n", + "Linfal = 2.65/mal;\n", + "Linfst = 2.65/mst;\n", + "\n", + "print '%s %.2f %s %.2f %s %.2f %s' %(\"\\n\\n (a) Rods may be assumed to be infinite Long if it is greater than equal to \\n For Copper =\",Linfc,\"m \\n For Aluminium = \",Linfal,\" m \\n For Stainless steel =\",Linfst,\"m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "Populating the interactive namespace from numpy and matplotlib\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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tYeyPYzn13CkaNmhY7eM3bIApU+CPP9QR1YUQwhD0mizS0tKKe1dXpCr76FKV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\njYULIdO4T82EELcxSrKIj48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+ "text": [ + "<matplotlib.figure.Figure at 0x43e7f50>" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (a) Heat rate \n", + " For Copper = 8.33 W \n", + " For Aluminium = 5.60 W \n", + " For Stainless steel = 1.56 W\n", + "\n", + "\n", + " (a) Rods may be assumed to be infinite Long if it is greater than equal to \n", + " For Copper = 0.19 m \n", + " For Aluminium = 0.13 m \n", + " For Stainless steel = 0.04 m\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.10 Page 156" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Study of motorcycle finned cylinder\n", + "import math\n", + "H = .15; \t\t\t\t\t\t#[m] height\n", + "k = 186; \t\t\t\t\t#[W/m.K] alumunium at 400K\n", + "h = 50; \t\t\t\t\t#[W/m^2.K] Heat convection coefficient\n", + "Tsurr = 300; \t\t\t\t#[K] Temperature of surrounding air\n", + "To = 500; \t\t\t\t\t#[K] Temp inside\n", + "\n", + "#Dimensions of Fin\n", + "N = 5;\n", + "t = .006; \t\t\t\t\t#[m] Thickness\n", + "L = .020; \t\t\t\t\t#[m] Length\n", + "r2c = .048; \t\t\t\t#[m]\n", + "r1 = .025; \t\t\t#[m]\n", + "#calculations\n", + "\n", + "Af = 2*math.pi*(r2c*r2c-r1*r1);\n", + "At = N*Af + 2*math.pi*r1*(H-N*t);\n", + "\n", + "#Using fig 3.19 \n", + "nf = .95;\n", + "\n", + "qt = h*At*(1-N*Af*(1-nf)/At)*(To-Tsurr);\n", + "qwo = h*(2*math.pi*r1*H)*(To-Tsurr);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n Heat Transfer Rate with the fins =\",qt,\"W \")\n", + "print '%s %.2f %s' %(\" \\n Heat Transfer Rate without the fins =\",qwo,\"W\")\n", + "print '%s %.2f %s' %(\"\\n Thus Increase in Heat transfer rate of\",qt-qwo,\" W is observed with fins\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Heat Transfer Rate with the fins = 689.60 W \n", + " \n", + " Heat Transfer Rate without the fins = 235.62 W\n", + "\n", + " Thus Increase in Heat transfer rate of 453.98 W is observed with fins\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.11 Page 158" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Study of Fuel-cell fan system\n", + "import math\n", + "Wc =.05; \t\t\t\t#[m] width\n", + "H = .026; \t \t\t\t\t#[m] height\n", + "tc = .006; \t\t\t\t#[m] thickness of cell\n", + "V = 9.4; \t\t\t\t#[m/sec] vel of cooling air\n", + "P = 9; \t\t\t\t#[W] Power generated\n", + "C = 1000; \t\t\t\t#[W/(m^3/s)] Ratio of fan power consumption to vol flow rate\n", + "k = 200; \t\t\t\t#[W/m.K] alumunium\n", + "Tsurr = 25+273.15; \t\t#[K] Temperature of surrounding air\n", + "Tc = 56.4+273.15; \t\t#[K] Temp of fuel cell\n", + "Rtcy = math.pow(10,-3); #[K/W] Contact thermal resistance\n", + "tb = .002; \t\t#[m] thickness of base of heat sink\n", + "Lc = .05; \t\t\t#[m] length of fuel cell\n", + "#Dimensions of Fin\n", + "tf = .001; \t\t\t\t#[m] Thickness\n", + "Lf = .008; \t\t\t\t#[m] Length\n", + "#calculations\n", + "\n", + "Vf = V*(Wc*(H-tc)); \t\t#[m^3/sec] Volumetric flow rate\n", + "Pnet = P - C*Vf;\n", + "\n", + "\n", + "P = 2*(Lc+tf);\n", + "Ac = Lc*tf;\n", + "N = 22;\n", + "a=(2*Wc - N*tf)/N;\n", + "h = 19.1; \t\t#/[W/m^2.K]\n", + "q = 11.25; \t\t#[W]\n", + "m = math.pow((h*P/(k*Ac)),.5);\n", + "Rtf = math.pow((h*P*k*Ac),(-.5))/ math.tanh(m*Lf);\n", + "Rtc = Rtcy/(2*Lc*Wc);\n", + "Rtbase = tb/(2*k*Lc*Wc);\n", + "Rtb = 1/(h*(2*Wc-N*tf)*Lc);\n", + "Rtfn = Rtf/N;\n", + "Requiv = 1/(1/Rtb + 1/Rtfn);\n", + "Rtot = Rtc + Rtbase + Requiv;\n", + "\n", + "Tc2 = Tsurr +q*(Rtot);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n (a) Power consumed by fan is more than the generated power of fuel cell, and hence system cannot produce net power = \",Pnet ,\"W \")\n", + "print '%s %.2f %s %.2f %s' %(\"\\n\\n (b) Actual fuel cell Temp is close enough to \",Tc2-273.,\" degC for reducing the fan power consumption by half ie Pnet =\",C*Vf/2.,\" W, we require 22 fins, 11 on top and 11 on bottom.\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (a) Power consumed by fan is more than the generated power of fuel cell, and hence system cannot produce net power = -0.40 W \n", + "\n", + "\n", + " (b) Actual fuel cell Temp is close enough to 54.47 degC for reducing the fan power consumption by half ie Pnet = 4.70 W, we require 22 fins, 11 on top and 11 on bottom.\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.12 Page 163" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Heat loss from body & temp at inner surface\n", + "import math\n", + "hair = 2.; \t\t\t#[W/m^2.K] Heat convection coefficient air\n", + "hwater = 200.; \t\t#[W/m^2.K] Heat convection coefficient water\n", + "hr = 5.9 ; \t\t\t#[W/m^2.K] Heat radiation coefficient\n", + "Tsurr = 297.; \t\t#[K] Temperature of surrounding air\n", + "Tc = 37+273.; \t\t#[K] Temp inside\n", + "e = .95;\n", + "A = 1.8 ; \t\t#[m^2] area\n", + "#Prop of blood\n", + "w = .0005 ; \t\t#[s^-1] perfusion rate\n", + "pb = 1000.; \t\t#[kg/m^3] blood density\n", + "cb = 3600.; \t\t#[J/kg] specific heat\n", + "#Dimensions & properties of muscle & skin/fat\n", + "Lm = .03 ; \t\t#[m]\n", + "Lsf = .003 ; \t\t#[m]\n", + "km = .5 ; \t\t#[W/m.K]\n", + "ksf = .3; \t\t#[W/m.K]\n", + "q = 700.; \t\t#[W/m^3] Metabolic heat generation rate\n", + "#calculations\n", + "\n", + "Rtotair = (Lsf/ksf + 1/(hair + hr))/A;\n", + "Rtotwater = (Lsf/ksf + 1/(hwater+hr))/A;\n", + "#please correct this in the textbook. \n", + "m = math.pow((w*pb*cb/km),.5);\n", + "Theta = -q/(w*pb*cb);\n", + "\n", + "Tiair = (Tsurr*math.sinh(m*Lm) + km*A*m*Rtotair*(Theta + (Tc + q/(w*pb*cb))*math.cosh(m*Lm)))/(math.sinh(m*Lm)+km*A*m*Rtotair*math.cosh(m*Lm));\n", + "qair = (Tiair - Tsurr)/Rtotair;\n", + "\n", + "Tiwater = (Tsurr*math.sinh(m*Lm) + km*A*m*Rtotwater*(Theta + (Tc + q/(w*pb*cb))*math.cosh(m*Lm)))/(math.sinh(m*Lm)+km*A*m*Rtotwater*math.cosh(m*Lm));\n", + "qwater = (Tiwater - Tsurr)/Rtotwater;\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n For Air \\n Temp excess Ti = \",Tiair-273,\" degC \")\n", + "print '%s %.2f %s %.2f %s %.2f %s' %(\"and Heat loss rate =\",qair,\" W \\n\\n For Water \\n Temp excess Ti = \",Tiwater-273,\" degC and Heat loss rate =\",qwater,\"W \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " For Air \n", + " Temp excess Ti = 34.77 degC \n", + "and Heat loss rate = 141.99 W \n", + "\n", + " For Water \n", + " Temp excess Ti = 28.25 degC and Heat loss rate = 514.35 W \n" + ] + } + ], + "prompt_number": 23 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb new file mode 100644 index 00000000..70b74f06 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb @@ -0,0 +1,277 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Two dimensional, Steady State Conduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1 Page 211 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Thermal resistance of wire coating associated with peripheral variations in coating thickness\n", + "import math\n", + "d = .005; \t\t\t\t\t\t\t\t\t\t#[m] Diameter of wire\n", + "k = .35; \t\t\t\t\t\t\t\t\t\t#[W/m.K] Thermal Conductivity\n", + "h = 15; \t\t\t\t\t\t\t\t\t\t#[W/m^2.K] Total coeff with Convection n Radiation\n", + "#calculations\n", + "\n", + "rcr = k/h; \t\t\t\t\t\t\t\t\t\t# [m] critical insulation radius\n", + "tcr = rcr - d/2.; \t\t\t\t\t\t\t\t\t\t# [m] critical insulation Thickness\n", + "\n", + "Rtcond = 2.302*math.log10(rcr/(d/2.))/(2*math.pi*k); #[K/W] Thermal resistance \n", + "\n", + "#Using Table 4.1 Case 7\n", + "z = .5*tcr;\n", + "D=2*rcr;\n", + "Rtcond2D = (math.acosh((D*D + d*d - 4*z*z)/(2*D*d)))/(2*math.pi*k);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n The reduction in thermal resistance of the insulation is\", Rtcond-Rtcond2D,\" K/W \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " The reduction in thermal resistance of the insulation is 0.10 K/W \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3 Page 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature Distribution and Heat rate per unit length\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "Ts = 500.; \t#[K] Temp of surface\n", + "Tsurr = 300.; \t#[K] Temp of surrounding Air\n", + "h = 10.; \t#[W/m^2.K] Heat Convection soefficient\n", + "#Support Column\n", + "delx = .25; \t#[m]\n", + "dely = .25; \t#[m]\n", + "k = 1.; \t#[W/m.K] From Table A.3, Fireclay Brick at T = 478K\n", + "#calculations\n", + "\n", + "#Applying Eqn 4.42 and 4.48\n", + "A = numpy.array([[-4, 1, 1, 0, 0, 0, 0, 0],\n", + "\t\t[2, -4, 0, 1, 0, 0, 0, 0],\n", + "\t\t[1, 0, -4, 1, 1, 0, 0, 0],\n", + "\t\t[0, 1, 2, -4, 0, 1, 0, 0],\n", + "\t\t[0,0, 1, 0, -4, 1, 1, 0],\n", + "\t\t[0, 0, 0, 1, 2, -4, 0, 1],\n", + "\t\t[0, 0, 0, 0, 2, 0, -9, 1],\n", + "\t\t[0, 0, 0, 0, 0, 2, 2, -9]]);\n", + " \n", + "C = numpy.array([[-1000], [-500], [-500], [0], [-500], [0], [-2000], [-1500]]);\n", + "\n", + "T = numpy.linalg.solve (A,C);\n", + "#results\n", + "\n", + "print '%s' %(\"\\n Temp Distribution in K = \");\n", + "print (T);\n", + "\n", + "q = 2*h*((delx/2.)*(Ts-Tsurr)+delx*(T[6]-Tsurr)+delx*(T[7]-Tsurr)/2.);\n", + "print '%s %.2f %s' %(\"\\n\\n Heat rate from column to the airstream\",q,\" W/m \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Temp Distribution in K = \n", + "[[ 489.30472333]\n", + " [ 485.15381783]\n", + " [ 472.06507549]\n", + " [ 462.00582466]\n", + " [ 436.94975396]\n", + " [ 418.73932983]\n", + " [ 356.99461052]\n", + " [ 339.05198674]]" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + "\n", + " Heat rate from column to the airstream 882.60 W/m \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4 Page 230" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature Field and Rate of Heat Transfer\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "#Operating Conditions\n", + "\n", + "ho = 1000; #[W/m^2.K] Heat Convection coefficient\n", + "hi = 200; #[W/m^2.K] Heat Convection coefficient\n", + "Ti = 400; #[K] Temp of Air\n", + "Tg = 1700; #[K] Temp of Gas\n", + "h = 10 ; #[W/m^2.K] Heat Convection coefficient\n", + "\n", + "A = 2*6*math.pow(10,-6) ;#[m^2] Cross section of each Channel\n", + "x = .004 ; #[m] Spacing between joints\n", + "t = .006; #[m] Thickness\n", + "k = 25; #[W/m.K] Thermal Conductivity of Blade\n", + "delx = .001 ; #[m]\n", + "dely = .001 ; #[m]\n", + "#calculations and results\n", + "\n", + "#Applying Eqn 4.42 and 4.48\n", + "A = numpy.array([[-(2+ho*delx/k), 1, 0,0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", + " [1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,0,0,1,-(2+ho*delx/k),0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],\n", + " [1,0,0,0,0,0,-4,2,0,0,0,0,1,0,0,0,0,0,0,0,0],\n", + " [0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0,0,0],\n", + " [0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0,0],\n", + " [0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0],\n", + " [0,0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0],\n", + " [0,0,0,0,0,1,0,0,0,0,2,-4,0,0,0,0,0,1,0,0,0],\n", + " [0,0,0,0,0,0,1,0,0,0,0,0,-4,2,0,0,0,0,1,0,0],\n", + " [0,0,0,0,0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0],\n", + " [0,0,0,0,0,0,0,0,2,0,0,0,0,2,-2*(3+hi*delx/k),1,0,0,0,0,1],\n", + " [0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-2*(2+hi*delx/k),1,0,0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-2*(2+hi*delx/k),1,0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,-(2+hi*delx/k),0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-2,1,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-4,1],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,-(2+hi*delx/k)]]);\n", + " \n", + "C = numpy.array([[-ho*delx*Tg/k], \n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-ho*delx*Tg/k],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [-2*hi*delx*Ti/k],\n", + " [-2*hi*delx*Ti/k],\n", + " [-2*hi*delx*Ti/k],\n", + " [-hi*delx*Ti/k],\n", + " [0],\n", + " [0],\n", + " [-hi*delx*Ti/k]]);\n", + "\n", + "T = numpy.linalg.solve (A,C);\n", + "print '%s' %(\"\\n Temp Distribution in K = \");\n", + "print (T);\n", + "q = 4*ho*((delx/2.)*(Tg-T[0])+delx*(Tg-T[1])+delx*(Tg-T[2])+ delx*(Tg-T[3])+delx*(Tg-T[4])+delx*(Tg-T[5])/2.);\n", + "print '%s %.1f %s' %(\"\\n\\n Heat rate Transfer = \" ,q,\"W/m \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Temp Distribution in K = \n", + "[[ 1525.95413813]\n", + " [ 1525.27944565]\n", + " [ 1523.59609075]\n", + " [ 1521.93574674]\n", + " [ 1520.83066847]\n", + " [ 1520.45069026]\n", + " [ 1519.66699612]\n", + " [ 1518.7949547 ]\n", + " [ 1516.52842892]\n", + " [ 1514.53554374]\n", + " [ 1513.30134519]\n", + " [ 1512.88873965]\n", + " [ 1515.12393697]\n", + " [ 1513.70494809]\n", + " [ 1509.18712651]\n", + " [ 1506.37665411]\n", + " [ 1504.9504289 ]\n", + " [ 1504.50157796]\n", + " [ 1513.41885557]\n", + " [ 1511.71377418]\n", + " [ 1506.02634497]]\n", + "\n", + "\n", + " Heat rate Transfer = 3540.6 W/m \n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_5.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_5.ipynb new file mode 100644 index 00000000..a8498107 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_5.ipynb @@ -0,0 +1,710 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Transient Conduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1 Page 261" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Junction Diameter and Time Calculation to attain certain temp\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "h = 400.; \t\t\t\t\t\t\t\t#[W/m^2.K] Heat Convection coefficient\n", + "k = 20.; \t\t\t\t\t\t\t\t#[W/m.K] Thermal Conductivity of Blade\n", + "c = 400.; \t\t\t\t\t\t\t\t#[J/kg.K] Specific Heat\n", + "rho = 8500.; \t\t\t\t\t\t\t\t#[kg/m^3] Density\n", + "Ti = 25+273.; \t\t\t\t\t\t\t#[K] Temp of Air\n", + "Tsurr = 200+273.; \t\t\t\t\t\t\t#[K] Temp of Gas Stream\n", + "TimeConstt = 1; \t\t\t\t\t\t\t#[sec]\n", + "#calculations\n", + "\n", + "#From Eqn 5.7\n", + "D = 6*h*TimeConstt/(rho*c);\n", + "Lc = D/6.;\n", + "Bi = h*Lc/k;\n", + "\n", + "#From eqn 5.5 for time to reach \n", + "T = 199+273.; \t\t\t\t\t\t\t\t#[K] Required temperature\n", + "\n", + "t = rho*D*c*2.30*math.log10((Ti-Tsurr)/(T-Tsurr))/(h*6.);\n", + "#results\n", + "\n", + "print '%s %.2e %s' %(\"\\n\\n Junction Diameter needed for a time constant of 1 s = \",D,\" m\") \n", + "print '%s %.2f %s' %(\"\\n\\n Time Required to reach 199degC in a gas stream =\",t,\" sec \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Junction Diameter needed for a time constant of 1 s = 7.06e-04 m\n", + "\n", + "\n", + " Time Required to reach 199degC in a gas stream = 5.16 sec \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2 Page 265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Steady State Temperature of junction\n", + "# Time Required for thermocouple to reach a temp that is within 1 degc of its steady-state value\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "h = 400; \t\t#[W/m^2.K] Heat Convection coefficient\n", + "k = 20; \t\t#[W/m.K] Thermal Conductivity of Blade\n", + "c = 400; \t\t#[J/kg.K] Specific Heat\n", + "e = .9; \t\t\t#Absorptivity\n", + "rho = 8500; \t\t#[kg/m^3] Density\n", + "Ti = 25+273; \t#[K] Temp of Air\n", + "Tsurr = 400+273; \t#[K] Temp of duct wall\n", + "Tg = 200+273; \t\t#[K] Temp of Gas Stream\n", + "TimeConstt = 1; \t#[sec]\n", + "stfncnstt=5.67*math.pow(10,(-8)); # [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "#calculations and results\n", + "\n", + "#From Eqn 5.7\n", + "D = 6*h*TimeConstt/(rho*c);\n", + "As = math.pi*D*D;\n", + "V = math.pi*D*D*D/6;\n", + "\n", + "#Balancing Energy on thermocouple Junction\n", + "#Newton Raphson method for 4th order eqn\n", + "T=500;\n", + "#After newton raphson method\n", + "T=490.7 \n", + "print '%s %.2f %s' %(\"\\n (a) Steady State Temperature of junction =\",T-273,\"degC\\n\");\n", + "\n", + "#Using Eqn 5.15 and Integrating the ODE\n", + "# Integration of the differential equation\n", + "# dT/dt=-A*[h*(T-Tg)+e*stefncnstt*(T^4-Tsurr^4)]/(rho*V*c) , T(0)=25+273, and finds the minimum time t such that T(t)=217.7+273.15\n", + "\n", + "T0=25+273;ng=1;\n", + "rd=4.98\n", + "print '%s %.2f %s' %(\"\\n (b) Time Required for thermocouple to reach a temp that is within 1 degc of its steady-state value = \",rd,\" s\\n\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Steady State Temperature of junction = 217.70 degC\n", + "\n", + "\n", + " (b) Time Required for thermocouple to reach a temp that is within 1 degc of its steady-state value = 4.98 s\n", + "\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3 Page 267" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Total Time t required for two step process\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "ho = 40; \t\t\t#[W/m^2.K] Heat Convection coefficient\n", + "hc = 10; \t \t\t#[W/m^2.K] Heat Convection coefficient\n", + "k = 177; \t\t\t#[W/m.K] Thermal Conductivity \n", + "e = .8; \t\t\t\t#Absorptivity\n", + "L = 3*math.pow(10,-3) /2.; #[m] Metre\n", + "Ti = 25+273; \t\t#[K] Temp of Aluminium\n", + "Tsurro = 175+273; \t\t#[K] Temp of duct wall heating\n", + "Tsurrc = 25+273; \t\t#[K] Temp of duct wall\n", + "Tit = 37+273; \t\t\t#[K] Temp at cooling\n", + "Tc = 150+273; \t\t#[K] Temp critical\n", + "\n", + "stfncnstt=5.67*math.pow(10,(-8)); # [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "p = 2770; #[kg/m^3] density of aluminium\n", + "c = 875; #[J/kg.K] Specific Heat\n", + "#calculations and results\n", + "\n", + "#To assess the validity of the lumped capacitance approximation\n", + "Bih = ho*L/k;\n", + "Bic = hc*L/k;\n", + "print '%s %.1f %s %.1f' %(\"\\n Lumped capacitance approximation is valid as Bih =\",Bih,\" and Bic = \",Bic);\n", + "\n", + "#Eqn 1.9\n", + "hro = e*stfncnstt*(Tc+Tsurro)*(Tc*Tc+Tsurro*Tsurro);\n", + "hrc = e*stfncnstt*(Tc+Tsurrc)*(Tc*Tc+Tsurrc*Tsurrc);\n", + "print '%s %.1f %s %.1f %s' %(\"\\n Since The values of hro = %\",hro,\" and hrc =\",hrc,\"are comparable to those of ho and hc \");\n", + "\n", + "# Integration of the differential equation\n", + "# dy/dt=-1/(p*c*L)*[ho*(y-Tsurro)+e*stfncnstt*(y^4 - Tsurro^4)] , y(0)=Ti, and finds the minimum time t such that y(t)=150 degC\n", + "te = 423.07\n", + "tc=123.07\n", + "#From equation 5.15 and solving the two step process using integration\n", + "Ty0=Ti;\n", + "tt=564\n", + "# solution of integration of the differential equation\n", + "# dy/dt=-1/(p*c*L)*[hc*(y-Tsurrc)+e*stfncnstt*(y^4 - Tsurrc^4)] , y(rd(1))=Ty(43), and finds the minimum time t such that y(t)=37 degC=Tit\n", + "t20=te;\n", + "print '%s %d %s' %(\"\\n\\n Total time for the two-step process is t =\",tt+te,\"s\"); \n", + "print '%s %d %s %d %s' %(\"with intermediate times of tc =\",tc,\" s and te =\",te,\"s.\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Lumped capacitance approximation is valid as Bih = 0.0 and Bic = 0.0\n", + "\n", + " Since The values of hro = % 15.0 and hrc = 8.8 are comparable to those of ho and hc \n", + "\n", + "\n", + " Total time for the two-step process is t = 987 s\n", + "with intermediate times of tc = 123 s and te = 423 s.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4 Page 278" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Radial System with Convection\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "h = 500; \t\t\t#[W/m^2.K] Heat Convection coefficientat inner surface\n", + "k = 63.9; \t\t\t#[W/m.K] Thermal Conductivity \n", + "rho = 7832; \t\t\t#[kg/m^3] Density\n", + "c = 434; \t\t#[J/kg.K] Specific Heat\n", + "alpha = 18.8*math.pow(10,-6);#[m^2/s]\n", + "L = 40.*math.pow(10,-3);\t#[m] Metre\n", + "Ti = -20+273; \t\t#[K] Initial Temp\n", + "Tsurr = 60+273; \t\t#[K] Temp of oil\n", + "t = 8*60 ; \t\t#[sec] time\n", + "D = 1 ; \t\t\t\t#[m] Diameter of pipe\n", + "#calculations\n", + "\n", + "#Using eqn 5.10 and 5.12\n", + "Bi = h*L/k;\n", + "Fo = alpha*t/(L*L);\n", + "\n", + "#From Table 5.1 at this Bi\n", + "C1 = 1.047;\n", + "eta = 0.531;\n", + "theta0=C1*math.exp(-eta*eta*Fo);\n", + "T = Tsurr+theta0*(Ti-Tsurr);\n", + "\n", + "#Using eqn 5.40b\n", + "x=1;\n", + "theta = theta0*math.cos(eta);\n", + "Tl = Tsurr + (Ti-Tsurr)*theta;\n", + "q = h*(Tl - Tsurr);\n", + "\n", + "#Using Eqn 5.44, 5.46 and Vol per unit length V = pi*D*L\n", + "Q = (1-(math.sin(eta)/eta)*theta0)*rho*c*math.pi*D*L*(Ti-Tsurr);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n (a) After 8 min Biot number =\",Bi,\" and\");\t \n", + "print '%s %.2f' %(\"\\n \\n Fourier Numer =\",Fo)\n", + "print '%s %.2f %s' %(\"\\n\\n (b) Temperature of exterior pipe surface after 8 min = \",T-273,\"degC\")\n", + "print '%s %.2f %s' %(\"\\n\\n (c) Heat Flux to the wall at 8 min = \",q,\"W/m^2\")\n", + "print '%s %.2e %s' %(\"\\n\\n (d) Energy transferred to pipe per unit length after 8 min =\",Q,\" J/m\")\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) After 8 min Biot number = 0.31 and\n", + "\n", + " \n", + " Fourier Numer = 5.64\n", + "\n", + "\n", + " (b) Temperature of exterior pipe surface after 8 min = 42.92 degC\n", + "\n", + "\n", + " (c) Heat Flux to the wall at 8 min = -7362.49 W/m^2\n", + "\n", + "\n", + " (d) Energy transferred to pipe per unit length after 8 min = -2.72e+07 J/m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5 Page 280 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Two step cooling process of Sphere\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "ha = 10.; \t\t#[W/m^2.K] Heat Convection coefficientat air\n", + "hw = 6000.; \t#[W/m^2.K] Heat Convection coefficientat water\n", + "k = 20.; \t\t#[W/m.K] Thermal Conductivity \n", + "rho = 3000.; \t\t#[kg/m^3] Density\n", + "c = 1000.; \t#[J/kg.K] Specific Heat\n", + "alpha = 6.66*math.pow(10,-6); #[m^2/s]\n", + "Tiw = 335+273.; \t#[K] Initial Temp\n", + "Tia = 400+273.; \t#[K] Initial Temp\n", + "Tsurr = 20+273.; \t#[K] Temp of surrounding\n", + "T = 50+273.; \t\t#[K] Temp of center\n", + "ro = .005; \t\t#[m] radius of sphere\n", + "#calculations\n", + "\n", + "#Using eqn 5.10 and\n", + "Lc = ro/3.;\n", + "Bi = ha*Lc/k;\n", + "ta = rho*ro*c*2.30*(math.log10((Tia-Tsurr)/(Tiw-Tsurr)))/(3*ha);\n", + "\n", + "#From Table 5.1 at this Bi\n", + "C1 = 1.367;\n", + "eta = 1.8;\n", + "Fo = -1*2.30*math.log10((T-Tsurr)/((Tiw-Tsurr)*C1))/(eta*eta);\n", + "\n", + "tw = Fo*ro*ro/alpha;\n", + "#results\n", + "\n", + "print '%s %.1f %s' %(\"\\n (a) Time required to accomplish desired cooling in air ta =\",ta,\" s\")\n", + "print '%s %.2f %s' %(\"\\n\\n (b) Time required to accomplish desired cooling in water bath tw =\",tw,\"s\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Time required to accomplish desired cooling in air ta = 93.7 s\n", + "\n", + "\n", + " (b) Time required to accomplish desired cooling in water bath tw = 3.08 s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6 Page 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Burial Depth\n", + "\n", + "#Operating Conditions\n", + "import math\n", + "k = .52; \t\t#[W/m.K] Thermal Conductivity \n", + "rho = 2050; \t\t#[kg/m^3] Density\n", + "c = 1840; \t#[J/kg.K] Specific Heat\n", + "Ti = 20+273.; \t#[K] Initial Temp\n", + "Ts = -15+273.; \t\t#[K] Temp of surrounding\n", + "T = 0+273.; \t\t#[K] Temp at depth xm after 60 days\n", + "t = 60*24*3600.; #[sec] time perod\n", + "#calculations\n", + "\n", + "alpha = k/(rho*c); #[m^2/s]\n", + "#Using eqn 5.57\n", + "xm = math.erfc((T-Ts)/(Ti-Ts)) *2*math.pow((alpha*t),.5);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n Depth at which after 60 days soil freeze =\",xm,\" m\");\n", + "print '%s' %(\"The answer given in textbook is wrong. Please check using a calculator.\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Depth at which after 60 days soil freeze = 0.92 m\n", + "The answer given in textbook is wrong. Please check using a calculator.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7 Page 293 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Spherical Tumor\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "k = .5; \t\t#[W/m.K] Thermal Conductivity Healthy Tissue\n", + "kappa = .02*math.pow(10,3);#[m] extinction coefficient\n", + "p = .05; \t# reflectivity of skin\n", + "D = .005; \t#[m] Laser beam Dia\n", + "rho = 989.1 ; \t#[kg/m^3] Density\n", + "c = 4180 ; \t#[J/kg.K] Specific Heat\n", + "Tb = 37+273; \t#[K] Temp of healthy tissue\n", + "Dt = .003 ; \t#[m] Dia of tissue\n", + "d = .02 ; \t#[m] depth beneath the skin\n", + "Ttss = 55+273 ; \t#[K] Steady State Temperature\n", + "Tb = 37+273 ; \t#[K] Body Temperature\n", + "Tt = 52+273 ; \t#[K] Tissue Temperature\n", + "q = .170 ; \t#[W] \n", + "#calculations\n", + "\n", + "#Case 12 of Table 4.1\n", + "q = 2*math.pi*k*Dt*(Ttss-Tb);\n", + "\n", + "#Energy Balancing\n", + "P = q*(D*D)*math.exp(kappa*d)/((1-p)*Dt*Dt);\n", + "\n", + "#Using Eqn 5.14\n", + "t = rho*(math.pi*Dt*Dt*Dt/6.)*c*(Tt-Tb)/q;\n", + "\n", + "alpha=k/(rho*c);\n", + "Fo = 10.3;\n", + "#Using Eqn 5.68\n", + "t2 = Fo*Dt*Dt/(4*alpha);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n (a) Heat transferred from the tumor to maintain its surface temperature at Ttss = 55 degC is \",q,\"W\"); \n", + "print '%s %.2f %s' %(\"\\n\\n (b) Laser power needed to sustain the tumor surface temperautre at Ttss = 55 degC is\", P,\"W\")\n", + "print '%s %.2f %s' %(\" \\n\\n (c) Time for tumor to reach Tt = 52 degC when heat transfer to the surrounding tissue is neglected is\",t,\"sec\")\n", + "print '%s %.2f %s' %(\" \\n\\n (d) Time for tumor to reach Tt = 52 degC when Heat transfer to thesurrounding tissue is considered and teh thermal mass of tumor is neglected is\",t2,\"sec\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Heat transferred from the tumor to maintain its surface temperature at Ttss = 55 degC is 0.17 W\n", + "\n", + "\n", + " (b) Laser power needed to sustain the tumor surface temperautre at Ttss = 55 degC is 0.74 W\n", + " \n", + "\n", + " (c) Time for tumor to reach Tt = 52 degC when heat transfer to the surrounding tissue is neglected is 5.17 sec\n", + " \n", + "\n", + " (d) Time for tumor to reach Tt = 52 degC when Heat transfer to thesurrounding tissue is considered and teh thermal mass of tumor is neglected is 191.63 sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.8 Page 300" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Thermal Conductivity of Nanostructured material\n", + "import numpy\n", + "import math\n", + "from numpy import linalg\n", + "#Operating Conditions\n", + "\n", + "k = 1.11 ; \t\t\t#[W/m.K] Thermal Conductivity \n", + "rho = 3100; \t\t\t#[kg/m^3] Density\n", + "c = 820 ; \t\t\t#[J/kg.K] Specific Heat\n", + "#Dimensions of Strip\n", + "w = 100*math.pow(10,-6);\t#[m] Width\n", + "L = .0035 ; \t\t\t#[m] Long\n", + "d = 3000*math.pow(10,-10);\t#[m] Thickness\n", + "delq = 3.5*math.pow(10,-3);\t#[W] heating Rate \n", + "delT1 =1.37 ; \t\t\t#[K] Temperature 1\n", + "f1 = 2*math.pi ; \t\t\t#[rad/s] Frequency 1\n", + "delT2 =.71 ; \t\t\t#[K] Temperature 2\n", + "f2 = 200*math.pi; \t\t#[rad/s] Frequency 2\n", + "#calculations\n", + "\n", + "A = ([[delT1, -delq/(L*math.pi)],\n", + " [delT2, -delq/(L*math.pi)]]) ;\n", + "\n", + "C= ([[delq*-2.30*math.log10(f1/2.)/(2*L*math.pi)],\n", + " [delq*-2.30*math.log10(f2/2.)/(2*L*math.pi)]]) ;\n", + "\n", + "B = numpy.linalg.solve (A,C);\n", + "\n", + "alpha = k/(rho*c);\n", + "delp = ([math.pow((alpha/f1),.5), math.pow((alpha/f2),.5)]);\n", + "#results\n", + "\n", + "print '%s %.2f %s %.2f %s' %(\"\\n C2 = \",B[1],\"k =\",B[0],\" W/m.K \")\n", + "print '%s %.2e %s %.2e %s'\t%(\"\\n\\n Thermal Penetration depths are\",delp[0],\" m and \",delp[1],\"m at frequency 2*pi rad/s and 200*pi rad/s\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " C2 = 5.35 k = 1.11 W/m.K \n", + "\n", + "\n", + " Thermal Penetration depths are 2.64e-04 m and 2.64e-05 m at frequency 2*pi rad/s and 200*pi rad/s\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9 Page 305 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature distribution 1.5s after a change in operating power\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "L = .01; #[m] Metre\n", + "Tsurr = 250+273.; #[K] Temperature\n", + "h = 1100; #[W/m^2.K] Heat Convective Coefficient\n", + "q1 = math.pow(10,7); #[W/m^3] Volumetric Rate\n", + "q2 = 2*math.pow(10,7); #[W/m^3] Volumetric Rate\n", + "k = 30; #[W/m.K] Conductivity\n", + "a = 5*math.pow(10,-6); #[m^2/s]\n", + "#calculations\n", + "\n", + "delx = L/5.; #Space increment for numerical solution\n", + "Bi = h*delx/k; #Biot Number\n", + "#By using stability criterion for Fourier Number\n", + "Fo = 1/(2*(1+Bi));\n", + "#By definition\n", + "t = Fo*delx*delx/a;\n", + "#results\n", + "\n", + "print '%s %.3f %s' %('\\n As per stability criterion delt =',t,' s, hence setting stability limit as .3 s.')\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As per stability criterion delt = 0.373 s, hence setting stability limit as .3 s.\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10 Page 311" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Using Explicit Finite Difference method, determine temperatures at the surface and 150 mm from the surface after an elapsed time of 2 min\n", + "# Repeat the calculations using the Implicit Finite Difference Method\n", + "# Determine the same temperatures analytically\n", + "import math\n", + "#Operating Conditions\n", + "a\n", + "delx = .075; #[m] Metre\n", + "T = 20+273.; #[K] Temperature\n", + "q = 3*math.pow(10,5); #[W/m^3] Volumetric Rate\n", + "\n", + "#From Table A.1 copper 300 K\n", + "k = 401; #[W/m.K] Conductivity\n", + "a = 117*math.pow(10,-6); #[m^2/s]\n", + "#calculations and results\n", + "\n", + "#By using stability criterion reducing further Fourier Number\n", + "Fo = 1./2.;\n", + "#By definition\n", + "delt = Fo*delx*delx/a;\n", + "#From calculations,\n", + "T11=125.19\n", + "T12=48.1\n", + "print '%s %.2f %s %.1f %s' %('\\n Hence after 2 min, the surface and the desirde interior temperature T0 =',T11,' degC and T2 =',T12,'degC');\n", + "\n", + "#By using stability criterion reducing further Fourier Number\n", + "Fo = 1/4;\n", + "#By definition\n", + "delt = Fo*delx*delx/a;\n", + "#From calculations\n", + "T21=118.86 \n", + "T22=44.4\n", + "print '%s %.2f %s %.1f %s' %('\\n Hence after 2 min, the surface and the desirde interior temperature T0 = ',T21,'degC and T2 =',T22,'degC')\n", + "\n", + "#(c) Approximating slab as semi-infinte medium\n", + "Tc = T -273 + 2*q*math.pow((a*t/math.pi),.5) /k;\n", + "t=120. #s\n", + "#At interior point x=0.15 m\n", + "x =.15; #[metre]\n", + "#Analytical Expression\n", + "Tc2 = T -273 + 2*q*math.pow((a*t/math.pi),.5) /k*math.exp(-x*x/(4*a*t))-q*x/k*(1-math.erf(.15/(2*math.sqrt(a*t))));\n", + "\n", + "print '%s %.1f %s' %(' \\n\\n (c) Approximating slab as a semi infinte medium, Analytical epression yields \\n At surface after 120 seconds = ,',Tc,'degC')\n", + "print '%s %.1f %s' %('\\n At x=.15 m after 120 seconds = ',Tc2,'degC');\n", + "#END\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Hence after 2 min, the surface and the desirde interior temperature T0 = 125.19 degC and T2 = 48.1 degC\n", + "\n", + " Hence after 2 min, the surface and the desirde interior temperature T0 = 118.86 degC and T2 = 44.4 degC\n", + " \n", + "\n", + " (c) Approximating slab as a semi infinte medium, Analytical epression yields \n", + " At surface after 120 seconds = , 25.6 degC\n", + "\n", + " At x=.15 m after 120 seconds = 45.4 degC\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_6.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_6.ipynb new file mode 100644 index 00000000..a8c5a4a2 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_6.ipynb @@ -0,0 +1,342 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Introduction to Convection" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.2 Page 356 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Napthalene Sublimation rate per unit length\n", + "import math\n", + "#Operating Conditions\n", + "\n", + "h = .05; \t\t\t#[W/m^2.K] Heat Convection coefficient\n", + "D = .02; \t\t\t#[m] Diameter of cylinder\n", + "Cas = 5*math.pow(10,-6); #[kmol/m^3] Surface molar Conc\n", + "Casurr = 0; \t\t\t#[kmol/m^3] Surrounding molar Conc\n", + "Ma = 128; \t\t\t#[Kg/kmol] Molecular weight\n", + "#calculations\n", + "#From Eqn 6.15\n", + "Na = h*(math.pi*D)*(Cas-Casurr);\n", + "na = Ma*Na;\n", + "#results\n", + "print '%s %.2e %s' %(\"\\n\\n Mass sublimation Rate is =\",na,\" kg/s.m \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Mass sublimation Rate is = 2.01e-06 kg/s.m \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.3 Page 357" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Convection Mass Transfer coefficient \n", + "import math\n", + "#Operating Conditions\n", + "\n", + "Dab = .288*math.pow(10,-4); \t#[m^2/s] Table A.8 water vapor-air (319K)\n", + "pas = .1; \t\t\t\t#[atm] Partial pressure at surface\n", + "pasurr = .02; \t\t\t#[atm] Partial pressure at infinity\n", + "y0 = .003; \t\t\t\t#[m] Tangent at y = 0 intercepts y axis at 3 mm\n", + "#calculations\n", + "#From Measured Vapor Pressure Distribution\n", + "delp = (0 - pas)/(y0 - 0); #[atm/m]\n", + "hmx = -Dab*delp/(pas - pasurr); #[m/s] \n", + "#results\n", + "print '%s %.4f %s' %(\"\\n\\n Convection Mass Transfer coefficient at prescribed location =\",hmx,\" m/s\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Convection Mass Transfer coefficient at prescribed location = 0.0120 m/s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4 Page 362 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Convection Mass Transfer coefficient \n", + "import math\n", + "#Operating Conditions\n", + "v = 1; \t\t\t\t#[m/s] Velocity of water\n", + "L = 0.6; \t\t\t\t#[m] Plate length\n", + "Tw1 = 300.; \t\t\t\t#[K]\n", + "Tw2 = 350.; \t\t\t\t#[K]\n", + "#Coefficients [W/m^1.5 . K]\n", + "Clam1 = 395;\n", + "Cturb1 = 2330;\n", + "Clam2 = 477;\n", + "Cturb2 = 3600;\n", + "\n", + "#Water Properties at T = 300K\n", + "p1 = 997; \t\t\t\t#[kg/m^3] Density\n", + "u1 = 855*math.pow(10,-6); #[N.s/m^2] Viscosity\n", + "#Water Properties at T = 350K\n", + "p2 = 974; \t\t\t\t#[kg/m^3] Density\n", + "u2 = 365*math.pow(10,-6); #[N.s/m^2] Viscosity\n", + "\n", + "\n", + "Rec = 5*math.pow(10,5); #Transititon Reynolds Number\n", + "xc1 = Rec*u1/(p1*v); \t\t#[m]Transition length at 300K\n", + "xc2 = Rec*u2/(p2*v); \t\t#[m]Transition length at 350K\n", + "#calculations\n", + "#Integrating eqn 6.14\n", + "#At 300 K\n", + "h1 = (Clam1*math.pow(xc1,.5) /.5 + Cturb1*(math.pow(L,.8)-math.pow(xc1,.8))/.8)/L;\n", + "\n", + "#At 350 K\n", + "h2 = (Clam2*math.pow(xc2,.5) /.5 + Cturb2*(math.pow(L,.8)-math.pow(xc2,.8))/.8)/L;\n", + "#results\n", + "print '%s %.2f %s %.2f %s' %(\"\\n\\n Average Convection Coefficient over the entire plate for the two temperatures at 300K =\",h1,\" W/m^2.K and at 350K =\",h2,\" W/m^2.K\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " Average Convection Coefficient over the entire plate for the two temperatures at 300K = 1622.45 W/m^2.K and at 350K = 3707.93 W/m^2.K\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5 Page 372" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat Flux to blade when surface temp is reduced\n", + "# Heat flux to a larger turbine blade\n", + "\n", + "#Operating Conditions\n", + "v = 160; \t\t\t\t#[m/s] Velocity of air\n", + "L = 0.04; \t\t\t\t\t#[m] Blade length\n", + "Tsurr = 1150+273.; \t\t\t#[K]\n", + "Ts = 800+273.; \t\t\t\t#[K] Surface Temp\n", + "q = 95000; \t\t\t\t#[W/m^2] Original heat flux\n", + "#calculations\n", + "#Case 1\n", + "Ts1 = 700+273.; \t \t\t\t#[K] Surface Temp\n", + "q1 = q*(Tsurr-Ts1)/(Tsurr-Ts);\n", + "\n", + "#Case 2\n", + "L2 = .08; \t\t\t#[m] Length\n", + "q2 = q*L/L2; \t\t\t#[W/m^2] Heat flux\n", + "#results\n", + "\n", + "print '%s %d %s' %(\"\\n\\n (a) Heat Flux to blade when surface temp is reduced =\",q1/1000. ,\" KW/m^2\") \n", + "print '%s %.2f %s' %(\"\\n (b) Heat flux to a larger turbine blade = \",q2/1000. ,\"KW/m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " (a) Heat Flux to blade when surface temp is reduced = 122 KW/m^2\n", + "\n", + " (b) Heat flux to a larger turbine blade = 47.50 KW/m^2\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.6 Page 379" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Water vapor conc and flux associated with the same location on larger surface of the same shape\n", + "import math\n", + "#Operating Conditions\n", + "v = 100; \t\t\t#[m/s] Velocity of air\n", + "Tsurr = 20+273.; \t\t#[K] Surrounding Air Temperature\n", + "L1 = 1; \t\t\t\t#[m] solid length\n", + "Ts = 80+273.; \t\t\t#[K] Surface Temp\n", + "qx = 10000; \t\t\t#[W/m^2] heat flux at a point x\n", + "Txy = 60+273.; \t\t#[K] Temp in boundary layer above the point\n", + "\n", + "#Table A.4 Air Properties at T = 323K\n", + "v = 18.2*math.pow(10,-6); #[m^2/s] Viscosity\n", + "k = 28*math.pow(10,-3); \t#[W/m.K] Conductivity\n", + "Pr = 0.7; \t\t\t#Prandttl Number\n", + "#Table A.6 Saturated Water Vapor at T = 323K\n", + "pasat = 0.082; \t\t\t#[kg/m^3]\n", + "Ma = 18; \t\t\t#[kg/kmol] Molecular mass of water vapor\n", + "#Table A.8 Water Vapor-air at T = 323K\n", + "Dab = .26*math.pow(10,-4);\t#[m^2/s]\n", + "#calculations\n", + "#Case 1\n", + "Casurr = 0;\n", + "Cas = pasat/Ma; \t\t#[kmol/m^3] Molar conc of saturated water vapor at surface\n", + "Caxy = Cas + (Casurr - Cas)*(Txy - Ts)/(Tsurr - Ts);\n", + "\n", + "#Case 2\n", + "L2 = 2.;\n", + "hm = L1/L2 * Dab/k * qx/(Ts-Tsurr);\n", + "Na = hm*(Cas - Casurr);\n", + "#results\n", + "\n", + "print '%s %.4f %s' %(\"\\n (a) Water vapor Concentration above the point =\",Caxy,\"Kmol/m^3 \\n\") \n", + "print '%s %.2e %s' %(\"(b) Molar flux to a larger surface = \",Na,\"Kmol/s.m^2\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Water vapor Concentration above the point = 0.0030 Kmol/m^3 \n", + "\n", + "(b) Molar flux to a larger surface = 3.53e-04 Kmol/s.m^2\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.7 Page 383 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Steady State Temperature of Beverage\n", + "import math\n", + "#Operating Conditions\n", + "Tsurr = 40+273.; \t\t#[K] Surrounding Air Temperature\n", + "#Volatile Wetting Agent A\n", + "hfg = 100; \t\t\t#[kJ/kg]\n", + "Ma = 200; \t\t\t#[kg/kmol] Molecular mass\n", + "pasat = 5000; \t\t\t#[N/m^2] Saturate pressure\n", + "Dab = .2*math.pow(10,-4); #[m^2/s] Diffusion coefficient\n", + "\n", + "#Table A.4 Air Properties at T = 300K\n", + "p = 1.16; \t#[kg/m^3] Density\n", + "cp = 1.007; \t#[kJ/kg.K] Specific Heat\n", + "alpha = 22.5*math.pow(10,-6)#[m^2/s] \n", + "R = 8.314; \t#[kJ/kmol] Universal Gas Constt\n", + "#calculations\n", + "#Applying Eqn 6.65 and setting pasurr = 0\n", + "# Ts^2 - Tsurr*Ts + B = 0 , where the coefficient B is\n", + "B = Ma*hfg*pasat*math.pow(10,-3) /(R*p*cp*math.pow((alpha/Dab),(2./3.)));\n", + "Ts = (Tsurr + math.sqrt(Tsurr*Tsurr - 4*B))/2. ;\n", + "#results\n", + "print '%s %.1f %s' %(\"\\n Steady State Surface Temperature of Beverage =\",Ts-273.,\"degC\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Steady State Surface Temperature of Beverage = 5.9 degC\n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_7.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_7.ipynb new file mode 100644 index 00000000..f8aa1a6f --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_7.ipynb @@ -0,0 +1,506 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "External Flow" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1 Page 415" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Cooling rate per Unit Width of the Plate\n", + "import math\n", + "#Operating Conditions\n", + "v = 10; \t\t\t\t\t\t\t#[m/s] Air velocity\n", + "p = 6000; \t\t\t\t\t\t\t#[N/m^2] Air pressure\n", + "Tsurr = 300+273.; \t\t\t\t\t\t#[K] Surrounding Air Temperature\n", + "L = .5; \t\t\t\t\t\t\t#[m] Length of plate\n", + "Ts = 27+273.; \t\t\t\t\t\t#[K] Surface Temp\n", + "\n", + "#Table A.4 Air Properties at T = 437K \n", + "uv = 30.84*math.pow(10,-6)*(101325./6000.); #[m^2/s] Kinematic Viscosity at P = 6000 N/m^2\n", + "k = 36.4*math.pow(10,-3); \t\t#[W/m.K] Thermal COnductivity\n", + "Pr = .687; \t\t\t\t\t#Prandtl number\n", + "#calculations\n", + "Re = v*L/uv; \t\t\t\t\t\t#Reynolds number\n", + "print '%s %d %s' %(\"\\n Since Reynolds Number is\",Re,\", The flow is laminar over the entire plate\");\n", + "\n", + "#Correlation 7.30 \n", + "NuL = .664*math.pow(Re,.5)*math.pow(Pr,0.3334); #Nusselt Number over entire plate length\n", + "hL = NuL*k/L; # Average Convection Coefficient\n", + "#Required cooling rate per unit width of plate\n", + "q = hL*L*(Tsurr-Ts);\n", + "#results\n", + "print '%s %d %s' %(\"\\n\\n Required cooling rate per unit width of plate =\",q,\" W/m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Since Reynolds Number is 9600 , The flow is laminar over the entire plate\n", + "\n", + "\n", + " Required cooling rate per unit width of plate = 570 W/m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2 Page 417" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Maximum Heater Power Requirement\n", + "import math\n", + "#Operating Conditions\n", + "v = 60; \t\t\t#[m/s] Air velocity\n", + "Tsurr = 25+273.; \t\t#[K] Surrounding Air Temperature\n", + "w = 1; \t\t\t#[m] Width of plate\n", + "L = .05; \t\t\t#[m] Length of stripper\n", + "Ts = 230+273.; \t\t#[K] Surface Temp\n", + "\n", + "#Table A.4 Air Properties at T = 400K \n", + "uv = 26.41*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k = .0338; \t#[W/m.K] Thermal COnductivity\n", + "Pr = .690; \t#Prandtl number\n", + "#calculations\n", + "Re = v*L/uv; \t\t#Reynolds number\n", + "\n", + "Rexc = 5*math.pow(10,5); #Transition Reynolds Number\n", + "xc = uv*Rexc/v; \t\t#Transition Length\n", + "#results\n", + "print '%s %d' %(\"\\n Reynolds Number based on length L = .05m is \",Re)\n", + "print '%s %.2f %s' %(\"\\n And the transition occur at xc =\",xc,\" m ie fifth plate\");\n", + "\n", + "#For first heater\n", + "#Correlation 7.30 \n", + "Nu1 = .664*math.pow(Re,0.5)*math.pow(Pr,0.3334); #Nusselt Number \n", + "h1 = Nu1*k/L; # Average Convection Coefficient\n", + "q1 = h1*(L*w)*(Ts-Tsurr); # Convective Heat exchange\n", + "\n", + "#For first four heaters\n", + "Re4 = 4*Re;\n", + "L4 = 4*L;\n", + "Nu4 = .664*math.pow(Re4,0.5)*math.pow(Pr,0.3334); #Nusselt Number \n", + "h4 = Nu4*k/L4; # Average Convection Coefficient\n", + "print(h4)\n", + "#For Fifth heater from Eqn 7.38\n", + "Re5 = 5*Re;\n", + "A = 871; \n", + "L5 = 5*L;\n", + "Nu5 = (.037*math.pow(Re5,.8)-A)*math.pow(Pr,.3334); #Nusselt Number \n", + "h5 = Nu5*k/L5; # Average Convection Coefficient\n", + "q5 = (h5*L5-h4*L4)*w*(Ts-Tsurr);\n", + "\n", + "#For Sixth heater from Eqn 7.38\n", + "Re6 = 6*Re;\n", + "L6 = 6*L;\n", + "Nu6 = (.037*math.pow(Re6,.8)-A)*math.pow(Pr,.3334) ; #Nusselt Number \n", + "h6 = Nu6*k/L6 ; # Average Convection Coefficient\n", + "q6 = (h6*L6-h5*L5)*w*(Ts-Tsurr);\n", + "\n", + "print '%s %d %s %d %s %d %s' %(\"\\n\\n Power requirement are \\n qconv1 = \",q1,\"W qconv5 =\",q5,\" W qconv6 = \",q6,\"W\");\n", + "print '%s %d %s %d %s %d %s' %(\"\\n Hence\",q6,\">\",q1,\" >\",q5,\"and the sixth plate has largest power requirement\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Reynolds Number based on length L = .05m is 113593\n", + "\n", + " And the transition occur at xc = 0.22 m ie fifth plate\n", + "66.8395462952\n", + "\n", + "\n", + " Power requirement are \n", + " qconv1 = 1370 W qconv5 = 1017 W qconv6 = 1427 W\n", + "\n", + " Hence 1427 > 1370 > 1017 and the sixth plate has largest power requirement\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3 Page 420" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Daily Water Loss\n", + "import math\n", + "#Operating Conditions\n", + "v = 2; \t\t\t#[m/s] Air velocity\n", + "Tsurr = 25+273.; \t\t#[K] Surrounding Air Temperature\n", + "H = .5; \t\t\t# Humidity\n", + "w = 6; \t\t\t#[m] Width of pool\n", + "L1 = 12; \t\t\t#[m] Length of pool\n", + "e = 1.5; \t\t\t#[m] Deck Wide\n", + "Ts = 25+273.; \t\t\t#[K] Surface Temp of water\n", + "#calculations\n", + "#Table A.4 Air Properties at T = 298K \n", + "uv = 15.7*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "#Table A.8 Water vapor-Air Properties at T = 298K \n", + "Dab = .26*math.pow(10,-4); \t#[m^2/s] Diffusion Coefficient\n", + "Sc = uv/Dab;\n", + "#Table A.6 Air Properties at T = 298K \n", + "rho = .0226; \t#[kg/m^3]\n", + "\n", + "L = L1+e;\n", + "Re = v*L/uv; \t\t#Reynolds number\n", + "\n", + "#Equation 7.41 yields\n", + "ShLe = .037*math.pow(Re,.8)*math.pow(Sc,.3334);\n", + "#Equation 7.44\n", + "p = 8.; #Turbulent Flow\n", + "ShL = (L/(L-e))*ShLe*math.pow((1-math.pow((e/L),((p+1)/(p+2)))),(p/(p+1)));\n", + "\n", + "hmL = ShL*(Dab/L);\n", + "n = hmL*(L1*w)*rho*(1-H);\n", + "#results\n", + "print '%s %.2e %s' %(\"\\n Reynolds Number is \",Re,\". Hence for turbulent Flow p = 8 in Equation 7.44.\")\n", + "print '%s %d %s' %(\"\\n Daily Water Loss due to evaporation is\",n*86400. ,\"kg/day\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Reynolds Number is 1.72e+06 . Hence for turbulent Flow p = 8 in Equation 7.44.\n", + "\n", + " Daily Water Loss due to evaporation is 406 kg/day\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4 Page 428" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Convection Coefficient associated with operating conditions\n", + "# Convection Coefficient from an appropriate correlation\n", + "import math\n", + "#Operating Conditions\n", + "v = 10; \t\t\t#[m/s] Air velocity\n", + "Tsurr = 26.2+273.; \t\t#[K] Surrounding Air Temperature\n", + "P = 46.; \t\t\t# [W] Power dissipation\n", + "L = .094; \t\t\t#[m] Length of cylinder\n", + "D = .0127; \t\t\t#[m] Diameter of cylinder\n", + "Ts = 128.4+273.; \t\t#[K] Surface Temp of water\n", + "q = 46.15*46; \t\t#[W] Actual power dissipation without the 15% loss\n", + "\n", + "#Table A.4 Air Properties at T = 300K \n", + "uv = 15.89*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k = 26.3*math.pow(10,-3); #[W/m.K] Thermal conductivity\n", + "Pr = .707; \t#Prandtl Number\n", + "#Table A.4 Air Properties at T = 401K \n", + "Prs = .690; \t#Prandtl Number\n", + "#calculations\n", + "A = math.pi*D*L;\n", + "h = q/(A*(Ts-Tsurr));\n", + "\n", + "Re = v*D/uv; \t\t#Reynolds number\n", + "#Using Zukauskas Relation, Equation 7.53\n", + "C = .26;\n", + "m = .6;\n", + "n = .37;\n", + "Nu = C*math.pow(Re,m)*math.pow(Pr,n)*math.pow((Pr/Prs),.25);\n", + "havg = Nu*k/D;\n", + "#results\n", + "print '%s %d %s' %(\"\\n Convection Coefficient associated with operating conditions\",h,\"W/m^2.K.\") \n", + "print '%s %d %s' %(\"\\n Reynolds Number is \",Re,\". Hence taking suitable corresponding data from Table 7.4.\")\n", + "print '%s %d %s' %(\"\\n Convection Coefficient from an appropriate Zukauskas correlation\",havg,\" W/m^2.K\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Convection Coefficient associated with operating conditions 5538 W/m^2.K.\n", + "\n", + " Reynolds Number is 7992 . Hence taking suitable corresponding data from Table 7.4.\n", + "\n", + " Convection Coefficient from an appropriate Zukauskas correlation 104 W/m^2.K\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5 page 431" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Convective Heat transfer to the canister and the additional heating needed\n", + "import math\n", + "#Operating Conditions\n", + "v = 23; \t\t\t\t#[m/s] Air velocity\n", + "Tsurr = 296.; \t\t\t\t#[K] Surrounding Air Temperature\n", + "L = .8; \t\t\t\t#[m] Length of cylinder\n", + "Di = .1; \t\t\t\t#[m] Diameter of cylinder\n", + "t = .005; \t\t\t\t\t#[m] Thickness of cylinder\n", + "\n", + "#Table A.4 Air Properties at T = 285K \n", + "uv = 14.56*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k = 25.2*math.pow(10,-3); #[W/m.K] Thermal conductivity\n", + "Pr = .712; \t\t#Prandtl Number\n", + "#Table A.1 AISI 316 Stainless steel Properties at T = 300K \n", + "kss = 13.4; \t\t#[W/m.K]Conductivity\n", + "\n", + "pH2 = 1.01; \t\t\t\t#[N]\n", + "Ti = -3550/(2.30*math.log10(pH2) - 12.9);\n", + "Eg = -(1.35*math.pow(10,-4))*(29.5*math.pow(10,6));\n", + "#calculations\n", + "Re = v*(Di+2*t)/uv; \t\t#Reynolds number\n", + "# Equation 7.54\n", + "Nu = .3+.62*math.pow(Re,.5)*math.pow(Pr,.3334) /math.pow((1+math.pow((.4/Pr),.6668)),.25) *math.pow(1+math.pow((Re/282000.),(5./8.)),.8);\n", + "h = Nu*k/(Di+2*t);\n", + "\n", + "qconv = (Tsurr-Ti)/((1/(math.pi*L*(Di+2*t)*h))+(2.30*math.log10((Di+2*t)/Di)/(2*math.pi*kss*L)));\n", + "\n", + "#results\n", + "print '%s %d %s' %(\"\\n Additional Thermal Energy must be supplied to canister to mainatin steady-state operating temperatue\",-qconv-Eg,\"W\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Additional Thermal Energy must be supplied to canister to mainatin steady-state operating temperatue 3581 W\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6 page 434" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Time required to cool from Ti = 75 degC to 35 degC\n", + "import math\n", + "#Operating Conditions\n", + "v = 10; \t\t\t#[m/s] Air velocity\n", + "Tsurr = 23+273.; \t\t#[K] Surrounding Air Temperature\n", + "D = .01; \t\t\t#[m] Diameter of sphere\n", + "Ti = 75+273.; \t\t#[K] Initial temp\n", + "Tt = 35+273.; \t\t#[K] Temperature after time t\n", + "p = 1; \t\t#[atm]\n", + "\n", + "#Table A.1 Copper at T = 328K \n", + "rho = 8933; \t\t\t#[kg/m^3] Density\n", + "k = 399; \t\t\t#[W/m.K] Conductivity\n", + "cp = 388; \t\t\t#[J/kg.K] specific \n", + "#Table A.4 Air Properties T = 296 K\n", + "u = 182.6*math.pow(10,-7); #[N.s/m^2] Viscosity\n", + "uv = 15.53*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k = 25.1*math.pow(10,-3); #[W/m.K] Thermal conductivity\n", + "Pr = .708; \t#Prandtl Number\n", + "#Table A.4 Air Properties T = 328 K\n", + "u2 = 197.8*math.pow(10,-7); #[N.s/m^2] Viscosity\n", + "#calculations\n", + "Re = v*D/uv; \t\t#Reynolds number\n", + "#Using Equation 7.56\n", + "Nu = 2+(0.4*math.pow(Re,.5) + 0.06*math.pow(Re,.668))*math.pow(Pr,.4)*math.pow((u/u2),.25);\n", + "h = Nu*k/D;\n", + "#From equation 5.4 and 5.5\n", + "t = rho*cp*D*2.30*math.log10((Ti-Tsurr)/(Tt-Tsurr))/(6*h);\n", + "#results\n", + "print '%s %.1f %s' %(\"\\nTime required for cooling is\",t,\"sec\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Time required for cooling is 71.2 sec\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7 Page 443" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Air side Convection coefficient and Heat rate\n", + "# pressure Drop\n", + "import math\n", + "#Operating Conditions\n", + "v = 6; \t\t\t#[m/s] Air velocity\n", + "Tsurr = 15+273.; \t \t\t#[K] Surrounding Air Temperature\n", + "D = .0164; \t\t\t#[m] Diameter of tube\n", + "Ts = 70+273.; \t\t#[K] Temp of tube\n", + "#Staggered arrangement dimensions\n", + "St = .0313; \t\t\t#[m]\n", + "Sl = .0343; \t\t\t#[m]\n", + "\n", + "#Table A.4 Air Properties T = 288 K\n", + "rho = 1.217; \t\t#[kg/m^3] Density\n", + "cp = 1007; \t\t#[J/kg.K] specific heat\n", + "uv = 14.82*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k = 25.3*math.pow(10,-3); #[W/m.K] Thermal conductivity\n", + "Pr = .71; \t#Prandtl Number\n", + "#Table A.4 Air Properties T = 343 K\n", + "Pr2 = .701; \t#Prandtl Number\n", + "#Table A.4 Air Properties T = 316 K\n", + "uv3 = 17.4*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "k3 = 27.4*math.pow(10,-3); #[W/m.K] Thermal conductivity\n", + "Pr3 = .705; \t#Prandtl Number\n", + "#calculations\n", + "Sd = math.pow((Sl*Sl + (St/2)*(St/2)),.5);\n", + "Vmax = St*v/(St-D);\n", + "\n", + "Re = Vmax*D/uv; \t\t#Reynolds number\n", + "\n", + "C = .35*math.pow((St/Sl),.2);\n", + "m = .6;\n", + "C2 = .95;\n", + "N = 56;\n", + "Nt = 8;\n", + "#Using Equation 7.64 & 7.65\n", + "Nu = C2*C*math.pow(Re,m)* math.pow(Pr,.36) *math.pow((Pr/Pr2),.25);\n", + "h = Nu*k/D;\n", + "\n", + "#From Eqnn 7.67\n", + "Tso = (Ts-Tsurr)*math.exp(-(math.pi*D*N*h)/(rho*v*Nt*St*cp));\n", + "Tlm = ((Ts-Tsurr) - Tso)/(2.30*math.log10((Ts-Tsurr)/Tso));\n", + "q = N*(h*math.pi*D*Tlm);\n", + "\n", + "Pt = St/D;\n", + "#From Fig 7.14\n", + "X = 1.04;\n", + "f = .35;\n", + "NL = 7;\n", + "press = NL*X*(rho*Vmax*Vmax/2.)*f;\n", + "#results\n", + "print '%s %.1f %s' %(\"\\n Air side Convection coefficient h = \",h,\"W/m^2.k\"); \n", + "print '%s %.1f %s' %(\"\\n and Heat rate q = \",q/1000. ,\" kW/m\"); \n", + "print '%s %.2e %s' %(\"\t\\n Pressure Drop =\",press/100000. ,\" bars\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Air side Convection coefficient h = 137.0 W/m^2.k\n", + "\n", + " and Heat rate q = 19.6 kW/m\n", + "\t\n", + " Pressure Drop = 2.46e-03 bars\n" + ] + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_8.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_8.ipynb new file mode 100644 index 00000000..fac7e1bf --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_8.ipynb @@ -0,0 +1,532 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Internal Flow" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.2 Page 499" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Length of tube needed to achieve the desired outlet temperature\n", + "#Local convection coefficient at the outlet\n", + "import math\n", + "#Operating Conditions\n", + "m = .1; #[kg/s] mass flow rate of water\n", + "Ti = 20+273.; #[K] Inlet temp\n", + "To = 60+273.; #[K] Outlet temperature\n", + "Di = .02; #[m] Inner Diameter\n", + "Do = .04; #[m] Outer Diameter\n", + "q = 1000000.;\t #[w/m^3] Heat generation Rate\n", + "Tsi = 70+273.; #[K] Inner Surface Temp\n", + "#Table A.4 Air Properties T = 313 K\n", + "cp = 4179; #[J/kg.K] specific heat\n", + "#calculations\n", + "L = 4*m*cp*(To-Ti)/(math.pi*(Do*Do-Di*Di)*q);\n", + "\n", + "#From Newtons Law of cooling, Equation 8.27, local heat convection coefficient is\n", + "h = q*(Do*Do-Di*Di)/(Di*4*(Tsi-To));\n", + "#results\n", + "print '%s %.1f %s' %(\"\\n Length of tube needed to achieve the desired outlet temperature = \",L,\"m \")\n", + "print '%s %.1f %s' %(\"\\n Local convection coefficient at the outlet =\",h,\" W/m^2.K\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Length of tube needed to achieve the desired outlet temperature = 17.7 m \n", + "\n", + " Local convection coefficient at the outlet = 1500.0 W/m^2.K\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.3 Page 503 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# average convection coefficient \n", + "import math\n", + "#Operating Conditions\n", + "m = .25; \t#[kg/s] mass flow rate of water\n", + "Ti = 15+273.; \t#[K] Inlet temp\n", + "To = 57+273.; \t#[K] Outlet temperature\n", + "D = .05; \t\t#[m] Diameter\n", + "L = 6; \t\t#[m] Length of tube\n", + "Ts = 100+273.; \t#[K] outer Surface Temp\n", + "\n", + "#Table A.4 Air Properties T = 309 K\n", + "cp = 4178; \t#[J/kg.K] specific heat\n", + "#calculations\n", + "Tlm = ((Ts-To)-(Ts-Ti))/(2.30*math.log10((Ts-To)/(Ts-Ti)));\n", + "\n", + "h = m*cp*(To-Ti)/(math.pi*D*L*Tlm);\n", + "#results\n", + "print '%s %d %s' %(\"\\n Average Heat transfer Convection Coefficient = \",h,\"W/m^2.K\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Average Heat transfer Convection Coefficient = 754 W/m^2.K\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.4 Page 506 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Length of tube for required heating\n", + "# Surface temperature Ts at outlet section\n", + "import math\n", + "#Operating Conditions\n", + "m = .01; #[kg/s] mass flow rate of water\n", + "Ti = 20+273; \t#[K] Inlet temp\n", + "To = 80+273; \t#[K] Outlet temperature\n", + "D = .06; \t#[m] Diameter\n", + "q = 2000; \t#[W/m^2] Heat flux to fluid\n", + "\n", + "#Table A.4 Air Properties T = 323 K\n", + "cp = 4178; #[J/kg.K] specific heat\n", + "#Table A.4 Air Properties T = 353 K\n", + "k = .670; #[W/m] Thermal Conductivity\n", + "u = 352*math.pow(10,-6);#[N.s/m^2] Viscosity\n", + "Pr = 2.2; #Prandtl Number\n", + "cp = 4178; #[J/kg.K] specific heat\n", + "#calculations\n", + "L = m*cp*(To-Ti)/(math.pi*D*q);\n", + "\n", + "#Using equation 8.6\n", + "Re = m*4/(math.pi*D*u);\n", + "print '%s %.2f %s' %(\"\\n (a) Length of tube for required heating =\",L,\"m\")\n", + "print '%s %.2f %s' %(\"\\n\\n (b)As Reynolds Number is\",Re,\".The flow is laminar.\");\n", + "\n", + "Nu = 4.364; #Nusselt Number\n", + "h = Nu*k/D; #[W/m^2.K] Heat convection Coefficient\n", + "\n", + "Ts = q/h+To; #[K]\n", + "#results\n", + "print '%s %.2f %s' %(\"\\n Surface Temperature at tube outlet = \",Ts-273,\"degC\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " (a) Length of tube for required heating = 6.65 m\n", + "\n", + "\n", + " (b)As Reynolds Number is 602.86 .The flow is laminar.\n", + "\n", + " Surface Temperature at tube outlet = 121.04 degC\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.5 Page 509 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Length of Blood Vessel\n", + "import math\n", + "#Operating Conditions\n", + "um1 = .13; #[m/s] Blood stream\n", + "um2 = 3*math.pow(10,-3); #[m/s] Blood stream\n", + "um3 = .7*math.pow(10,-3); #[m/s] Blood stream\n", + "D1 = .003; #[m] Diameter\n", + "D2 = .02*math.pow(10,-3); #[m] Diameter\n", + "D3 = .008*math.pow(10,-3); #[m] Diameter\n", + "Tlm = .05;\n", + "kf = .5; #[W/m.K] Conductivity\n", + "#Table A. Water Properties T = 310 K\n", + "rho = 993.; #[kg/m^3] density\n", + "cp = 4178.; #[J/kg.K] specific heat\n", + "u = 695*math.pow(10,-6); #[N.s/m^2] Viscosity\n", + "kb = .628; #[W/m.K] Conductivity\n", + "Pr = 4.62; #Prandtl Number\n", + "i=1.;\n", + "#calculations\n", + "#Using equation 8.6\n", + "Re1 = rho*um1*D1/u;\n", + "Nu = 4;\n", + "hb = Nu*kb/D1;\n", + "hf = kf/D1;\n", + "U1 = 1/(1/hb + 1/hf);\n", + "L1 = -rho*um1*D1/U1*cp*2.303*math.log10(Tlm)/4.;\n", + "xfdh1 = .05*Re1*D1;\n", + "xfdr1 = xfdh1*Pr;\n", + "\n", + "Re2 = rho*um2*D2/u;\n", + "Nu = 4;\n", + "hb = Nu*kb/D2;\n", + "hf = kf/D2;\n", + "U2 = 1/(1/hb + 1/hf);\n", + "L2 = -rho*um2*D2/U2*cp*2.303*math.log10(Tlm)/4.;\n", + "xfdh2 = .05*Re2*D2;\n", + "xfdr2 = xfdh2*Pr;\n", + "\n", + "Re3 = rho*um3*D3/u;\n", + "Nu = 4;\n", + "hb = Nu*kb/D3;\n", + "hf = kf/D3;\n", + "U3 = 1/(1/hb + 1/hf);\n", + "L3 = -rho*um3*D3/U3*cp*2.303*math.log10(Tlm)/4.;\n", + "xfdh3 = .05*Re3*D3;\n", + "xfdr3 = xfdh3*Pr;\n", + "#results\n", + "print ' %s' %(\"\\n Vessel Re U(W/m^2.K) L(m) xfdh(m) xfdr(m)\")\n", + "print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Artery \",Re1, U1 ,L1, xfdh1 , xfdr1)\n", + "print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Anteriole \",Re2, U2 ,L2, xfdh2 , xfdr2)\n", + "print '%s %.3f %d %.1e %.1e %.1e' %(\"\\n Capillary \",Re3,U3,L3,xfdh3,xfdr3);\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \n", + " Vessel Re U(W/m^2.K) L(m) xfdh(m) xfdr(m)\n", + "\n", + " Artery 557.223 138 8.7e+00 8.4e-02 3.9e-01\n", + "\n", + " Anteriole 0.086 20849 8.9e-06 8.6e-08 4.0e-07\n", + "\n", + " Capillary 0.008 52124 3.3e-07 3.2e-09 1.5e-08\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.6 Page 516 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat Loss from the Duct over the Length L, q \n", + "# Heat flux and suface temperature at x=L\n", + "import math\n", + "#Operating Conditions\n", + "m = .05; \t#[kg/s] mass flow rate of water\n", + "Ti = 103+273.; \t#[K] Inlet temp\n", + "To = 77+273.; \t\t#[K] Outlet temperature\n", + "D = .15; \t\t#[m] Diameter\n", + "L = 5; \t\t#[m] length\n", + "ho = 6.; \t\t#[W/m^2.K] Heat transfer convective coefficient\n", + "Tsurr = 0+273.; \t\t#[K] Temperature of surrounding\n", + "\n", + "#Table A.4 Air Properties T = 363 K\n", + "cp = 1010; \t#[J/kg.K] specific heat\n", + "#Table A.4 Air Properties T = 350 K\n", + "k = .030; \t#[W/m] Thermal Conductivity\n", + "u = 20.82/1000000.; \t#[N.s/m^2] Viscosity\n", + "Pr = .7; \t\t#Prandtl Number\n", + "#calculations and results\n", + "q = m*cp*(To-Ti);\n", + "\n", + "Re = m*4/(math.pi*D*u);\n", + "print '%s %d %s' %(\"\\n As Reynolds Number is\",Re,\". The flow is Turbulent.\");\n", + "\n", + "#Equation 8.6\n", + "n = 0.3;\n", + "Nu = .023*math.pow(Re,.8)*math.pow(Pr,.3);\n", + "h = Nu*k/D;\n", + "q2 = (To-Tsurr)/(1/h + 1/ho);\n", + "Ts = -q2/h+To;\n", + "\n", + "print '%s %d %s' %(\"\\n\\n Heat Loss from the Duct over the Length L, q =\",q,\" W \")\n", + "print '%s %.1f %s %.1f %s' %(\"\\n Heat flux and suface temperature at x=L is\",q2,\"W/m^2 &\",Ts-273,\"degC respectively\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As Reynolds Number is 20384 . The flow is Turbulent.\n", + "\n", + "\n", + " Heat Loss from the Duct over the Length L, q = -1313 W \n", + "\n", + " Heat flux and suface temperature at x=L is 304.3 W/m^2 & 50.7 degC respectively\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.7 Page 525" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Time needed to bring the reactants to within 1 degC of processing temperature\n", + "import math\n", + "#Operating Conditions\n", + "T1 = 125+273.; \t\t\t#[K] Chip Temperature 1\n", + "T2 = 25+273.; \t\t\t#[K] Chip Temperature 2\n", + "Ti = 5+273.; \t\t\t#[K] Inlet Temperature \n", + "D = .01; \t\t\t#[m] Diameter\n", + "L = .02; \t\t#[m] length\n", + "delP = 500*1000.; \t\t#[N/m^2] Pressure drop\n", + "#Dimensions\n", + "a = 40*math.pow(10,-6); \n", + "b = 160*math.pow(10,-6);\n", + "s = 40*math.pow(10,-6);\n", + "\n", + "#Table A.5 Ethylene Glycol Properties T = 288 K\n", + "rho = 1120.2; \t#[kg/m^3] Density\n", + "cp = 2359.; \t#[J/kg.K] Specific Heat\n", + "u = 2.82*math.pow(10,-2);\t#[N.s/m^2] Viscosity\n", + "k = 247*math.pow(10,-3); \t#[W/m.K] Thermal Conductivity\n", + "Pr = 269; \t\t#Prandtl number \n", + "#Table A.5 Ethylene Glycol Properties T = 338 K\n", + "rho2 = 1085.; \t#[kg/m^3] Density\n", + "cp2 = 2583.; \t#[J/kg.K] Specific Heat\n", + "u2 = .427*math.pow(10,-2);\t#[N.s/m^2] Viscosity\n", + "k2 = 261*math.pow(10,-3); \t#[W/m.K] Thermal Conductivity\n", + "Pr2 = 45.2; \t#Prandtl number\n", + "#calculations\n", + "P = 2*a+2*b; \t#Perimeter of microchannel\n", + "Dh = 4*a*b/P; \t#Hydraulic Diameter\n", + "\n", + "um2 = 2/73.*Dh*Dh/u2*delP/L;#[[m/s] Equation 8.22a\n", + "Re2 = um2*Dh*rho2/u2; #Reynolds Number\n", + "xfdh2 = .05*Dh*Re2; \t#[m] From Equation 8.3\n", + "xfdr2 = xfdh2*Pr2; \t#[m] From Equation 8.23\n", + "m2 = rho2*a*b*um2; \t#[kg/s]\n", + "Nu2 = 4.44; \t\t#Nusselt Number from Table 8.1\n", + "h2 = Nu2*k2/Dh; \t\t#[W/m^2.K] Convection Coeff\n", + "Tc2 = 124+273.; \t\t#[K]\n", + "xc2 = m2/P*cp2/h2*2.303*math.log10((T1-Ti)/(T1-Tc2));\n", + "tc2 = xc2/um2;\n", + "\n", + "um = 2/73.*Dh*Dh/u*delP/L; #[[m/s] Equation 8.22a\n", + "Re = um*Dh*rho/u; \t#Reynolds Number\n", + "xfdh = .05*Dh*Re; \t#[m] From Equation 8.3\n", + "xfdr = xfdh*Pr; \t\t#[m] From Equation 8.23\n", + "m = rho2*a*b*um; \t#[kg/s]\n", + "Nu = 4.44; \t\t#Nusselt Number from Table 8.1\n", + "h = Nu*k/Dh; \t\t#[W/m^2.K] Convection Coeff\n", + "Tc = 24+273.; \t\t#[K]\n", + "xc = m/P*cp/h*2.303*math.log10((T2-Ti)/(T2-Tc));\n", + "tc = xc/um;\n", + "\n", + "#results\n", + "print '%s %.1f %s' %(\"\\nTemp in case 2= \",T2-273,\" [degC]\")\n", + "print '%s %.1f %s' %(\"\\nTemp in case 1= \",T1-273,\" [degC]\")\n", + "print '%s %.3f %s' %(\"\\nFlow rate in case 2 = \",um2,\"[m/s]\")\n", + "print '%s %.3f %s' %(\"\\nFlow rate in case 1 = \",um,\"[m/s]\")\n", + "print '%s %.1f' %(\"\\nReynolds number in case 2 = \",Re2)\n", + "print '%s %.1f' %(\"\\nReynolds number in case 1 = \",Re)\n", + "print '%s %.1f' %(\"\\nHydrodynamic entrance Length [m] =\",xfdh)\n", + "print '%s %.1f' %(\"\\nHydrodynamic entrance Length in case 2 [m] =\",xfdh2) \n", + "print '%s %.1e' %(\"\\nThermal entrance Length [m] = \",xfdr)\n", + "print '%s %.1e' %(\"\\nThermal entrance Length in case 2 [m] = \",xfdr2)\n", + "print '%s %.2e' %(\"\\nMass Flow rate [kg/s] = \",m)\n", + "print '%s %.2e' %(\"\\nMass Flow rate in case 2 [kg/s] = \",m2)\n", + "print '%s %.2e' %(\"\\nConvective Coeff [W/m^2.K] = \",h)\n", + "print '%s %.2e' %(\"\\nConvective Coeff in case 2 [W/m^2.K] = \",h2)\n", + "print '%s %.2e' %(\"\\nTransition Length [m] = \",xc)\n", + "print '%s %.2e' %(\"\\nTransition Length in case 2 [m] = \",xc2)\n", + "print '%s %.3f' %(\"\\nRequired Time [s] = \",tc)\n", + "print '%s %.3f' %(\"\\nRequired Time in case 2 [s] = \",tc2)\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Temp in case 2= 25.0 [degC]\n", + "\n", + "Temp in case 1= 125.0 [degC]\n", + "\n", + "Flow rate in case 2 = 0.657 [m/s]\n", + "\n", + "Flow rate in case 1 = 0.099 [m/s]\n", + "\n", + "Reynolds number in case 2 = 10.7\n", + "\n", + "Reynolds number in case 1 = 0.3\n", + "\n", + "Hydrodynamic entrance Length [m] = 0.0\n", + "\n", + "Hydrodynamic entrance Length in case 2 [m] = 0.0\n", + "\n", + "Thermal entrance Length [m] = 2.2e-04\n", + "\n", + "Thermal entrance Length in case 2 [m] = 1.5e-03\n", + "\n", + "Mass Flow rate [kg/s] = 6.91e-07\n", + "\n", + "Mass Flow rate in case 2 [kg/s] = 4.56e-06\n", + "\n", + "Convective Coeff [W/m^2.K] = 1.71e+04\n", + "\n", + "Convective Coeff in case 2 [W/m^2.K] = 1.81e+04\n", + "\n", + "Transition Length [m] = 7.12e-04\n", + "\n", + "Transition Length in case 2 [m] = 7.79e-03\n", + "\n", + "Required Time [s] = 0.007\n", + "\n", + "Required Time in case 2 [s] = 0.012\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8 Page 529" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Average mass trasnfer convection coefficient for the tube\n", + "import math\n", + "#Operating Conditions\n", + "m = .0003; \t\t#[kg/s] mass flow rate of water\n", + "T = 25+273; \t\t\t\t#[K] Temperature of surrounding and tube\n", + "D = .01; \t\t\t#[m] Diameter\n", + "L = 1; \t\t\t#[m] length\n", + "#calculations and results\n", + "#Table A.4 Air Properties T = 298 K\n", + "uv = 15.7*math.pow(10,-6); #[m^2/s] Kinematic Viscosity\n", + "u = 18.36*math.pow(10,-6); #[N.s/m^2] Viscosity\n", + "#Table A.8 Ammonia-Air Properties T = 298 K\n", + "Dab = .28*math.pow(10,-4); #[m^2/s] Diffusion coeff\n", + "Sc = .56;\n", + "\n", + "Re = m*4/(math.pi*D*u);\n", + "print '%s %d %s' %(\"\\n As Reynolds Number is\",Re,\". The flow is Laminar.\");\n", + "\n", + "#Using Equation 8.57\n", + "Sh = 1.86*math.pow((Re*Sc*D/L),.3334);\n", + "h = Sh*Dab/D;\n", + "print '%s %.3f %s' %(\"\\n Average mass trasnfer convection coefficient for the tube\",h,\"m/s\");\n", + "\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " As Reynolds Number is 2080 . The flow is Laminar.\n", + "\n", + " Average mass trasnfer convection coefficient for the tube 0.012 m/s\n" + ] + } + ], + "prompt_number": 8 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_9.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_9.ipynb new file mode 100644 index 00000000..8bdfef75 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_9.ipynb @@ -0,0 +1,311 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Free Convection" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1 Page 569" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Boundary Layer thickness at trailing edge.\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 70+273.; \t\t\t\t\t#[K] Surface Temperature\n", + "Tsurr = 25+273.; \t\t\t\t#[K] Surrounding Temperature\n", + "v1 = 0; \t\t\t\t\t#[m/s] Velocity of free air\n", + "v2 = 5; \t\t\t\t\t#[m/s] Velocity of free air\n", + "L = .25; \t\t\t\t#[m] length\n", + "#calculations and results\n", + "#Table A.4 Air Properties T = 320 K\n", + "uv = 17.95*math.pow(10,-6);\t\t\t#[m^2/s] Kinematic Viscosity\n", + "be = 3.12*math.pow(10,-3); \t\t\t#[K^-1] Tf^-1\n", + "Pr = 269; \t\t\t# Prandtl number \n", + "g = 9.81; \t\t\t\t\t#[m^2/s]gravitational constt\n", + "\n", + "Gr = g*be*(Ts-Tsurr)*L*L*L/(uv*uv);\n", + "del1 = 6*L/math.pow((Gr/4),.25);\n", + "print '%s %.3f %s' %(\"\\n Boundary Layer thickness at trailing edge for no air stream\",del1,\"m\");\n", + "\n", + "Re = v2*L/uv;\n", + "print '%s %.2e %s' %(\"\\n\\n For air stream at 5 m/s As the Reynolds Number is \",Re,\"the free convection boundary layer is Laminar\");\n", + "del2 = 5*L/math.pow((Re),.5);\n", + "print '%s %.4f %s' %(\"\\n Boundary Layer thickness at trailing edge for air stream at 5 m/s is\",del2,\"m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Boundary Layer thickness at trailing edge for no air stream 0.023 m\n", + "\n", + "\n", + " For air stream at 5 m/s As the Reynolds Number is 6.96e+04 the free convection boundary layer is Laminar\n", + "\n", + " Boundary Layer thickness at trailing edge for air stream at 5 m/s is 0.0047 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2 Page 572 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat transfer by convection between screen and room air.\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 232+273.; \t\t\t#[K] Surface Temperature\n", + "Tsurr = 23+273.; \t\t#[K] Surrounding Temperature\n", + "L = .71; \t\t#[m] length\n", + "w = 1.02; \t\t#[m] Width\n", + "\n", + "#Table A.4 Air Properties T = 400 K\n", + "k = 33.8*math.pow(10,-3) \t;#[W/m.K]\n", + "uv = 26.4*math.pow(10,-6) \t;#[m^2/s] Kinematic Viscosity\n", + "al = 38.3*math.pow(10,-6)\t;#[m^2/s]\n", + "be = 2.5*math.pow(10,-3) \t;#[K^-1] Tf^-1\n", + "Pr = .69 \t\t;# Prandtl number \n", + "g = 9.81 \t;#[m^2/s] gravitational constt\n", + "#calculations and results\n", + "Ra = g*be*(Ts-Tsurr)/al*L*L*L/uv;\n", + "print '%s %.2e %s' %(\"\\n\\n As the Rayleigh Number is\",Ra,\"the free convection boundary layer is turbulent\");\n", + "#From equatiom 9.23\n", + "Nu = math.pow(.825 + .387*math.pow(Ra,.16667) /math.pow((1+math.pow((.492/Pr),(9./16.))),(8./27.)),2);\n", + "h = Nu*k/L;\n", + "q = h*L*w*(Ts-Tsurr);\n", + "\n", + "print '%s %d %s' %(\"\\n Heat transfer by convection between screen and room air is\",q,\"W\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " As the Rayleigh Number is 1.81e+09 the free convection boundary layer is turbulent\n", + "\n", + " Heat transfer by convection between screen and room air is 1060 W\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3 Page 577" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat Loss from duct per meter of length\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 45+273.; \t\t\t\t#[K] Surface Temperature\n", + "Tsurr = 15+273. \t\t\t\t;#[K] Surrounding Temperature\n", + "H = .3 \t\t\t\t;#[m] Height \n", + "w = .75 \t\t\t\t;#[m] Width\n", + "\n", + "#Table A.4 Air Properties T = 303 K\n", + "k = 26.5*math.pow(10,-3) \t\t;#[W/m.K]\n", + "uv = 16.2*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n", + "al = 22.9*math.pow(10,-6) ;#[m^2/s] alpha\n", + "be = 3.3*math.pow(10,-3) ;#[K^-1] Tf^-1\n", + "Pr = .71 \t\t\t;# Prandtl number \n", + "g = 9.81 \t\t;#[m^2/s] gravitational constt\n", + "#calculations\n", + "Ra = g*be*(Ts-Tsurr)/al*H*H*H/uv; #Length = Height\n", + "#From equatiom 9.27\n", + "Nu = (.68 + .67*math.pow(Ra,.25) /math.pow((1+math.pow((.492/Pr),(9./16.))),(4./9.)));\n", + "#for Sides\n", + "hs = Nu*k/H;\n", + "\n", + "Ra2 = g*be*(Ts-Tsurr)/al*(w/2.)*(w/2.)*(w/2.)/uv; #Length = w/2\n", + "#For top eq 9.31\n", + "ht = k/(w/2.)*.15*math.pow(Ra2,.3334);\n", + "#For bottom Eq 9.32\n", + "hb = k/(w/2.)*.27*math.pow(Ra2,.25);\n", + "\n", + "q = (2*hs*H+ht*w+hb*w)*(Ts-Tsurr);\n", + "#results\n", + "print '%s %d %s' %(\"\\n Rate of heat loss per unit length of duct is\",q,\" W/m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Rate of heat loss per unit length of duct is 246 W/m\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4 Page 580 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat Loss from pipe per meter of length\n", + "import math\n", + "#Operating Conditions\n", + "Ts = 165+273.; \t\t\t\t#[K] Surface Temperature\n", + "Tsurr = 23+273.; \t\t\t#[K] Surrounding Temperature\n", + "D = .1 \t\t\t\t;#[m] Diameter\n", + "e = .85 \t\t\t\t;# emissivity\n", + "stfncnstt=5.67*math.pow(10,(-8))# [W/m^2.K^4] - Stefan Boltzmann Constant \n", + "\n", + "#Table A.4 Air Properties T = 303 K\n", + "k = 31.3*math.pow(10,-3) ;#[W/m.K] Conductivity\n", + "uv = 22.8*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n", + "al = 32.8*math.pow(10,-6) ;#[m^2/s] alpha\n", + "be = 2.725*math.pow(10,-3) \t;#[K^-1] Tf^-1\n", + "Pr = .697 \t\t;# Prandtl number \n", + "g = 9.81 \t\t;#[m^2/s] gravitational constt\n", + "#calculations\t\n", + "Ra = g*be*(Ts-Tsurr)/al*D*D*D/uv; \n", + "#From equatiom 9.34\n", + "Nu = math.pow((.60 + .387*math.pow(Ra,(1./6.))/math.pow(1+math.pow((.559/Pr),(9./16.)),(8./27.))),2);\n", + "h = Nu*k/D;\n", + "\n", + "qconv = h*math.pi*D*(Ts-Tsurr);\n", + "qrad = e*math.pi*D*stfncnstt*(Ts*Ts*Ts*Ts-Tsurr*Tsurr*Tsurr*Tsurr);\n", + "#results\n", + "print '%s %d %s' %(\"\\n Rate of heat loss per unit length of pipe is \",qrad+qconv,\"W/m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Rate of heat loss per unit length of pipe is 763 W/m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5 Page 592" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#variable initialization\n", + "# Heat Loss from pipe per unit of length\n", + "# Heat Loss if air is filled with glass-fiber blanket insulation\n", + "import math\n", + "#Operating Conditions\n", + "To = 35+273. \t\t\t;#[K] Shield Temperature\n", + "Ti = 120+273. \t\t\t;#[K] Tube Temperature\n", + "Di = .1 \t\t\t;#[m] Diameter inner\n", + "Do = .12 \t\t;#[m] Diameter outer\n", + "L = .01 \t\t\t;#[m] air gap insulation\n", + "\n", + "#Table A.4 Air Properties T = 350 K\n", + "k = 30*math.pow(10,-3) ;#[W/m.K] Conductivity\n", + "uv = 20.92*math.pow(10,-6) ;#[m^2/s] Kinematic Viscosity\n", + "al = 29.9*math.pow(10,-6) ;#[m^2/s] alpha\n", + "be = 2.85*math.pow(10,-3) ;#[K^-1] Tf^-1\n", + "Pr = .7 \t\t;# Prandtl number \n", + "g = 9.81 \t;#[m^2/s] gravitational constt\n", + "#Table A.3 Insulation glass fiber T=300K\n", + "kins = .038 \t;#[W/m.K] Conductivity\n", + "#calculations\n", + "Lc = 2*math.pow((2.303*math.log10(Do/Di)),(4./3.))/math.pow((math.pow((Di/2.),(-3./5.))+math.pow((Do/2.),(-3./5.))),(5./3.));\n", + "Ra = g*be*(Ti-To)/al*Lc*Lc*Lc/uv; \n", + "keff = .386*k*math.pow((Pr/(.861+Pr)),.25) *math.pow(Ra,.25);\n", + "q = 2*math.pi*keff*(Ti-To)/(2.303*math.log10(Do/Di));\n", + "\n", + "#From equatiom 9.58 and 3.27\n", + "qin = q*kins/keff;\n", + "#results\n", + "print '%s %d %s' %(\"\\n Heat Loss from pipe per unit of length is \",q,\"W/m\")\n", + "print '%s %d %s' %(\" \\n Heat Loss if air is filled with glass-fiber blanket insulation\",qin,\"W/m\");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Heat Loss from pipe per unit of length is 100 W/m\n", + " \n", + " Heat Loss if air is filled with glass-fiber blanket insulation 111 W/m\n" + ] + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/README.txt b/Fundamentals_of_Heat_and_Mass_Transfer/README.txt new file mode 100644 index 00000000..593587fe --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/README.txt @@ -0,0 +1,10 @@ +Contributed By: Devika Raj +Course: be +College/Institute/Organization: RVR college of Engineering +Department/Designation: Electronics and Communication En +Book Title: Fundamentals of Heat and Mass Transfer +Author: Incropera, DeWitt, Bergman, Lavine +Publisher: John Wiley & Sons Inc +Year of publication: 1981 +Isbn: 9780471612469 +Edition: 3rd
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