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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": {} + } + ] +}
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