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diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/README.txt b/Heat_Transfer_Principles_And_Applications_by_Dutta/README.txt new file mode 100644 index 00000000..1af1e4ae --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/README.txt @@ -0,0 +1,10 @@ +Contributed By: Manish Punjabi +Course: mtech +College/Institute/Organization: IIT +Department/Designation: Contributor Operations Research +Book Title: Heat Transfer Principles And Applications +Author: Dutta +Publisher: PHI Learning Pvt. Ltd., New Delhi +Year of publication: 2006 +Isbn: 8120316258 +Edition: 1
\ No newline at end of file diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch10.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch10.ipynb new file mode 100644 index 00000000..6ff17007 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch10.ipynb @@ -0,0 +1,148 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10 : Unsteady State And Multidimensional Heat Conduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.8 Page No : 444" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The bottom surface temperature of given slab is 10.3 C\n", + "The top surface temperature of given slab is 19.4 C\n", + "The mid plane temperature of given slab is 12.6 C\n" + ] + } + ], + "source": [ + "# Variables\n", + "l = 0.05 \t\t\t#m,thickness of margarine slab\n", + "ro = 990. \t\t\t#Kg/m**3, density of margarine slab \n", + "cp = 0.55 \t\t\t#Kcal/kg C, ddpecific heat of slab\n", + "k = 0.143 \t\t\t#kcal/h mC, thermal conductivity of slab\n", + "Ti = 4. \t\t\t#C, initial temp\n", + "To = 25. \t\t\t#C, ambient temp.\n", + "t = 4. \t\t\t#hours, time\n", + "h = 8. \t\t\t#kcal/h m**2 C\n", + "\n", + "#calculation\n", + "Fo = k*t/(ro*cp*l**2) \t\t\t#, fourier no.\n", + "Bi = h*l/k \t\t\t#Biot no.\n", + "#from fig. 10.6 a\n", + "Tcbar = 0.7 \t\t\t#Tcbar = (Tc-To)/(Ti-To)\n", + "Tc = To+Tcbar*(Ti-To) \t\t\t#C, centre temp.\n", + "#from fig 10.6 b\n", + "#(T-To)/(Tc-To) = 0.382\n", + "T = 0.382*(Tc-To)+To \t\t\t#c,top surface temp.\n", + "#again from fig. 10.6 b\n", + "Tm = 0.842*(Tc-To)+To \t\t\t#, mid plane temp.\n", + "\n", + "# Results\n", + "print \"The bottom surface temperature of given slab is %.1f C\"%(Tc);\n", + "print \"The top surface temperature of given slab is %.1f C\"%(T);\n", + "print \"The mid plane temperature of given slab is %.1f C\"%(Tm);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.9 Page No : 449" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "i) time required for the cantre-line temp.to drop down to 200 C is 229 s\n", + "ii)the temp. at half radius at that moment is 161 C \n", + "iii)the amount of heat that has been transfered to the liquid is 19647 Kj\n" + ] + } + ], + "source": [ + "import math \n", + "# Variables\n", + "Ti = 870. \t\t\t#C, initial temp.\n", + "To = 30. \t\t\t#C, ambient temp.\n", + "Tc = 200. \t\t\t#C, centre line temp.\n", + "h = 2000. \t\t\t#W/m**2 C, surface heat transfer coefficient\n", + "a = 0.05 \t\t\t#m, radius of cylinder \n", + "k = 20. \t\t\t#W/m C, thermal conductivity\n", + "ro = 7800. \t\t\t#kg/m**3, density\n", + "cp = 0.46*10**3 \t\t\t#j/kg C, specific heat\n", + "\n", + "#calculation\n", + "#i\n", + "Bi = h*a/k \t\t\t#Biot no.\n", + "alpha = k/(ro*cp) \t\t\t#m**2/C, thermal diffusivity\n", + "Tcbar = (Tc-To)/(Ti-To) \t\t\t# dimensionless centre line temp.\n", + "#from fig 10.7 a\n", + "fo = 0.51 \t\t\t#fourier no. fo = alpha*t/a**2\n", + "t = fo*a**2/alpha \t\t\t#s, time\n", + "\n", + "#ii\n", + "#at the half radius, r/a = 0.5 & Bi = 5\n", + "T = To+0.77*(Tc-To) \t\t\t#from fig. 10.7 b\n", + "\n", + "#iii\n", + "x = Bi**2*fo\n", + "#for x = 12.75 & Bi = 5.0. fig.10.9 b gives\n", + "#q/qi = 0.83\n", + "qi = math.pi*a**2*(1)*ro*cp*(Ti-To) \t\t\t#kj, initial amount of heat energy \n", + " #present in 1 m length of shaft\n", + "q = 0.83*qi \t\t\t#j, amount of heat transfered \n", + "\n", + "# Results\n", + "print \"i) time required for the cantre-line temp.to drop down to 200 C is %.0f s\"%(t);\n", + "print \"ii)the temp. at half radius at that moment is %.0f C \"%(T);\n", + "print \"iii)the amount of heat that has been transfered to the liquid is %d Kj\"%(q*10**-3)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb new file mode 100644 index 00000000..b98ede25 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch11.ipynb @@ -0,0 +1,322 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11 : Boundary layer heat transfer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1 Page No : 478" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "i) Boundary layer thickness is 0.0033 m\n", + "Local drag coefficient is 8.72e-04 \n", + "total drag force is 0.615 N \n", + "Shear stress is 0.285 N/m**2\n" + ] + } + ], + "source": [ + "import math \n", + "#Variable\n", + "v = 1. \t\t\t#m/s\n", + "#temprature\n", + "T = 25. \t\t\t# degree celcius\n", + "#length of plate,l = 1m\n", + "l = 1. \t\t\t#m\n", + "#width of plate,w = 0.5m\n", + "w = 0.5 \t\t\t#m\n", + "#angle of incidence,theta = 0 degree\n", + "theta = 0. \t\t\t#degree\n", + "\n", + "#Calculation\n", + "#for water at 25 degree celcius ,momentum diffusivity,\n", + "MD = 8.63*(10**-7) \t\t\t# m**2/s\n", + "#local Reynold no.\n", + "x = 0.5 \t\t\t#m\n", + "Re = x*v/MD \n", + "#from Eq. 11.39,the boundary layer thickness is\n", + "t = 5*x/(Re**0.5)\n", + "\n", + "\n", + "#Results\n", + "print \"i) Boundary layer thickness is %.4f m\"%(t)\n", + "\n", + "#local drag coefficient\n", + "#CD = local drag force per unit area (F)/kinetic energy per unit volume(KE)\n", + "#F = 0.332*rho*v**2*Re**0.5 and KE = 0.5*rho*v**2\n", + "CD = 0.332*v**2*(Re**-0.5)/(0.5)*v**2\n", + "\n", + "print \"Local drag coefficient is %.2e \"%(CD)\n", + "\n", + "#From eq 11.44, the drag force acting on one side of the plate is\n", + "#kinetic viscocity\n", + "mu = 8.6*(10**-4)\n", + "fd = 0.664*mu*v*(l*v/MD)**0.5*w\n", + "#the total force acting on both sides of the plate\n", + "\n", + "tfd = 2*fd\n", + "print \"total drag force is %.3f N \"%(tfd)\n", + "\n", + "#shear stress at any point in the boundary layer\n", + "#at a point in the boundary layer,\n", + "x = 0.5 \t\t\t#m\n", + "y = t/2\n", + "# n = blasius dimensionless variable\n", + "n = y/(MD*x/v)**0.5\n", + "#From table 11.1, at n = 2.5,f\"(n) = 0.218\n", + "#shear stress = tau\n", + "fn = 0.218 \t\t\t#f\"(n) = fn\n", + "tau = (mu*v*(v/(MD*x))**0.5)*fn\n", + "print \"Shear stress is %.3f N/m**2\"%(tau)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2 Page No : 488" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Thermal boundary layer thickness is 8.7 mm \n", + "heat transfer coeff is 6.9 W/m**2 C\n" + ] + } + ], + "source": [ + "#Variable\n", + "Ts = 200. \t\t\t# C,temp. of air\n", + "Ta = 30. \t\t\t#C, temp .of surface\n", + "Va = 8. \t\t\t#m/s, velocity of air\n", + "d = 0.75 \t\t\t#m, dismath.tant from leading edge\n", + "\n", + "#Calculation and Results\n", + "Tm = (Ts+Ta)/2 \t\t\t#C, Mean temp. of boundary layer\n", + "mu = 2.5*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "P = 0.69 \t\t\t#prndatl no.\n", + "k = 0.036 \t\t\t#W/m c, thermal conductivity\n", + "Re = d*Va/mu \t\t\t#reynold no.\n", + "t = 5*d/(Re**0.5*P**(1./3)) \t\t\t#m, thermal boundary layer thickness\n", + "print \"Thermal boundary layer thickness is %.1f mm \"%(t*10**3)\n", + "\n", + "N = (0.332*Re**(0.5)*P**(1./3)) \t\t\t#Nusslet no.\n", + "h = k*N/d \t\t\t#heat transfer coefficent\n", + "print \"heat transfer coeff is %.1f W/m**2 C\"%(h)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3 Page No : 489" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Local rate of heat exchange is 235 W/m2\n", + "Plate temperature is :108 Celsius \n" + ] + } + ], + "source": [ + "# Variables\n", + "#Free strean velocity (v1) and temp.(t1) on side 1\n", + "v1 = 6. \t\t\t#m/s\n", + "t1 = 150. \t\t\t#degree celcius\n", + "#same on side 2\n", + "v2 = 3. \t\t\t#m/s\n", + "t2 = 50. \t\t\t#degree celcius\n", + "#dismath.tant\n", + "x = 0.7 \t\t\t#m\n", + "#The plate temp. is assumed to be equal to the mean of the bulk air temp on the two sides of the plates\n", + "T = 100. \t\t\t#degree celcius\n", + "\n", + "# Calculations\n", + "#Side 1\n", + "#mean air temp.\n", + "tm1 = (T+t1)/2\n", + "#From thermophysical properties:kinetic vismath.cosity (kv),Prandtl no.(P), thermal conductivity (k)\n", + "kv1 = 2.6*10**-5 \t\t\t#m**2/s\n", + "P1 = 0.69\n", + "k1 = 0.0336 \t\t\t#W/m degree celcius\n", + "#Reynold no.\n", + "Re1 = x*v1/kv1\n", + "#Nusslet no(N1)\n", + "a = 1/3.\n", + "N1 = 0.332*(Re1)**0.5*P1**a\n", + "h1 = k1*N1/x\n", + "#Side 2 of the plate\n", + "tm2 = (T+t2)/2\n", + "#Similarly\n", + "kv2 = 2.076*(10)**-5 \t\t\t#m**2/s\n", + "P2 = 0.70\n", + "k2 = 0.03 \t\t\t#W/m degree celcius\n", + "Re2 = x*v2/kv2\n", + "N2 = 0.332*(Re2)**0.5*P2**a\n", + "h2 = k2*N2/x\n", + "#overall heat transfer coeff. \n", + "U = h1*h2/(h1+h2)\n", + "#The local rate of heat exchange\n", + "RH = U*(t1-t2)\n", + "\n", + "# Results\n", + "print \"Local rate of heat exchange is %.0f W/m2\"%(RH)\n", + "#the plate temp is given by\n", + "TP = t2+(t1-t2)*U/h2\n", + "print \"Plate temperature is :%.0f Celsius \"%(TP)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.4 Page No : 490" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The temprature of plate after 1 hour is 82 C\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "T1 = 120. \t\t\t#C, initial temp.\n", + "T2 = 25. \t\t\t#C, Final temp.\n", + "Tm = (T1+T2)/2 \t\t\t#C, mean temp.\n", + "rho = 8880. \t\t\t#kg/m**3, density of plate\n", + "#Properties of air at mean temp.\n", + "mu = 2.07*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "k = 0.03 \t\t\t#W/m C, thermal conductivity\n", + "l = 0.4 \t\t\t#m, length of plate\n", + "w = 0.3 \t\t\t#m, width of plate\n", + "d = 0.0254 \t\t\t#m, thickness of plate\n", + "Vinf = 1. \t\t\t#m/s, air velocity\n", + "Re = l*Vinf/mu \t\t\t#REynold no.\n", + "\n", + "#from eq. 11.90 (b)\n", + "Nu = 0.664*(Re)**(1./2)*(Pr)**(1./3) \t\t\t#average Nusslet no.\n", + "#Nu = l*h/k\n", + "h = Nu*k/l \t\t\t#W/m**2 C, heat transfer coefficient\n", + "#Rate of change of temp. is given by\n", + "A = 2*l*w \t\t\t#m**2. area of plate\n", + "t = 1*3600. \t\t\t#s, time\n", + "cp = 0.385*10.**3 \t\t\t#j/kg K, specific heat\n", + "m = l*w*d*rho \t\t\t#kg, mass of plate\n", + "\n", + "#-d/dt(m*cp8dt) = A*hv*(T1-T2)\n", + "#appling the boundary condition \n", + "T = (T1-T2)*math.exp(-A*h*t/(m*cp))+T2\n", + "print \"The temprature of plate after 1 hour is %.0f C\"%(T)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5 Page No : 508" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nusslet no is: 388 \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "#Reynold no (Re),friction factor(f),Prandlt no. (P)\n", + "Re = 7.44*(10**4)\n", + "f = 0.00485\n", + "P = 5.12\n", + "x = P-1 \t\t\t#assume\n", + "\n", + "# Calculations\n", + "#according to Von Karmen anamath.logy\n", + "N = ((f/2)*Re*P)/(1+(5*math.sqrt(f/2))*(x+math.log(1+(5./6)*x)))\n", + "\n", + "# Results\n", + "print \"Nusslet no is: %.0f \"%(N)\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch2.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch2.ipynb new file mode 100644 index 00000000..5fcf0a36 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch2.ipynb @@ -0,0 +1,580 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 :Steady State conduction In one dimension" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1 Page No : 14" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat gain is 16.27 W\n", + "interface temp. between brick and cork is 24.2 C\n", + "interface temp. between cement and cork is -13.6 C\n", + "thermal resistance offered by brick layer is 12.9 percent\n", + "thermal resistance offered by cork layer is 84.1 percent\n", + "thermal resistance offered by cement layer is 3.0 percent\n", + "Additional thickness of cork to be provided = 5.1 cm\n" + ] + } + ], + "source": [ + "# Variables\n", + "A = 1. \t\t\t#m**2, area\n", + "#for inner layer (cement)\n", + "ti = 0.06 \t\t\t#m, thickness\n", + "ki = 0.72 \t\t\t#W/m C, thermal conductivity\n", + "Ti = -15. \t\t\t#C, temprature\n", + "#for middle layer (cork)\n", + "tm = 0.1 \t\t\t#m, thickness\n", + "km = 0.043 \t\t\t#W/m C, thermal conductivity\n", + "#for outer layer(brick)\n", + "to = 0.25 \t\t\t#m, thickness\n", + "ko = 0.7 \t\t\t#W/m C, thermal conductivity\n", + "To = 30. \t\t\t#C, temprature\n", + "\n", + "# Calculation and Results\n", + "#Thermal resistance of outer layer \t\t\t#C/W\n", + "Ro = to/(ko*A) \n", + "#Thermal resistance of middle layer \t\t\t#C/W\n", + "Rm = tm/(km*A) \n", + "#Thermal resistance of inner layer \t\t\t#C/W\n", + "Ri = ti/(ki*A)\n", + "Rt = Ro+Rm+Ri\n", + "tdf = To-Ti \t\t\t#temp driving force\n", + "#(a)\n", + "Q = tdf/Rt \t\t\t#rate of heat gain\n", + "print \"the rate of heat gain is %.2f W\"%(Q)\n", + "\n", + "#(b)\n", + "#from fig. 2.4\n", + "td1 = Q*to/(ko*A) \t\t\t#C temp. drop across the brick layer\n", + "T1 = To-td1 \t\t\t#interface temp. between brick and cork\n", + "#similarly\n", + "td2 = Q*tm/(km*A) \t\t\t#C temp. drop across the cork layer\n", + "T2 = T1-td2 \t\t\t#C, interface temp. between cement and cork\n", + "print \"interface temp. between brick and cork is %.1f C\"%(T1)\n", + "print \"interface temp. between cement and cork is %.1f C\"%(T2)\n", + "\n", + "\n", + "#(c)\n", + "Rpo = Ro/Rt \t\t\t#thermal resistance offered by brick layer\n", + "Rpm = Rm/Rt \t\t\t#thermal resistance offered by cork layer\n", + "Rpi = Ri/Rt \t\t\t#thermal resistance offered by cement layer\n", + "print \"thermal resistance offered by brick layer is %.1f percent\"%(Rpo*100)\n", + "print \"thermal resistance offered by cork layer is %.1f percent\"%(Rpm*100)\n", + "print \"thermal resistance offered by cement layer is %.1f percent\"%(Rpi*100)\n", + "\n", + "#second part\n", + "x = 30. \t\t\t#percentage dec in heat transfer \n", + "Q1 = Q*(1-x/100) \t\t\t#W, desired rate of heat flow\n", + "Rth = tdf/Q1 \t\t\t#C/W, required thermal resistance\n", + "Rad = Rth-Rt \t\t\t#additional thermal resistance\n", + "Tad = Rad*km*A\n", + "print \"Additional thickness of cork to be provided = %.1f cm\"%(Tad*100)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2 Page No : 15" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rate of heat loss is 50.7 W\n", + "thermal conductivities of insulating layer is 0.1633 W/m C\n" + ] + } + ], + "source": [ + "# Variables\n", + "#outer thickness of brickwork (to) & inner thickness (ti)\n", + "to = 0.15 \t\t\t#m thickness\n", + "ti = 0.012 \t\t\t#m thickness\n", + "#thickness of intermediate layer(til)\n", + "til = 0.07 \t\t\t#m thick\n", + "#thermal conductivities of brick and wood\n", + "kb = 0.70 \t\t\t#W/m celcius\n", + "kw = 0.18 \t\t\t#W/m celcius\n", + "#temp. of outside and inside wall\n", + "To = -15 \t\t\t#celcius\n", + "Ti = 21 \t\t\t#celcius\n", + "#area\n", + "A = 1 \t\t\t#m**2\n", + "\n", + "\n", + "# Calculations and Results\n", + "#(a)\n", + "#Thermal resistance of brick , wood and insulating layer\n", + "TRb = to/(kb*A) \t\t\t#C/W\n", + "TRw = ti/(kw*A) \t\t\t#C/W\n", + "TRi = 2*TRb \t\t\t#C/W\n", + "#Total thermal resistance\n", + "TR = TRb+TRw+TRi \t\t\t#C/W\n", + "#Temp. driving force\n", + "T = Ti-To \t\t\t#C\n", + "#Rate of heat loss\n", + "Q = T/TR\n", + "print \"Rate of heat loss is %.1f W\"%(Q)\n", + "#(b)thermal conductivities of insulating layer\n", + "k = til/(A*TRi)\n", + "print \"thermal conductivities of insulating layer is %.4f W/m C\"%(k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3 Page No : 19" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rate of heat loss is 4095 W\n", + "interface temp.is 183 C\n", + "Fractional resistance offered by the special brick layer is 0.353 \n" + ] + } + ], + "source": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "#Length & Inside rdius of gas duct\n", + "L = 1. \t\t\t#m\n", + "ri = 0.5 \t\t\t#m radius\n", + "#Properties of inner and outer layer\n", + "ki = 1.3 \t\t\t#W/m C, thermal conductivity of inner bricks\n", + "ti = 0.27 \t\t\t#m, inner layer thickness \n", + "ko = 0.92 \t\t\t#W/m C, thermal conductivity of special bricks \n", + "to = 0.14 \t\t\t#m, outer layer thickness\n", + "Ti = 400. \t\t\t#C, inner layer temp.\n", + "To = 65. \t\t\t#C, outer layer temp.\n", + "\n", + "#calculation and Results\n", + "r_ = ri+ti \t\t\t#m, outer radius of fireclay brick layer\n", + "ro = r_+to \t\t\t#m, outer radius of special brick layer\n", + "#Heat transfer resistance\n", + "#Heat transfer resistance of fireclay brick\n", + "R1 = (math.log(r_/ri))/(2*math.pi*L*ki)\n", + "#Heat transfer resistance of special brick\n", + "R2 = (math.log(ro/r_))/(2*math.pi*L*ko)\n", + "#Total resistance\n", + "R = round(R1+R2,4)\n", + "#Driving force\n", + "T = Ti-To\n", + "#Rate of heat loss\n", + "Q = T/(R)\n", + "print \"Rate of heat loss is %d W\"%(Q)\n", + "#interface temp.\n", + "Tif = Ti-(Q*R1)\n", + "print \"interface temp.is %d C\"%(Tif)\n", + "#Fractional resistance offered by the special brick layer\n", + "FR = R2/(R1+R2)\n", + "print \"Fractional resistance offered by the special brick layer is %.3f \"%(FR)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4 Page No : 20" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The hot end temp. is 148 C\n", + "The temprature gradient at hot end is -294.7 C/m\n", + "The temprature gradient at cold end is -1179 C/m\n", + "the temprature at 0.15m away from the cold end is 131 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "d1 = 0.06 \t\t\t#m, one end diameter of steel rod\n", + "d2 = 0.12 \t\t\t#m,other end diameter of steel rod\n", + "l = 0.2 \t\t\t#m length of rod\n", + "T2 = 30. \t\t\t#C, temp. at end 2\n", + "Q = 50. \t\t\t#W, heat loss\n", + "k = 15. \t\t\t#W/m c, thermal conductivity of rod\n", + "\n", + "# Calculation and Results\n", + "#T = 265.8-(7.07/(0.06-0.15*x))........(a)\n", + "#(a)\n", + "x1 = 0\n", + "#from eq. (a)\n", + "T1 = 265.8-(7.07/(0.06-0.15*x1))\n", + "print \"The hot end temp. is %.0f C\"%(T1)\n", + "#(b) from eq. (i)\n", + "C = 50 \t\t\t#integration consmath.tant\n", + "#from eq. (i)\n", + "D1 = -C/(math.pi*d1**2*k) \t\t\t#D = dT/dx, temprature gradient\n", + "print \"The temprature gradient at hot end is %.1f C/m\"%(D1)\n", + "#similarly\n", + "D2 = -1179 \t\t\t#at x = 0.2m\n", + "print \"The temprature gradient at cold end is %.0f C/m\"%(D2)\n", + "\n", + "#(c)\n", + "x2 = 0.15 \t\t\t#m, given,\n", + "x3 = l-x2 \t\t\t#m, section away from the cold end\n", + "#from eq. (a)\n", + "T2 = 265.8-(7.07/(0.06-0.15*x3))\n", + "print \"the temprature at 0.15m away from the cold end is %.0f C\"%(T2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5 Page No : 24" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat transfer is -3746 W\n", + "Refrigeration capacity is 1.07 tons\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "#inside and outside diameter and Temp. of sphorical vessel\n", + "do = 16. \t\t\t#m, diameter \n", + "t = 0.1 \t\t\t#m, thick \n", + "Ri = do/2 \t\t\t#m, inside radius \n", + "Ro = Ri+t \t\t\t#m. outside radius\n", + "To = 27. \t\t\t#C, temperature\n", + "Ti = 4. \t\t\t#C ammonia\n", + "k = 0.02 \t\t\t#W/m C, thermal conductivity of foam layer \n", + "\n", + "# Calculations and Results\n", + "#from eq. 2.23 the rate of heat transfer\n", + "Q = (Ti-To)*(4*math.pi*k*Ro*Ri)/(Ro-Ri)\n", + "print \"the rate of heat transfer is %.0f W\"%(Q)\n", + "#Refrigeration capacity(RC)\n", + "#3516 Watt = 1 ton\n", + "RC = -Q/3516\n", + "print \"Refrigeration capacity is %.2f tons\"%(RC)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6 Page No : 28" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the temprature midway in the rod at steady state is 167.3 C\n", + "Temprature gradient at one end of the rod is 559 C/W\n", + "Temprature gradient at other end of the rod is 521.8 C/W\n" + ] + } + ], + "source": [ + "import math \n", + "# Variables\n", + "d = 0.05 \t\t\t#m, diameter of rod\n", + "l = 0.5 \t\t\t#m, length of rod\n", + "T1 = 30. \t\t\t#CTemp. at one end (1)\n", + "T2 = 300. \t\t\t#C, temp at other end (2)\n", + "\n", + "# Calculations and Results\n", + "x1 = l/2 \t\t\t#m, at mid plane\n", + "#temprature distribution ,\n", + "#comparing with quadratic eq. ax**2+bx+c \n", + "#and its solution as x = (-b+math.sqrt(b**2-4*a*c))/2*a\n", + "a = 1.35*10**-4\n", + "b = 1\n", + "c = -(564*x1+30.1)\n", + "T = (-b+math.sqrt(b**2-4*a*c))/(2*a)\n", + "print \"the temprature midway in the rod at steady state is %.1f C\"%(T)\n", + "\n", + "#Temprature gradient at the ends of the rod\n", + "x2 = 0 \t\t\t#m, at one end\n", + "a1 = 1.35*10**-4\n", + "b1 = 1\n", + "c1 = -(564*x2+30.1)\n", + "T1 = (-b1+math.sqrt(b1**2-4*a1*c1))/(2*a1)\n", + "k1 = 202+0.0545*T1 \n", + "C1 = 113930 \t\t\t#integration consmath.tant from eq. (1)\n", + "TG1 = C1/k1 \t\t\t#C/W, temprature gradient, dT/dx\n", + "#similarly\n", + "x3 = 0.5\n", + "a2 = 1.35*10**-4\n", + "b2 = 1\n", + "c2 = -(564*x3+30.1)\n", + "T2 = (-b2+math.sqrt(b2**2-4*a2*c2))/(2*a2)\n", + "k2 = 202+0.0545*T2\n", + "TG2 = C1/k2\n", + "print \"Temprature gradient at one end of the rod is %.0f C/W\"%(TG1)\n", + "print \"Temprature gradient at other end of the rod is %.1f C/W\"%(TG2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7 Page No : 29" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "At the surface x = 0, the temp. is 600 C\n", + "At the surface x = 0.3m, the temp. is 270 C\n", + "Rhe average temprature of the wall is 615 C\n", + "The maximum temprature occurs at 0.104 m\n", + "The maximum temp. is 730 C\n", + "heat flux at left surface is -58750 W/m**2\n", + "heat flux at right surface is 110450 W/m**2\n", + "The average volumetric rate if heat genaration is 564000 W/m**3 \n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "# Variables\n", + "#temprature distribution in wall\n", + "\n", + "t = 0.3 \t\t\t#m, thickness of wall\n", + "k = 23.5 \t\t\t#W/m c thermal conductivity of wall\n", + "\n", + "# Calculations and Results\n", + "x1 = 0\n", + "T1 = 600+2500*x1-12000*x1**2 \t\t\t#C, at surface\n", + "x2 = 0.3\n", + "T2 = 600+2500*x2-12000*x2**2 \t\t\t#C, at x = 0.3\n", + "\n", + "def f3(x): \n", + " return 600+2500*x-12000*x**2\n", + "\n", + "Tav = 1/t* quad(f3,0,0.3)[0]\n", + "\n", + "print \"At the surface x = 0, the temp. is %.0f C\"%(T1)\n", + "print \"At the surface x = 0.3m, the temp. is %.0f C\"%(T2)\n", + "print \"Rhe average temprature of the wall is %.0f C\"%(Tav)\n", + "\n", + "#(b)\n", + "\n", + "#for maximum temprature D = 0\n", + "x3 = 2500/24000.\n", + "print \"The maximum temprature occurs at %.3f m\"%(x3)\n", + "Tmax = 600+2500*x3-12000*x3**2\n", + "print \"The maximum temp. is %.0f C\"%(Tmax)\n", + "\n", + "#(c)\n", + "D1 = 2500-24000*x1 \t\t\t#at x = 0, temprature gradient\n", + "Hf1 = -k*D1 \t\t\t#W/m**2, heat flux at left surface(x = 0)\n", + "D2 = 2500-24000*x2 \t\t\t#at x = 0.3, temprature gradient\n", + "Hf2 = -k*D2 \t\t\t#W/m**2, heat flux at right surface(x = 0.3)\n", + "print \"heat flux at left surface is %.0f W/m**2\"%(Hf1)\n", + "print \"heat flux at right surface is %.0f W/m**2\"%(Hf2)\n", + "\n", + "#(d)\n", + "Qt = Hf2-Hf1 \t\t\t#W/m**2, total rate of heat loss\n", + "Vw = 0.3 \t\t\t#m**3/m**2, volume of wall per unit surface area\n", + "Hav = Qt/Vw \t\t\t#W/m**3, average volumetric rate\n", + "print \"The average volumetric rate if heat genaration is %.0f W/m**3 \"%(Hav) \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8 Page No : 30" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum temp. will occur at a position 0.209 m\n", + "The maximum temprature is 152.6 C\n" + ] + } + ], + "source": [ + "import math \n", + "# Variables\n", + "ka = 24 \t\t\t#W/mC thermal conductivitiy of material A\n", + "tA = 0.1 \t\t\t#m, thickness of A material\n", + "kB = 230 \t\t\t#W/mC thermal conductivity of metl B\n", + "kC = 200 \t\t\t#W/mC thermal conductivity of metal C\n", + "tB = 0.1 \t\t\t#m, thickness of B metal\n", + "tC = 0.1 \t\t\t#m, thickness of C metal\n", + "TBo = 100 \t\t\t#C, outer surface temp. of B wall\n", + "TCo = 100 \t\t\t#C, outer surface temp. of C wall\n", + "Q = 2.5*10**5 \t\t\t#W/m**3, heat generated\n", + "\n", + "# Calculations and Results\n", + "#At D = 0\n", + "x = 2175./10416\n", + "print \"The maximum temp. will occur at a position %.3f m\"%(x)\n", + "x1 = x\n", + "TA = -5208*x1**2+2175*x1-74.5\n", + "print \"The maximum temprature is %.1f C\"%(TA)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9 Page No : 36" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "This radial position does not fall within layer 1. Therefore no temprature maximum occurs in this layer.\n", + " Similarly no temprature maximum occurs in layer 2.\n", + "The maximum temprature at the outer boundary is 200 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "di = 0.15 \t\t\t#m, inner diameter\n", + "do = 0.3 \t\t\t#m, outer diameter\n", + "Q1 = 100.*10**3 \t\t\t#W/,m**3,inner rate of heat generation\n", + "Q2 = 40.*10**3 \t\t\t#W/m**3, outer rate of heat generation\n", + "Ti = 100. \t\t\t#C, temp.at inside surface\n", + "To = 200. \t\t\t#C, temp. at outside surface\n", + "k1 = 30. \t\t\t#W/m C, thermal conductivity of material for inner layer\n", + "k2 = 10. \t\t\t#W/m C, thermal conductivity of material for outer layer\n", + "\n", + "# Calculations and Results\n", + "#T1 = 364+100*math.log(r)-833.3*r**2 (1)\n", + "#T2 = 718+216*math.log(r)-1000*r**2 (2)\n", + "#(b)from eq. 1\n", + "r = math.sqrt(100./2*833.3)\n", + "print \"This radial position does not fall within layer 1. Therefore no temprature maximum occurs in this layer.\"\n", + "#similarly\n", + "print \" Similarly no temprature maximum occurs in layer 2.\"\n", + "ro = di \t\t # m, outer boundary\n", + "Tmax = To\n", + "print \"The maximum temprature at the outer boundary is %.0f C\"%(Tmax)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch3.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch3.ipynb new file mode 100644 index 00000000..ba532e83 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch3.ipynb @@ -0,0 +1,873 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3 : Heat transfer coefficient" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1 Page No : 53" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The time required for melting the ice is 4274 s\n" + ] + } + ], + "source": [ + "# Variables\n", + "di = 0.06 \t\t\t#m,initial diameter of iceball\n", + "T1 = 30. \t\t\t#C, room temp.\n", + "T2 = 0. \t\t\t#ice ball temp.\n", + "h = 11.4 \t\t\t#W/m**2 C, heat transfer coefficient\n", + "x = 40. \t\t\t#% for reduction\n", + "rho = 929. \t\t\t#kg/m**3, density of ice\n", + "Lv = 3.35*10**5 \t\t\t#j/kg, latent heat of fusion\n", + "\n", + "# Calculations\n", + "# m = 4/3*math.pi*r**3 \t\t\t#kg,mass of ice ball\n", + "#rate of melting = -dm/dt\n", + "#rate of heat adsorption = -4*math.pi*r**2*rho*dr/dt*lamda\n", + "#at initial time t = 0\n", + "C1 = di/2 \t\t\t#consmath.tant of integration\n", + "#if the volume of the ball is reduced by 40% of the original volume \n", + "r = ((1-x/100)*(di/2)**3)**(1./3)\n", + "#time required for melting umath.sing eq. 1\n", + "t = (di/2-r)/(h*(T1-T2)/(rho*Lv))\n", + "\n", + "# Results\n", + "print \"The time required for melting the ice is %.0f s\"%(t)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2 Page No : 54" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The time required for the heating coil is 4.9 s\n" + ] + } + ], + "source": [ + "import math\n", + "from scipy.integrate import quad \n", + "#calculate the time required for the heating coil.\n", + "\n", + "# Variables\n", + "P = 1.*10**3 \t\t\t#W, electrical heating capacity\n", + "V = 220. \t\t\t#V, applied voltage\n", + "d = 0.574*10**-3 \t\t\t#m, diameter of wire\n", + "R = 4.167 \t\t\t#ohm, electrical resistance\n", + "Tr = 21. \t\t\t#C, room temp.\n", + "h = 100. \t\t\t#W/m**2 C, heat transfer coefficient\n", + "rho = 8920. \t\t\t#kg/m**3, density of wire\n", + "cp = 384. \t\t\t#j/kg C, specific heat of wire\n", + "percent = 63. \t\t\t#%, percent of the steady state\n", + "\n", + "#Calculation\n", + "R_ = V**2/P \t\t\t#ohm, total electrical resistance\n", + "l = R_/R \t\t\t#m, length of wire\n", + "A = math.pi*d*l \t\t\t#m**2, area of wire\n", + "Tf = P/(h*A)+Tr \t\t\t#final temp.\n", + "dtf = Tf-Tr \t\t\t#C. steady state temp. rise\n", + "#temp. of wire after 63% rise\n", + "T = Tr+(percent/100)*dtf \n", + "#rate of heat accumulation on the wire\n", + "#d/dt(m*cp*T) (1)\n", + "#rate of heat loss\n", + "#h*A*(T-Tr).........................(2)\n", + "#heat balance eq. (1) = (2)\n", + "m = math.pi*d**2*l*rho/4 \t\t\t#kg. mass of wire\n", + "#integrating heat balance eq.\n", + "\n", + "def f6(T): \n", + " return 1/((P/(m*cp))-((h*A)/(m*cp))*(T-Tr))\n", + "\n", + "t = quad(f6,21,322)[0]\n", + "\n", + "# Results\n", + "print \"The time required for the heating coil is %.1f s\"%(t)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3 Page No : 56" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " the heat transfer coefficient is 11.63 W/m**2 C \n", + "So there is no heat flow at other surface of the wall \n", + "average volumetric rate of heat generation is 6396 W/m**3\n" + ] + } + ], + "source": [ + "# Variables\n", + "t = 0.2 \t\t\t#m, thickness of wall\n", + "k = 1.163 \t\t\t#W/m C, thermal conductivity of material\n", + "Ta = 30 \t\t\t#C, ambient temp\n", + "\n", + "# Calculations and Results\n", + "#(a) at x = 0.2 let T = T1 at x = x1\n", + "x1 = 0.2\n", + "T1 = 250-2750*x1**2\n", + "#let D = dT/dx\n", + "D = -5500*0.2 \t\t\t#C/m, at x = 0.2\n", + "h = -k*D/(T1-Ta)\n", + "print \" the heat transfer coefficient is %.2f W/m**2 C \"%(h)\n", + "\n", + "#(b)at other surface of wall, x = 0 = x2 (say)\n", + "x2 = 0\n", + "a = -5500*0\n", + "print \"So there is no heat flow at other surface of the wall \"\n", + "\n", + "#(c)\n", + "A = 1 \t\t\t#m**2, area\n", + "Vw = A*x1 \t\t\t#m**3, volume of wall\n", + "HL = h*(T1-Ta) \t\t\t#W, heat loss from unit area\n", + "Vav = HL/x1\n", + "print \"average volumetric rate of heat generation is %.0f W/m**3\"%(Vav)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4 Page No : 61" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rate of heat loss is 150.9 W\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math\n", + "# Variables\n", + "id_ = 97.*10**-3 \t\t\t#m,internal diameter of steam pipe\n", + "od = 114.*10**-3 \t\t\t#m,outer diameter of steam pipe\n", + "pr = 30. \t\t\t#bar, absolute pressure os saturated steam\n", + "Ti = 234. \t\t\t#C, temp. at 30 bar absolute pressure\n", + "Ts = 55. \t\t\t#C, skin temp.\n", + "To = 30. \t\t\t#C, ambient temp.\n", + "kc = 0.1 \t\t\t#W/m C, thermal conductivity of wool\n", + "kw = 43. \t\t\t#W/m C, thermal conductivity of pipe\n", + "h = 8. \t\t\t#W/m**2 C, external air film coefficient \n", + "L = 1. \t\t\t#m, assume length\n", + "\n", + "#Calculation\n", + "ri = id_/2 \t\t\t#m, \n", + "r1 = (114.*10**-3)/2 \t\t\t#m,outer radius of steam pipe\n", + "\n", + "#thermal resistance of insulation\n", + "#Ri = math.log(ro/r1)/(2*math.pi*L*kc)\n", + "#Thermal resistance of pipe wall\n", + "Rp = math.log(r1/ri)/(2*math.pi*L*kw)\n", + "#RT = Ri+Rp\n", + "DF = Ti-Ts \t\t\t#C, driving force\n", + "#At steady state the rate of heat flow through the insulation\n", + "# and the outer air film are equ\n", + "\n", + "#by trial and error method :\n", + "def f(ro): \n", + " return (Ti-Ts)/(math.log(ro/r1)/kc+math.log(r1/ri)/kw)-(h*ro*(Ts-To))\n", + "ro = fsolve(f,0.1)\n", + "th = ro-r1 \t\t\t#m, required thickness of insulation\n", + "Q = 2*math.pi*ro*h*L*(Ts-To)\n", + "\n", + "# Results\n", + "print \"The rate of heat loss is %.1f W\"%(Q)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5 Page No : 62" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "effective thickness of air is 0.75 mm\n", + "effective thickness of liquid films is 2.6 mm.\n", + "the overall heat transfer coefficient based on i.d of pipe is 2.707 W/m**2 C\n", + "the overall heat transfer coefficient based on od of pipe is 1.025 W/m**2 C\n", + "the percentage of total resistance offered by air film. is 10.25 percent\n", + "Rate of heat loss is 21.2 W\n", + "insulation skin temp.is 32.8 C\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "w1 = 8. \t\t\t#%, solubility of alcohol\n", + "w2 = 92. \t\t\t#%, solubility of water\n", + "k1 = 0.155 \t\t\t#W/m C, thermal conductivity of alcohol\n", + "k2 = 0.67 \t\t\t#W/m C thermal conductivity of water\n", + "ka = 0.0263 \t\t\t#W/m C thermal conductivity of air\n", + "kw = 45. \t\t\t#W/m Cthermal conductivity of pipe wall\n", + "ki = 0.068 \t\t\t#W/m C , thermal cond. of glass\n", + "id_ = 53.*10**-3 \t\t\t#m, internal diameter of pipe\n", + "od = 60.*10**-3 \t\t\t#m, outer diameter of pipe\n", + "t = 0.04 \t\t\t#m, thickness of insulation\n", + "hi = 800. \t\t\t#W/m**2 C, liquid film coefficient\n", + "ho = 10. \t\t\t#W/m**2 C, air film coefficient\n", + "L = 1. \t\t\t#m, length of pipe\n", + "T1 = 75. \t\t\t#C, initial temp.\n", + "T2 = 28. \t\t\t#C, ambient air temp.\n", + "\n", + "# Calculations and Results\n", + "#(a)\n", + "km = (w1/100)*k1+(w2/100)*k2-0.72*(w1/100)*(w2/100)*(-(k1-k2))\n", + "deli = km/hi \t\t\t#m, effective thickness of liquid film\n", + "delo = ka/ho \t\t\t#m, effective thickness of air film\n", + "print \"effective thickness of air is %.2f mm\"%(deli*10**3)\n", + "print \"effective thickness of liquid films is %.1f mm.\"%(delo*10**3)\n", + "\n", + "#(b)\n", + "Ai = 2*math.pi*id_/2*L \t\t\t#m**2, inside area\n", + "ri = id_/2 \t\t\t#m,inside radius of pipe\n", + "r_ = od/2 \t\t\t#m, outside radius of pipe\n", + "ro = r_+t \t \t\t#m, outer radius of insulation\n", + "Ao = 2*math.pi*ro*L \t\t \t#m**2, outer area\n", + "#from eq. 3.11, overall heat transfer coefficient\n", + "Ui = 1/(1/hi+(Ai*math.log(r_/ri))/(2*math.pi*L*kw)+(Ai*math.log(ro/r_))/(2*math.pi*L*ki)+Ai/(Ao*ho))\n", + "print \"the overall heat transfer coefficient based on i.d of pipe is %.3f W/m**2 C\"%(Ui)\n", + "\n", + "#(c)\n", + "#frim eq. 3.14\n", + "Uo = Ui*Ai/Ao \n", + "print \"the overall heat transfer coefficient based on od of pipe is %.3f W/m**2 C\"%(Uo)\n", + "\n", + "#(d)\n", + "R = 1/(Ui*Ai) \t\t\t#C/W, total heat transfer resistance\n", + "Rair = 1/(Ao*ho) \t\t\t#C/W, heat transfer resistance of air film\n", + "p = Rair/R\n", + "print \"the percentage of total resistance offered by air film. is %.2f percent\"%(p*100)\n", + "\n", + "#(e)\n", + "Q = Ui*Ai*(T1-T2)\n", + "print \"Rate of heat loss is %.1f W\"%(Q)\n", + "\n", + "#(f)\n", + "Ts = Uo*Ao*(T1-T2)/(ho*Ao)+T2\n", + "print \"insulation skin temp.is %.1f C\"%(Ts)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6 Page No : 64" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Inlet liquid temp. should be 82 C \n", + " the insulation skin temp. at the flat top surface is 35 C \n", + "similarly the insulation skin temp at cylindrical surface is 38 C\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "id_ = 1.5 \t\t\t#m, internal diameter of math.tank\n", + "h = 2.5 \t\t\t#m, height of math.tank\n", + "t1 = 0.006 \t\t\t#m, thickness of wall\n", + "t2 = 0.04 \t\t\t#m, thickness of insulation\n", + "Ta = 25. \t\t\t#C, ambient temp.\n", + "T1 = 80. \t\t\t#C, outlet temp. of liquid\n", + "cp = 2000. \t\t\t#j/kg C, specific heat of liquid\n", + "FR = 700./3600 \t\t\t#KG/s, Liquid flow rate\n", + "\n", + "# Calculations and Results\n", + "ri = id_/2+t1 \t\t\t#m, inner radius of insulation\n", + "ro = ri+t2 \t\t\t#m, outer radius of insulation\n", + "ki = 0.05 \t\t\t#W/m C, thermal conductivity of insulation\n", + "hc = 4 \t\t\t#W/m**2 C, heat transfer coefficient at cylindrical surface\n", + "ht = 5.5 \t\t\t#W/m**2 C, heat transfer coefficient at flat surface\n", + "l = h+t1+t2 \t\t\t#m, height of the top of insulation\n", + "#fromm eq. 3.10\n", + "#heat transfer resistance of cylindrical wall\n", + "Rc = math.log(ro/ri)/(2*math.pi*l*ki)+1/(2*math.pi*ro*l*hc)\n", + "#heat transfer resistance of flat insulated top surface\n", + "Ri = (1/(math.pi*ro**2))*((ro-ri)/ki+1/ht)\n", + "tdf = T1-Ta \t\t\t#C, temp. driving force\n", + "Q = tdf/Rc + tdf/Ri \t\t\t#W, total rate of heat loss\n", + "Tt = Q/(FR*cp)+T1 \t\t\t#C, inlet temp. of liquid\n", + "print \"Inlet liquid temp. should be %.0f C \"%(Tt)\n", + "Q1 = tdf/Ri \t\t\t#W, rate of heat loss from flat surface\n", + "T1 = Q1/(math.pi*ro**2*ht)+Ta \n", + "print \" the insulation skin temp. at the flat top surface is %.0f C \"%(T1)\n", + "#similarly\n", + "T2 = 38\n", + "print \"similarly the insulation skin temp at cylindrical surface is %.0f C\"%(T2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.7 Page No : 66" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the heat imput to the boiling.is 191.2 W\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "id_ = 2.5*10**-2 \t\t\t#m, internal diameter of glass tube\n", + "t = 0.3*10**-2 \t\t\t#m, thickness of wall\n", + "l = 2.5 \t\t\t#m, length of nichrome wire\n", + "L = 0.12 \t\t\t#m, length of steel covered with heating coil\n", + "Re = 16.7 \t\t\t#ohm, electrical resistance\n", + "ti = 2.5*10**-2 \t\t\t#m, thickness of layer of insulation\n", + "kg = 1.4 \t\t\t#W/m C, thermal conductivity of glass\n", + "ki = 0.041 \t\t\t#W/m C, thermal conductivity of insulation\n", + "T1 = 91. \t\t\t#C, boiling temp. of liquid\n", + "T2 = 27. \t\t\t#C, ambient temp.\n", + "ho = 5.8 \t\t\t#W/m **2 C outside air film coefficient\n", + "V = 90. \t\t\t#V, voltage\n", + "\n", + "#Calculation\n", + "Rc = Re*l \t\t\t#ohm, resistance of heating coil\n", + "Q = V**2/Rc \t\t\t#W, rate of heat generation\n", + "ri = id_/2 \t\t\t#m, inner radius of glass tube\n", + "r_ = ri+t \t\t\t#m, outer radius of glass tube\n", + "ro = r_+ti \t\t\t#m,outer radius of insulation\n", + "#heat transfer resistance of glass wall\n", + "Rg = math.log(r_/ri)/(2*math.pi*L*kg)\n", + "#combined resistance of insulation and outer air film\n", + "Rt = math.log(ro/r_)/(2*math.pi*L*ki)+1/(2*math.pi*ro*L*ho)\n", + "#Rate of heat input to the boiling liquid in steel = Q1 = (Ts-T1)/Rg\n", + "#Rate of heat loss through insulation ,Q2 = (Ts-To)/(Rt)\n", + "#Q1+Q2 = Q\n", + "Ts = (Q+ T1/Rg +T2/Rt)/(1/Rg +1/Rt)\n", + "Q1 = (Ts-T1)/Rg\n", + "Q2 = Q-Q1\n", + "\n", + "# Results\n", + "print \"the heat imput to the boiling.is %.1f W\"%(Q1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.8 Page No : 68" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "maximum allowable current is 54.04 A\n", + "remp. at the centre of wire is 90.005 C\n", + "The temprature at the outer surface of insulation is 80.3 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "ri = 1.3*10**-3 \t\t\t#m, radius of 10 gauge wire\n", + "t = 1.3*10**-3 \t\t\t#m, thickness of rubber insulation\n", + "Ti = 90. \t\t\t#C, temp. 0f insulation\n", + "To = 30. \t\t\t#C, ambient temp.\n", + "h = 15. \t\t\t#W/m**2 C, air film coefficient\n", + "km = 380. \t\t\t#W/m C, thermal cond. of copper\n", + "kc = 0.14 \t\t\t#W/m C, thermal cond. of rubber(insulation)\n", + "Rc = 0.422/100 \t\t\t#ohm/m, eletrical resistance of copper wire\n", + "\n", + "# Calculations and Results\n", + "Tcmax = 90. \t\t\t#X, the maximum temp. in insulation\n", + "ro = ri+t \t\t\t#m, outside radius of 10 gauge wire\n", + "Sv = ((Tcmax-To)*(2*kc/ri**2))/(math.log(ro/ri)+kc/(h*ro))\n", + "I = (math.pi*ri**2*Sv/Rc)**0.5 \t\t\t#A, Current strength\n", + "print \"maximum allowable current is %.2f A\"%(I)\n", + "\n", + "#(b) at r = 0\n", + "Tm = To+(ri**2*Sv/2)*(1/km+(math.log(ro/ri))/kc+1/(h*ro))\n", + "print \"remp. at the centre of wire is %.3f C\"%(Tm)\n", + "\n", + "#at r = ro\n", + "Tc = 30+(ri**2*Sv/(2*kc))*(kc/(h*ro))\n", + "print \"The temprature at the outer surface of insulation is %.1f C\"%(Tc)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.9 Page No : 72" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "At x = 0.1 the temp. at the surface of slab A is 430 C\n", + "At x = 0.35 the temp. at the surface of slab A is 318 C\n", + " the maximum Temp. in A occurs at 0.2045 m\n", + " the maximum Temp. in A is 550.2 TAmax \n", + "temp. gradient at interface 2 of the slabs A is 2300 C/W\n", + "temp. gradient at interface 3 of the slabs A is -3200 C/W\n", + "temp. gradient at interface 2 of the slabs B is 3450 C/W\n", + "temp. gradient at interface 1 of the slabs B is 3450 C/W\n", + "temp. gradient at interface 3 of the slabs C is -1600 C/W\n", + "temp. gradient at interface 4 of the slabs C is -1600 C/W\n", + "The heat transfer coefficient at one surface of solid fluid interface is 766.7 W/m**2 C\n", + "The heat transfer coefficient at other surface of solid fluid interface is 1129 W/m**2 C\n" + ] + } + ], + "source": [ + "# Variables\n", + "tA = 0.25 \t\t\t#m, thickness of slab A\n", + "tB = 0.1 \t\t\t#m, thickness of slab B\n", + "tC = 0.15 \t\t\t#m, thickness of slab C\n", + "kA = 15. \t\t\t#W/m C, thermal comductivity of slab A\n", + "kB = 10. \t\t\t#W/m C, thermal comductivity of slab B\n", + "kC = 30. \t\t\t#W/m C, thermal comductivity of slab C\n", + "#Temprature distribution in slab A\n", + "T1 = 40. \t\t\t#C, fluid temp.\n", + "T2 = 35. \t\t\t#C, medium temp.\n", + "\n", + "# Calculations and Results\n", + "#(a)\n", + "x1 = tB \n", + "TA1 = 90.+4500*x1-11000*x1**2\n", + "#similarly at the right surface\n", + "x2 = tA+tB\n", + "TA2 = 90.+4500*x2-11000*x2**2\n", + "#let dTA/dx = D\n", + "D = 0 \t\t\t#for maximum temp.\n", + "x3 = 4500./22000\n", + "TAmax = 90.+4500*x3-11000*x3**2\n", + "print \"At x = 0.1 the temp. at the surface of slab A is %.0f C\"%(TA1)\n", + "print \"At x = 0.35 the temp. at the surface of slab A is %.0f C\"%(TA2)\n", + "print \" the maximum Temp. in A occurs at %.4f m\"%(x3)\n", + "print \" the maximum Temp. in A is %.1f TAmax \"%(TAmax)\n", + "\n", + "#(b)\n", + "#At the interface 2\n", + "D1 = 4500-2.*11000*x1 \t\t\t#C/W, D1 = dTA/dx, at x = 0.1\n", + "#At the interface 3\n", + "D2 = 4500-2.*11000*x2 \t\t\t#D12 = dTA/dx, at x = 0.35\n", + "#Temprature gradient in slab B and C\n", + "#by umath.sing the continuity of heat flux at interface (2)\n", + "D3 = -kA*D1/(-kB) \t\t\t#D3 = dTB/dx, at x = 0.1\n", + "#at interface (1)\n", + "D4 = D3 \t\t\t#D4 = dTB/dx at x = 0\n", + "#similarly \n", + "D5 = -1600. \t\t\t#C/W, dTB/dx, x = 0.35\n", + "D6 = D5 \t\t\t#at interface 4\n", + "print \"temp. gradient at interface 2 of the slabs A is %.0f C/W\"%(D1)\n", + "print \"temp. gradient at interface 3 of the slabs A is %.0f C/W\"%(D2)\n", + "print \"temp. gradient at interface 2 of the slabs B is %.0f C/W\"%(D3)\n", + "print \"temp. gradient at interface 1 of the slabs B is %.0f C/W\"%(D4)\n", + "print \"temp. gradient at interface 3 of the slabs C is %.0f C/W\"%(D5)\n", + "print \"temp. gradient at interface 4 of the slabs C is %.0f C/W\"%(D6)\n", + "\n", + "#(c)\n", + "#from D3 = 3450 and TB = beeta1*x+beeta2\n", + "beeta1 = 3450.\n", + "beeta2 = 85.\n", + "x = 0.\n", + "TB = beeta1*x+beeta2\n", + "#similary\n", + "TC = 877.5-1600*x\n", + "h1 = -kB*D4/(T1-TB)\n", + "#similarly\n", + "h2 = 1129.\n", + "print \"The heat transfer coefficient at one surface of solid fluid interface is %.1f W/m**2 C\"%(h1)\n", + "print \"The heat transfer coefficient at other surface of solid fluid interface is %.0f W/m**2 C\"%(h2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.10 Page No : 79" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the percentage increase in the rate of heat transfer is 103.6 percent \n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "id_ = 78.*10**-3 \t\t\t#m, actual internal dia of pipe\n", + "tw = 5.5*10**-3 \t\t\t#m, wall thickness\n", + "nl = 8. \t\t\t#no. of longitudinal fins\n", + "tf = 1.5*10**-3 \t\t\t#m, thickness of fin\n", + "w = 30.*10**-3 \t\t\t#m,breadth of fin\n", + "kf = 45. \t\t\t#W/m C, thermal conductivity of fin \n", + "Tw = 150. \t\t\t#C, wall temp.\n", + "To = 28. \t\t\t#C, ambient temp.\n", + "h = 75. \t\t\t#W/m**2C, surface heat transfer coefficient\n", + "\n", + "#Calculation\n", + "#from eq. 3.27\n", + "e = math.sqrt(2*h/(kf*tf)) \n", + "n = (1./(e*w))*math.tanh(e*w) \t\t\t#efficiency of fin\n", + "L = 1. \t\t\t#m, length of fin\n", + "Af = 2.*L*w \t\t\t#m**2, area of math.single fin\n", + "Atf = nl*Af \t\t\t#m**2 total area of fin\n", + "Qmax = h*Atf*(Tw-To) \t\t\t#W, maximum rate of heat transfer\n", + "Qa = n*Qmax \t\t\t#W, actual rate of heat transfer\n", + "Afw = L*tf \t\t\t#m**2, area of contact of fin with pipe wall\n", + "Atfw = Afw*nl \t\t\t#m**2 , area of contact of all fin with pipe wall\n", + "ro = id_/2+tw \t\t\t#m, outer pipe radius\n", + "A = 2*math.pi*L*ro \t\t\t#m**2 area per meter\n", + "Afree = A-Atfw \t\t\t#m**2, free outside area of finned pipe\n", + "#Rate of heat transfer from free area of pipe wall\n", + "Q1 = h*Afree*(Tw-To) \t\t\t#W, \n", + "#total rate of hewat gtransfer from finned pipe\n", + "Qtotal = Qa+Q1 \t\t\t#W\n", + "#Rate of heat transfer fromm unfinned pipe\n", + "Q2 = h*A*(Tw-To)\n", + "per = (Qtotal-Q2)/Q2\n", + "\n", + "# Results\n", + "print \"the percentage increase in the rate of heat transfer is %.1f percent \"%(per*100)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.11 Page No : 80" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rate of heat transfer in the absence of contact resistance is 11.585 KW\n", + "The actual rate of heat loss is 5.18kW is much less than this value. So there is a thermal contact resistance at the interface between the layers \n", + "The contact resistance is 0.001067 C/W \n", + "contact heat transfer coefficient is 298.2 W/m**2 C \n", + "The temprature jump is 5.5 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "id_ = 90.*10**-2 \t\t\t#m, internal diameter of steel\n", + "od = 110.*10**-2 \t\t\t#m, outer diameter of steel\n", + "Ti = 180. \t\t\t#C, inside temp. of steel\n", + "To = 170. \t\t\t#C, outside temp. of steel\n", + "k = 37. \t\t\t#W/m C, thermal conductivity of alloy\n", + "Q = 5.18*10**3 \t\t\t#W, Rate of heat loss\n", + "\n", + "# Calculations and Results\n", + "ri = id_/2 \t\t\t#m, inside radius of shell\n", + "ro = od/2 \t\t\t#m, outside radius of shell\n", + "r_ = 0.5 \t\t\t#m, boundary between the layers\n", + "L = 1 \t\t\t#m, length of shell\n", + "#Rate of heat transfer in the absence of contact resistance\n", + "Q1 = 2*math.pi*L*k*(Ti-To)/(math.log(ro/ri)) \n", + "print \"Rate of heat transfer in the absence of contact resistance is %.3f KW\"%(Q1/1000)\n", + "print \"The actual rate of heat loss is 5.18kW is much less than this value\\\n", + ". So there is a thermal contact resistance at the interface between the layers \"\n", + "\n", + "#(b)\n", + "Ri = (math.log(r_/ri)/(2*math.pi*L*k)) \t\t\t#C/W, resistance of inner layer\n", + "Ro = (math.log(ro/r_)/(2*math.pi*L*k)) \t\t\t#C/W, resistance of outer layer\n", + "Rc = ((Ti-To)/(Q))-(Ri+Ro) \t\t\t#C/W, contact resistance\n", + "print \"The contact resistance is %f C/W \"%(Rc)\n", + "Ac = 2*math.pi*L*r_ \t\t\t#m**2, area of contact surface of shell\n", + "hc = 1/(Ac*Rc) \t\t\t #W/m**2 c, contact heat transfer coefficient\n", + "print \"contact heat transfer coefficient is %.1f W/m**2 C \"%(hc)\n", + "\n", + "#(c)\n", + "dt = Q/(hc*Ac)\n", + "print \"The temprature jump is %.1f C\"%(dt)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.12 Page No : 84" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the critical thickness is 35.29 mm\n" + ] + } + ], + "source": [ + "# Variables\n", + "d = 5.2*10**-3 \t\t\t#m, diameter of copper wire\n", + "ri = d/2 \t\t\t#inner radius of insulation\n", + "kc = 0.43 \t\t\t#W/m C, thermal conductivity of PVC\n", + "Tw = 60. \t\t\t#C, temp. 0f wire\n", + "h = 11.35 \t\t\t#W/m**2 C, film coefficient\n", + "To = 21. \t\t\t#C, ambient temp.\n", + "\n", + "#calculation\n", + "Ro = kc/h \t\t\t#m,critical outer radius of insulation\n", + "t = Ro-ri\n", + "\n", + "# Results\n", + "print \"the critical thickness is %.2f mm\"%(t*10**3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.13 Page No : 85" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ro = 3.5 cm \n", + "Radius of bare pipe is larger than outer radius of insulation So critical insulation thickness does not exist \n" + ] + } + ], + "source": [ + "# calculate the critical insulation thickness.\n", + "\n", + "# Variables\n", + "d = 15.*10**-2 \t\t\t#m, length of steam main\n", + "t = 10.*10**-2 \t\t\t#m, thickness of insulation\n", + "ki = 0.035 \t\t\t#W/m C, thermal conductivity of insulation\n", + "h = 10. \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "#calculation\n", + "#from eq. 3.29\n", + "ro = ki/h\n", + "\n", + "# Results\n", + "print \"ro = %.1f cm \"%(ro*10**3)\n", + "print \"Radius of bare pipe is larger than outer radius of insulation So critical \\\n", + " insulation thickness does not exist \"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.14 Page No : 87" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The optimum insulation thickness is 71 mm\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve\n", + "import math\n", + "\n", + "# Variables\n", + "Ti = 172. \t\t\t#C, saturation temp.\n", + "To = 20. \t\t\t#C, ambient temp.\n", + "Cs = 700. \t\t\t#per ton, math.cost of steam\n", + "Lv = 487. \t\t\t#kcal/kg, latent heat of steam\n", + "ho = 10.32 \t\t\t#kcal/h m**2 C, outer heat transfer coefficient\n", + "kc = 0.031 \t\t\t#W/m C, thermal conductivity of insulation\n", + "n = 5. \t\t\t#yr, service life of insulation\n", + "i = 0.18 \t\t\t#Re/(yr)(Re), interest rate\n", + "\n", + "#Calculation\n", + "di = 0.168 \t\t\t#m, inner diameter of insulation\n", + "#Cost of insulation\n", + "Ci = 17360.-(1.91*10**4)*di \t\t\t#Rs/m**3\n", + "Ch = Cs/(1000*Lv) \t\t\t#Rs/cal, math.cost of heat energy in steam\n", + "sm = 1./(1+i)+1/(1+i)**2+1/(1+i)**3+1/(1+i)**4+1/(1+i)**n\n", + "#from eq. 3.33\n", + "ri = di/2 \t\t\t#m inner radius of insulation\n", + "L = 1 \t\t\t#m, length of pipe\n", + "#Pt = Ch*sm*2*math.pi*ri*L*( 1/(((ri/kc)*('math.log(ro/ri)'))+ri/(ho*ro)))*7.2*10**3*(Ti-To)+math.pi*(ro**2-ri**2)*L*Ci\n", + "#On differentiating , dpt/dro = -957.7*((1/ro)-(0.003/ro**2))/(math.log(ro)+(0.003/ro)+2.477)**2\n", + "def f(ro): \n", + " return -957.7*((1/ro)-(0.003/ro**2))/(math.log(ro)+(0.003/ro)+2.477)**2+98960*ro\n", + "ro = fsolve(f,0.1)\n", + "t = ro-ri\n", + "\n", + "# Results\n", + "print \"The optimum insulation thickness is %.0f mm\"%(t*1000)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch4.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch4.ipynb new file mode 100644 index 00000000..38ba4576 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch4.ipynb @@ -0,0 +1,771 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4 : Forced Convection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2 Page No : 112" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rate of heat loss is 5328 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "l = 2. \t\t\t#m, length of flat surface\n", + "T1 = 150. \t\t\t#C, surface temp.\n", + "p = 1. \t\t\t#atm, pressure\n", + "T2 = 30. \t\t\t#C, bulk air temp.\n", + "V = 12. \t\t\t#m/s, air velocity\n", + "\n", + "#Calculation\n", + "Tf = (T1+T2)/2 \t\t\t#C, mean air film temp.\n", + "mu = 2.131*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.031 \t\t\t#W/m C, thermal conductivity\n", + "rho = 0.962 \t\t\t#kg/m**3, density of air\n", + "cp = 1.01 \t\t\t#kj/kg C, specific heat of air\n", + "Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n", + "Remax = l*V*rho/mu \t\t\t#maximum Reynold no.\n", + "Re = 5.*10**5 \t\t\t#Reynold no. during transition to turbulent flow \n", + "L_ = (Re*mu)/(V*rho) \t\t\t#m,dismath.tance from the leading edge\n", + "#for laminar flow heat transfer coefficient h, \n", + "#h16.707*x**-(1/2)\n", + "#(a)\n", + "#h2 = 31.4*x**(-1/5)\n", + "#b\n", + "hav = 22.2\n", + "#c\n", + "Q = hav*l*p*(T1-T2)\n", + "\n", + "# Results\n", + "print \"The rate of heat loss is %.0f W\"%(Q)\n", + "\n", + "# rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3 Page No : 114" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The steady state temprature is 230 C\n", + "The recalculated value is almost equal to previous one.\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "d = 7.24*10**-4 \t\t\t#m, diameter of wire\n", + "l = 1. \t\t\t#m, length of wire\n", + "I = 8.3 \t\t\t#A, current in a wire\n", + "R = 2.625 \t\t\t#ohm/m, electrical resistance\n", + "V = 10. \t\t\t#m/s, air velocity\n", + "Tb = 27. \t\t\t#C, bulk air temp.\n", + "#the properties at bulk temp.\n", + "mu = 1.983*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.02624 \t\t\t#W/m C, thermal conductivity\n", + "rho = 1.1774 \t\t\t#kg/m**3, density of air\n", + "cp = 1.0057 \t\t\t#kj/kg C, specific heat of air\n", + "\n", + "# Calculations and Results\n", + "Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n", + "Re = d*V*rho/mu \t\t\t# Reynold no.\n", + "#from eq. 4.19, nusslet no.\n", + "Nu = 0.3+(0.62*Re**(1./2)*Pr**(1./3)/(1+(0.4/Pr)**(2./3))**(1./4))*(1+(Re/(2.82*10**5))**(5./8))**(4./5)\n", + "hav = Nu*k/d \t\t\t#W/m**2 C, average heat transfer coefficient\n", + "Q = I**2*R \t\t\t#W, rate of electrical heat generation\n", + "A = math.pi*d*l\n", + "dt = Q/(hav*A) \t\t\t#C,temp. difference\n", + "T = dt+Tb \t\t\t#C, steady state temp.\n", + "print \"The steady state temprature is %.0f C\"%(T)\n", + "\n", + "Tm = (T+Tb)/2 \t\t\t#C, mean air film temp.\n", + "#the properties at Tm temp.\n", + "mu1 = 2.30*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "k1 = 0.0338 \t\t\t#W/m C, thermal conductivity\n", + "rho1 = 0.878 \t\t\t#kg/m**3, density of air\n", + "cp1 = 1.014 \t\t\t#kj/kg C, specific heat of air\n", + "Re1 = d*V*rho1/mu1 \t\t\t# Reynold no.\n", + "Pr1 = (1.014*10**3*2.30*10**-5)/k1 \t\t\t#Prandtl no.\n", + "#from eq. 4.19, nusslet no.\n", + "Nu1 = 0.3+(0.62*Re1**(1./2)*Pr1**(1./3)/(1+(0.4/Pr1)**(2./3))**(1./4))*(1+(Re1/(2.82*10**5))**(5./8))**(4./5)\n", + "hav1 = Nu1*k1/d \t\t\t#W/m**2 C, average heat transfer coefficient\n", + "dt1 = Q/(hav1*A) \t\t\t#C,temp. difference\n", + "T1 = dt1+Tb \t\t\t#C, steady state temp.\n", + "print \"The recalculated value is almost equal to previous one.\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4 Page No : 116" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "initial rate of melting of ice is 0.0109 g/s\n", + "The required time is is 1665 s\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "di = 0.04 \t\t\t#m, diameter of ice ball\n", + "V = 2. \t\t\t#m/s, air velocity\n", + "T1 = 25. \t\t\t#C, steam temp.\n", + "T2 = 0.\n", + "#the properties of air\n", + "mu = 1.69*10**-5 \t\t\t#kg/ms, vismath.cosity\n", + "k = 0.026 \t\t\t#W/m C, thermal conductivity\n", + "rho = 1.248 \t\t\t#kg/m**3, density \n", + "cp = 1.005 \t\t\t#kj/kg C, specific heat \n", + "#propertice of ice\n", + "lamda = 334. \t\t\t#kj/kg, heat of fusion\n", + "rhoice = 920. \t\t\t#kg/m**3 density of ice\n", + "\n", + "# Calculations and Results\n", + "Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n", + "Re = di*V*rho/mu \t\t\t# Reynold no.\n", + "#from eq. 4.19, nusslet no.\n", + "Nu = 2+(0.4*Re**0.5+0.06*Re**(2./3))*Pr**0.4\n", + "hav = Nu*k/di \t\t\t#W/m**2 C, average heat transfer coefficient\n", + "Ai = math.pi*di**2 \t\t\t#initial area of sphere\n", + "Qi = Ai*hav*(T1-T2) \t\t\t#W = J/s, initial rate of heat transfer\n", + "Ri = Qi/lamda \t\t\t#initial rate of melting of ice\n", + "print \"initial rate of melting of ice is %.4f g/s\"%(Ri)\n", + "\n", + "#(b)\n", + "#mass of ice ball 4/3*math.pi*r**3\n", + "#Rate of melting = Rm = -d/dt(m)\n", + "#Rate of heat input required = -lamda*Rate of melting\n", + "#heat balance equation\n", + "# -lamda*(Rm) = h*4*math.pi*r**2*dt\n", + "#integrating and solving\n", + "rf = ((di/2)**3/2.)**(1./3)\n", + "#solving eq. 3\n", + "t1 = 1.355*10**-4/(8.136*10**-8)\n", + "print \"The required time is is %.0f s\"%(t1)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5 Page No : 121" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the required contact time is 1.43 s\n" + ] + } + ], + "source": [ + "from scipy.integrate import quad \n", + "# Variables\n", + "Vo = 0.5 \t\t\t#m/s air velocity\n", + "T1 = 800. \t\t\t#C, initial temp.\n", + "T2 = 550. \t\t\t#C, final temp.\n", + "Tam = 500. \t\t\t#C, air mean temp.\n", + "P = 1.2 \t\t\t#atm, pressure\n", + "#the properties of solid particles.\n", + "dp = 0.65*10**-3 \t\t\t#m, average particle diameter\n", + "cps = 0.196 \t\t\t#kcal/kg C, specific heat\n", + "rhos = 2550. \t\t\t#kg/m**3, density \n", + "#Properties of air\n", + "mu = 3.6*10**-5 \t\t\t#kg/ms, vismath.cosity\n", + "k = 0.05 \t\t\t#kcal/hm C, thermal conductivity\n", + "rho = 0.545 \t\t\t#kg/m**3, density of air\n", + "cp = 0.263 \t\t\t#kcal/kg C, specific heat of air\n", + "\n", + "#calculation\n", + "Pr = cp*mu*3600/k \t\t\t#Prandtl no.\n", + "Redp = dp*Vo*rho/mu \t\t\t# Reynold no.\n", + "#from eq. 4.29(b) heat transfer coefficient\n", + "h = (k/dp)*(2+0.6*(Redp)**(1./2)*(Pr)**(1./3))\n", + "Tg = 500 \t\t\t#C, gas temp.\n", + "#from heat balance equation\n", + "# -(dTs/dt) = 6h/(dp*rhos*cps)*(Ts-Tg)\n", + "\n", + "def f2(Ts): \n", + " return (1/(Ts-Tg))\n", + "\n", + "t = (dp*rhos*cps/(6*h))* quad(f2,550,800)[0]\n", + "\n", + "# Results\n", + "print \"the required contact time is %.2f s\"%(t*3600)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6 Page No : 126" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the required rate of flow of water is 1053 kg/h \n", + "the overall heat transfer coefficient is 300 W/m**2 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "mo_ = 1000. \t\t\t#kg/h, cooling rate of oil\n", + "cpo = 2.05 \t\t\t#kj/kg C, specific heat of oil\n", + "T1 = 70. \t\t\t#C, initial temp. of oil\n", + "T2 = 40. \t\t\t#C, temp. of oil after cooling\n", + "cpw = 4.17 \t\t\t#kj/kg C, specific heat of water\n", + "T3 = 42. \t\t\t#C, initial temp. of water\n", + "T4 = 28. \t\t\t#C, temp. of oil after cooling\n", + "A = 3. \t\t\t#m**2, heat exchange area\n", + "\n", + "# Calculation and Results\n", + "mw_ = mo_*cpo*(T1-T2)/(cpw*(T3-T4))\n", + "print \"the required rate of flow of water is %.0f kg/h \"%(mw_)\n", + "Q = mo_*cpo*(T1-T2)/3600 \t\t\t#kw, heat duty\n", + "dt1 = T1-T3 \t\t\t#C, hot end temp. difference\n", + "dt2 = T2-T4 \t\t\t#C, cold end temp. difference\n", + "LMTD = (dt1-dt2)/(math.log(dt1/dt2)) \t\t\t#math.log mean temp. difference\n", + "dtm = LMTD\n", + "U = Q*10**3/(A*dtm)\n", + "print \"the overall heat transfer coefficient is %.0f W/m**2 C\"%(round(U,-1))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7 Page No : 126" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The inlet temprature is Ti = 26 C\n", + "The outlet temprature is To = 107 C\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math\n", + "\n", + "# Variables\n", + "Q = 38700. \t\t\t#kcal/h, heat duty\n", + "W = 2000. \t\t\t#kg/h gas flow rate\n", + "cp = 0.239 \t\t\t#kcal/kg C, specific heat of nitrogen\n", + "A = 10. \t\t\t#m**2 ,heat exchanger area\n", + "U = 70. \t\t\t#kcal/hm**2 C, overall heat transfer coefficient\n", + "n = 0.63 \t\t\t#fin efficiency\n", + "\n", + "#Calculation\n", + "dt = Q/(W*cp) \t\t\t#C, temp. difference\n", + "#To-Ti = dt.........................(i)\n", + "dtm = Q/(U*A*n)\n", + "#(To-Ti)/(math.log((160-Ti)/(160-To))) = 87.8........(2)\n", + "#solving 1 and 2\n", + "def f(To): \n", + " return (To-(To-dt))/(math.log((160-(To-dt))/(160-To)))-87.8\n", + "\n", + "To = fsolve(f,100)\n", + "Ti = To-dt\n", + "\n", + "# Results\n", + "print \"The inlet temprature is Ti = %.0f C\"%(Ti)\n", + "print \"The outlet temprature is To = %.0f C\"%(To)\n", + "\n", + "# note : answers are slightly different because of fsolve function of python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.8 Page No : 127" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The outlet eater temp. is 109.8 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "V = 1.8 \t\t\t#m/s, velocity of hot water\n", + "T1 = 110. \t\t\t#C, initial temp.\n", + "l = 15. \t\t\t#m, length of pipe\n", + "t = 0.02 \t\t\t#m, thickness of insulation\n", + "kc = 0.12 \t\t\t#W/mC,thermal conductivity of insulating layer\n", + "ho = 10. \t\t\t#Wm**2 C, outside film coefficient\n", + "T2 = 20. \t\t\t#C, ambient temp.\n", + "#the properties of water at 110 C\n", + "mu = 2.55*10**-4 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.685 \t\t\t#W/m C, thermal conductivity\n", + "rho = 950. \t\t\t#kg/m**3, density of air\n", + "cp = 4.23 \t\t\t#kj/kg C, specific heat of air\n", + "di = 0.035 \t\t\t#m, actual internal dia. of pipe\n", + "ri = di/2. \t\t\t#m,internal radius\n", + "t1 = 0.0036 \t\t\t#m, actual thickness of 1-1/4 schedule 40 pipe\n", + "ro = ri+t1 \t\t\t#m, outer radius of pipe\n", + "r_ = ro+t \t\t\t#m, outer radius of insulation\n", + "kw = 43. \t\t\t#W/mC, thermal conductivity of steel\n", + "\n", + "#calculation\n", + "Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n", + "Re = di*V*rho/mu \t\t\t# Reynold no.\n", + "#from eq. 4.9, Nusslet no.\n", + "Nu = 0.023*(Re)**0.88*Pr**0.3\n", + "hi = Nu*k/di \t\t\t#W/m**2 C, average heat transfer coefficient\n", + "#the overall coefficient inside area basis Ui\n", + "Ui = 1./(1/hi+(ri*math.log(ro/ri))/kw+(ri*math.log(r_/ro))/kc+ri/(r_*ho)) \n", + "Ai = math.pi*di*l \t\t\t#m**2, inside area basis\n", + "W = math.pi*ri**2*V*rho \t\t\t#kg/s, water flow rate\n", + "#from the relation b/w LMTD and rate of heat loss\n", + "\n", + "def f(To): \n", + " return (W*cp*10**3)/(Ui*Ai)*(T1-To)-((T1-To)/math.log((T1-T2)/(To-T2)))\n", + "To = fsolve(f,100)\n", + "\n", + "# Results\n", + "print \"The outlet eater temp. is %.1f C\"%(To)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9 Page No : 129" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The exit water temp is 36 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "T1 = 28. \t\t\t#C, inlet temp. \n", + "T2 = 250. \t\t\t#C,bulk temp.\n", + "V = 10. \t\t\t#m/s, gas velocity\n", + "l = 20. \t\t\t#m, length of pipe\n", + "mw = 1.*3600 \t\t\t#kg/h, water flow rate\n", + "di = 4.1*10**-2 \t\t\t#m, inlet diameter\n", + "Tm = (T1+T2)/2 \t\t\t#C, mean temp.\n", + "ro = 0.0484 \t\t\t#m, outside radius\n", + "#properties of water\n", + "mu = 8.6*10**-4 \t\t\t#kg/ms, vismath.cosity\n", + "kw = 0.528 \t\t\t#kcal/h m C, thermal conductivity\n", + "kw_ = 0.528*1.162 \t\t\t#W/ m C, thermal conductivity\n", + "rho = 996. \t\t\t#kg/m**3, density of air\n", + "cp = 1*4.18 \t\t\t#kj/kg C, specific heat of air\n", + "cp_ = 1. \t\t\t#kcal/kg C\n", + "#properties of flue gas\n", + "mu1 = 2.33*10**-5 \t\t\t#kg/ms, vismath.cosity\n", + "ka = 0.0292 \t\t\t#kcal/h m C, thermal conductivity\n", + "rho1 = 0.891 \t\t\t#kg/m**3, density of air\n", + "cp1 = 0.243 \t\t\t#kcal/kg C, specific heat of air\n", + "Pr = 0.69\n", + "\n", + "#calculation\n", + "A = math.pi/4*di**2 \t\t\t#m**2, cross section of pipe\n", + "Vw = 1/(rho*A) \t\t\t#m/s, velocity of warer\n", + "Re = di*Vw*rho/mu \t\t\t# Reynold no.\n", + "Pr1 = cp*10**3*mu/kw_ \t\t\t#Prandtl no. for water\n", + "Nu = 0.023*Re**0.8*Pr1**0.4 \t\t\t#Nusslet no.\n", + "#water side heat transfer coefficient hi\n", + "hi = 206*kw/di\n", + "#gas side heat transfer coefficient ho\n", + "a = 41 \t\t\t#mm, i.d. schedule\n", + "Tw = 3.7 \t\t\t#mm, wall thickness\n", + "do = a+2*Tw \t\t\t#mm, outer diameter of pipe\n", + "Re1 = do*10**-3*V*rho1/mu1 \t\t\t# Reynold no\n", + "#from eq. 4.19, nusslet no.\n", + "Nu1 = 0.3+(0.62*Re1**(1./2)*Pr**(1./3)/(1+(0.4/Pr)**(2./3))**(1/4.))*(1+(Re1/(2.82*10**5))**(5./8))**(4/5.)\n", + "ho = (Nu1*ka/do)*10**3 \t\t\t#kcal/h m**2 C\n", + "Uo = 1/(ro/(di/2*hi)+1/ho) \t\t\t#kcal/h m**2 C, overall heat transfer coefficient\n", + "\n", + "#Heat balance\n", + "A1 = math.pi*ro*l \t\t\t#m62, outside area of pipe\n", + "#from the formula of LMTD\n", + "def f(T2_): \n", + " return mw*cp_*(T2_-T1)-Uo*A1*((T2_-T1)/math.log((T2-T1)/(T2-T2_)))\n", + "T2_ = fsolve(f,1)\n", + "\n", + "# Results\n", + "print \"The exit water temp is %.0f C\"%(T2_)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.10 Page No : 131" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The tube length is 123 m\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "dti = 0.0212 \t\t\t#m inner tube\n", + "dto = 0.0254 \t\t\t#cm, outer tube\n", + "dpi = 0.035 \t\t\t#cm, outer pipe\n", + "mo_ = 500. \t\t\t#kh/h, cooling rate of oil\n", + "To2 = 110. \t\t\t#C, initial temo. of oil\n", + "To1 = 70. \t\t\t#C, temp. after cooling of oil\n", + "Tw2 = 40. \t\t\t#C, inlet temp. of water\n", + "Tw1 = 29. \t\t\t#C, outlet temp. of water\n", + "#properties of oil\n", + "cpo = 0.478 \t\t\t#kcal/kg C\n", + "ko = 0.12 \t\t\t#kcal/h m C, thermal conductivity\n", + "rho = 850. \t\t\t#kg/m**3, density of oil\n", + "#properties of water\n", + "kw = 0.542 \t\t\t#kcal/h m C, thermal conductivity\n", + "kw_ = (kw*1.162) \t\t\t#kj/kg C\n", + "muw = 7.1*10**-4 \t\t\t#kg/ms, vismath.cosity of water\n", + "cpw = 1. \t\t\t#kcal/kg C\n", + "cpw_ = cpw*4.17 \t\t\t#kcal/kg C\n", + "rhow = 1000. \t\t\t#kg/m**3, density\n", + "\n", + "#calculation\n", + "HL = mo_*cpo*(To2-To1) \t\t\t#kcal/h, heat load of exchanger\n", + "mw_ = HL/(cpw*(Tw2-Tw1)) \t\t\t#kg/h water flow rate\n", + "mw_1 = mw_/(3600*10**3) \t\t\t#m**3/s water flow rate\n", + "A1 = (math.pi/4)*(dti)**2 \t\t\t#m**2, flow area of tube\n", + "Vw = mw_1/A1 \t\t\t#m/s water velocity\n", + "Rew = dti*Vw*rhow/muw \t\t\t#Reynold no.\n", + "Prw = cpw_*10**3*muw/kw_ \t\t\t#Prandtl no.\n", + "Nuw = 0.023*Rew**0.8*Prw**0.4 \t\t\t#nusslet no.\n", + "#water side heat transfer coefficient hi\n", + "hi = Nuw*kw/dti\n", + "\n", + "#oil side heat transfer coefficient\n", + "A2 = math.pi/4*(dpi**2-dto**2) \t\t\t#m**2, flow area of annulus\n", + "Vo = mo_/(3600*rho*A2) \t\t\t#m/s velocity of oil\n", + "de = (dpi**2-dto**2)/dto \t\t\t#m, equivalent dia of annulus\n", + "Tmo = (To2+To1)/2 \t\t\t#C,mean oil temp.\n", + "muoil = math.exp((5550./(Tmo+273))-19) \t\t\t#kg/ms, vismath.cosity of oil\n", + "Reo = de*Vo*rho/muoil\n", + "Pro = cpo*muoil*3600/ko \t\t\t#prandtl no. for oil \n", + "\n", + "#assume (1st approximation)\n", + "Nuo = 3.66\n", + "ho = Nuo*ko/de \t\t\t#kcal/h m**2 c\n", + "L = 1 \t\t\t#assume length of tube\n", + "Ai = math.pi*dti*L\n", + "Ao = math.pi*dto*L\n", + "#overall heat transfer coefficient 1st approximation\n", + "Uo = 1/(1/ho+Ao/(Ai*hi))\n", + "LMTD = ((To2-Tw2)-(To1-Tw1))/(math.log((To2-Tw2)/(To1-Tw1)))\n", + "Ao1 = HL/(Uo*LMTD) \t\t\t #m**2, heat transfer area\n", + "Lt = Ao1/(math.pi*dto) \t\t\t #m, tube length\n", + "#from eq. 4.8\n", + "Nuo1 = 1.86*(Reo*Pro/(Lt/de))**(1./3) \t\t\t#Nusslet no. \n", + "ho1 = Nuo1*ko/de\n", + "Tmw = (Tw1+Tw2)/2 \t\t\t#C, mean water temp.\n", + "#balancing heat transfer rate of oil and water\n", + "\n", + "#average wall temp. Twall\n", + "Twall = ((hi*dti*(-Tmw))-(ho1*dto*Tmo))/(-65.71216)\n", + "#vismath.cosity of oil at this temp.\n", + "muwall = math.exp((5550/(Twall+273))-19) \t\t\t#kg/ms, vismath.cosity of oil\n", + "#Nusslet no. \n", + "Nuo2 = 1.86*(Reo*Pro/(Lt/de))**(1./3)*(muoil/muwall)**0.14\n", + "ho2 = Nuo2*ko/de\n", + "Uo2 = 1/((1/ho2)+(Ao/(Ai*hi)))\n", + "Ao2 = HL/(Uo2*LMTD)\n", + "Lt_ = Ao2/(math.pi*dto)\n", + "\n", + "# Results\n", + "print \"The tube length is %d m\"%(Lt_)\n", + "\n", + "# rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.11 Page No : 135" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " the rate of heat transfer to water.is 6.93e+05 kcal/h\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "Ti = 260. \t\t\t#C, initial temp.\n", + "Ts = 70. \t\t\t#C, skin temp.\n", + "St = 0.15 \t\t\t#m,space between tubes in equilateral triangular arrangement\n", + "Sd = St \t\t\t#space between tubes\n", + "mu = 4.43*10**-5 \t\t\t#m**2/s, momentum diffusity\n", + "k = 0.0375 \t\t\t#W/m C, thermal conductivity\n", + "rho = 0.73 \t\t\t#kg/m**3, density of air\n", + "cp = 0.248 \t\t\t#kj/kg C, specific heat of air\n", + "V = 16. \t\t\t#m/s, velociity \n", + "d = 0.06 \t\t\t#m, outside diameter of tube\n", + "Nt = 15. \t\t\t#no. of tubes in transverse row\n", + "Nl = 14. \t\t\t#no. of tubes in longitudinal row\n", + "N = Nl*Nt \t\t\t#total no. of tubes\n", + "L = 1. \t\t\t#m, length\n", + "#Calculation\n", + "Sl = (math.sqrt(3)/2)*St\n", + "Pr = cp*mu*3600*rho/k \t\t\t#Prandtl no. of bulk air\n", + "Pr = 0.62\n", + "Prw = 0.70 \t\t\t#Prandtl no. of air at wall temp. 70 C\n", + "#from eq. 4.25\n", + "Vmax = (St/(St-d))*V\n", + "#from eq. 4.26\n", + "Vmax1 = (St/(2*(St-d)))*V\n", + "Redmax = d*Vmax/mu\n", + "p = St/Sl \t\t\t#pitch ratio\n", + "#from table 4.3\n", + "m = 0.6\n", + "C = 0.35*(St/Sl)**0.2\n", + "h = round((k/d)*C*(36163)**m*(Pr)**(0.36)*(Pr/Prw)**(0.25))\n", + "#from eq. 4.28\n", + "dt = round(190*math.exp(-math.pi*d*N*h/(rho*V*3600*Nt*St*cp)))\n", + "LMTD = ((Ti-Ts)-(dt))/math.log((Ti-Ts)/dt)\n", + "A = round(math.pi*d*L*N,1) \t\t\t#m**2, heat transfer area\n", + "Q = h*A*LMTD\n", + "\n", + "# Results\n", + "print \" the rate of heat transfer to water.is %.2e kcal/h\"%(Q)\n", + "\n", + "# Note : Value of LMTD is wrong in book please check." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.12 Page No : 140" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Outlet temp. of water for one pass through the tubes is 51 C\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "W = 0.057 \t\t\t#m**3/min/tube, flow rate of water\n", + "W_ = W*16.66 \t\t\t#kg/s. water flow rate\n", + "di = 0.0212 \t\t\t#m,inside diameter\n", + "Ti = 32. \t\t\t#C, inlet water temp.\n", + "Tw = 80. \t\t\t#C, wall temp.\n", + "L = 3. \t\t\t#m, length of pip\n", + "\n", + "#Calculation\n", + "V = (W/60)*(1/((math.pi/4)*di**2)) \t\t\t#m/s, water velocity\n", + "#the properties of water at mean liquid temp..\n", + "mu = 7.65*10**-4 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.623 \t\t\t#W/m C, thermal conductivity\n", + "rho = 995. \t\t\t#kg/m**3, density of air\n", + "cp = 4.17 \t\t\t#kj/kg C, specific heat of air\n", + "\n", + "Pr = cp*10**3*mu/k \t\t\t#Prandtl no.\n", + "Re = di*V*rho/mu \t\t\t# Reynold no.\n", + "#from eq. 4.19, nusslet no.\n", + "#from dittus boelter eq.\n", + "Nu = 0.023*Re**0.8*Pr**0.4 \t\t\t#Prandtl no.\n", + "f = 0.0014+0.125*Re**-0.32 \t\t\t#friction factor\n", + "#Reynold anamath.logy\n", + "St = f/2 \t\t\t#Smath.tanton no.\n", + "Nu1 = Re*Pr*St\n", + "#Prandtl anamath.logy\n", + "St1 = (f/2)/(1+5*(Pr-1)*math.sqrt(f/2))\n", + "Nu2 = St1*Re*Pr \n", + "#colburn analogy\n", + "Nu3 = Re*Pr**(1./3)*(f/2)\n", + "h = Nu3*k/(di) \t\t\t#W/m**2 C av heat transfer coefficient\n", + "#Q = W_*cp*10**3*(To-Ti) = h*A*LMTD\n", + "A = math.pi*di*L \t\t\t#m**2\n", + "def f(To): \n", + " return W_*cp*10**3*(To-Ti)-h*A*((To-Ti)/math.log((Tw-Ti)/(Tw-To)))\n", + "To = fsolve(f,1)\n", + "#Revised calculation\n", + "Tm = (Ti+To)/2 \t\t\t#C, mean liquid temp.\n", + "#the properties of water at new mean liquid temp..\n", + "mu1 = 6.2*10**-4 \t\t\t#m**2/s, vismath.cosity\n", + "k1 = 0.623 \t\t\t#W/m C, thermal conductivity\n", + "rho1 = 991. \t\t\t#kg/m**3, density of air\n", + "cp1 = 4.17 \t\t\t#kj/kg C, specific heat of air\n", + "\n", + "Pr1 = cp1*10**3*mu1/k1 \t\t\t#Prandtl no.\n", + "Re1 = di*V*rho1/mu1 \t\t\t# Reynold no.\n", + "#from dittus boelter eq.\n", + "f1 = 0.0014+0.125*Re1**(-0.32) \t\t\t#friction factor\n", + "#colburn anamath.logy\n", + "Nu4 = Re1*Pr1**(1./3)*(f1/2)\n", + "h1 = Nu4*k1/(di) \t\t\t#W/m**2 C av heat transfer coefficient\n", + "def f(To_): \n", + " return W_*cp*10**3*(To_-Ti)-h1*A*((To_-Ti)/math.log((Tw-Ti)/(Tw-To_)))\n", + "To_ = fsolve(f,1)\n", + "\n", + "print \"Outlet temp. of water for one pass through the tubes is %.0f C\"%(To_)\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb new file mode 100644 index 00000000..77c2b9da --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch5.ipynb @@ -0,0 +1,431 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 : free convection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1 Page No : 153" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rate of heat loss is 267 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "T1 = 65. \t\t\t#C, furnace temp.\n", + "T2 = 25. \t\t\t#C, ambient temp.\n", + "h = 1.5 \t\t\t#m, height of door\n", + "w = 1. \t\t\t#m, width of door\n", + "Tf = (T1+T2)/2 \t\t\t#c, average air film temp.\n", + "\n", + "# Calculations\n", + "Pr = 0.695 \t\t\t#Prandtl no.\n", + "mu = 1.85*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "beeta = 1/(Tf+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "k = 0.028 \t\t\t#W/m C, thermal conductivity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Grl = g*beeta*(T1-T2)*h**3/(mu**2) \t\t\t#Grashof no.\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#Nusslet no.\n", + "Nul = (0.825+(0.387*(Ral)**(1./6))/(1+(0.492/Pr)**(9./16))**(8./27))**2 \n", + "hav = Nul*k/h \t\t\t#average heat transfer coefficient\n", + "Ad = h*w \t\t\t#m**2, door area\n", + "dt = T1-T2 \t\t\t#temp. driving force\n", + "q = hav*Ad*dt \t\t\t#W,rate of heat loss\n", + "\n", + "# Results\n", + "print \"The rate of heat loss is %.0f W\"%(q)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2 Page No : 154" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the steady state temp. of the plate is 61.6 C\n" + ] + } + ], + "source": [ + "# Variables\n", + "T1 = 60. \t\t\t#C, plate temp.\n", + "T2 = 25. \t\t\t#C, ambient temp.\n", + "h = 1.\n", + "w = 1. \t\t\t#m, width of door\n", + "q = 170. \t\t\t#W, rate of heat transfer\n", + "Tf = (T1+T2)/2 \t\t\t#c, average air film temp.\n", + "#Properties of air at Tf\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "mu = 1.85*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "beeta = 1./(Tf+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "k = 0.028 \t\t\t#W/m C, thermal conductivity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "#Calculation\n", + "A = h*w \t\t\t#m**2, plate area\n", + "P = 2*(h+w) \t\t\t#m,perimeter of plate \n", + "L = A/P \t\t\t#m characteristic length\n", + "Grl = g*beeta*(T1-T2)*L**3/(mu**2) \t\t\t#Grashof no.\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#Nusslet no.\n", + "Nul = 0.54*(Ral)**(1./4) \t\t\t#Nusslet no.\n", + "hav = Nul*k/L \t\t\t#average heat transfer coefficient\n", + "Ts = q/(hav*A)+T2\n", + "\n", + "# Results\n", + "print \"the steady state temp. of the plate is %.1f C\"%(Ts)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3 Page No : 156" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The required time for cooling is 2.30 hr\n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "# Variables\n", + "d = 0.0254 \t\t\t#m, diameter of steel rod\n", + "l = 0.4 \t\t\t#m, length of rod\n", + "T1 = 80. \t\t\t#C, initial temp.\n", + "T2 = 30. \t\t\t#C, ambient temp.\n", + "T3 = 35. \t\t\t#c, temp. after cooling\n", + "rho = 7800. \t\t\t#kg/m**3 ,density of steel rod\n", + "cp = 0.473 \t\t\t#kj/kg C. specific heat\n", + "\n", + "#Calculation\n", + "m = math.pi/4*d**2*l*rho \t\t\t#kg. mass of cylinder\n", + "A = math.pi*d*l \t\t\t#m**2, area of cylinder\n", + "dt = T1-T2 \t\t\t#c, insmath.tanmath.taneous temp. difference\n", + "h = 1.32*(dt/d)**0.25 \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "def f0(T): \n", + " return 1./(T**(5./4))\n", + "\n", + "i = quad(f0,5,50)[0]\n", + "\n", + "t = i/(3.306*A/(m*cp*10**3))\n", + "\n", + "# Results\n", + "print \"The required time for cooling is %.2f hr\"%(t/3600.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4 Page No : 157" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat loss by free convection per meter length of pipe. is 107 W\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "id_ = 78.*10**-3 \t\t\t#m, internal diameter\n", + "od = 89.*10**-3 \t\t\t#m, outer diameter\n", + "Pg = 15. \t\t\t#kg/cm**2, gauge pressure\n", + "t = 2.*10**-2 \t\t\t#m, thickness of preformed mineral fibre\n", + "k = 0.05 \t\t\t#W/m C. thermal conductivity\n", + "Ta = 25. \t\t\t#C, ambient air temp.\n", + "Pr = 0.705 \t\t\t#Prandtl no.\n", + "#assume\n", + "Ts = 50. \t\t\t#C, skin temp.\n", + "l = 1. \t\t\t#m, length\n", + "Ti = 200.5 \t\t\t#C, initial temp.\n", + "rs = od/2+t \t\t\t#m, outer radius of insulation\n", + "ri = od/2 \t\t\t#m, inner radius of insulation\n", + "\n", + "# Calculations\n", + "Q = 2*math.pi*l*k*(Ti-Ts)/(math.log(rs/ri)) \t\t\t#W\n", + "#properties of air at taken at the mean film temp.\n", + "Tf = (Ta+Ts)/2 \t\t\t#C\n", + "mu = 1.76*10**-5 \t\t\t#m**2/s. vismath.cosity\n", + "beeta = (1/(Tf+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "k1 = 0.027 \t\t\t#W/m C, thermal conductivity\n", + "ds = 2*rs \t\t\t#m, outer dia. of insulated pipe\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Grd = g*beeta*(Ts-Ta)*ds**3/(mu**2) \t\t\t#Grashof no.\n", + "Rad = Grd*Pr \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "#Nusslet no. \n", + "Nu = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2 \n", + "hav = Nu*k1/ds \t\t\t#W/ m**2 C, average heat transfer coefficient\n", + "Ts = (Q/(math.pi*ds*l*hav))+Ta \t\t\t#C, skin temp.\n", + "#revised calculation by assuming\n", + "Ts1 = 70. \t\t\t#C, skin temp.\n", + "#Rate of heat transfer through insulation\n", + "Q1 = 2*math.pi*l*k*(Ti-Ts1)/(math.log(rs/ri))\n", + "Tf1 = (Ta+Ts1)/2 \t\t\t#C, average aie mean film temp.\n", + "mu1 = 1.8*10**-5 \t\t\t#m**2/s. vismath.cosity\n", + "beeta1 = (1/(Tf1+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "k1 = 0.0275 \t\t\t#W/m C, thermal conductivity\n", + "Pr1 = 0.703 \t\t\t#Prandtl no.\n", + "Grd1 = g*beeta1*(Ts1-Ta)*ds**3/(mu1**2) \t\t\t#Grashof no.\n", + "Rad = Grd1*Pr1 \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "# average heat transfer coefficient, in \t\t\t#W/ m**2 C,\n", + "hav1 = (0.60+(0.387*(Rad)**(1./6))/(1+(0.559/Pr)**(9./16))**(8./27))**2*(k1/ds)\n", + "Ts2 = (Q1/(math.pi*ds*l*hav1))+Ta\n", + "#again assume skin temp. = 74\n", + "Ts2 = 74 \t\t\t#C, assumed skin temp.\n", + "Q3 = 2*math.pi*l*k*(Ti-Ts2)/(math.log(rs/ri))\n", + "\n", + "# Results\n", + "print \"the rate of heat loss by free convection per meter length of pipe. is %.0f W\"%(Q3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5 Page No : 159" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The required insulation thickness is 0.188 m\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "# Variables\n", + "Ts = 65. \t\t\t#C, skin temp.\n", + "To = 30. \t\t\t#C, ambient temp.\n", + "Tw = 460. \t\t\t#C, wall temp.\n", + "Tf = (Ts+To)/2 \t\t\t#C,mean air film temp.\n", + "beeta = (1./(Tf+273)) \t\t\t#K**-1, coefficient of volumetric expansion\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "mu = 1.84*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "L = 10.5 \t\t\t#m, height of converter\n", + "di = 4. \t\t\t#m,diameter of converter\n", + "Pr = 0.705 \t\t\t#Prandtl no.\n", + "k = 0.0241 \t\t\t#kcal/h m C, thermal conductivity\n", + "\n", + "#Calculation\n", + "Grl = g*beeta*(Ts-To)*L**3/(mu**2) \t\t\t#Grashof no.\n", + "x = di/L \t\t\t#assume di/l = x\n", + "y = 35/(Grl)**(1./4) \t\t\t#assume 35/(Grl)**(3/4) = y\n", + "#for a verticla flat plate, from eq. 5.3\n", + "Ral = Grl*Pr \t\t\t#Rayleigh no.\n", + "#nusslet no.\n", + "Nu = (0.825+(0.387*(Ral)**(1./6))/(1+(0.496/Pr)**(9./16))**(8./27))**2\n", + "hav = Nu*k/L \t\t\t#kcal/h m**2 C, average heat transfer coefficient\n", + "#w = poly(0,\"w\")\n", + "#Dav = (4+(4+2*w))/2 \t\t\t#average diameter\n", + "#Aav = math.pi*Dav*L \t\t\t#average heat transfer area\n", + "#Qi = math.pi*Dav*L*0.0602*(Tw-Ts)/w \t\t\t#Rate of heat transfer through insulation\n", + "#rate of heat transfer from the outer surface of the insulation by free convection\n", + "#Qc = hav*math.pi*Dav*L*(Ts-To) \n", + "#Qi = Qc\n", + "def f(w): \n", + " return math.pi*(4+w)*L*0.0602*(Tw-Ts)/w-hav*math.pi*(4+2*w)*L*(Ts-To)\n", + "w = fsolve(f,0.1)\n", + "\n", + "# Results\n", + "print \"The required insulation thickness is %.3f m\"%(w)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6 Page No : 162" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat transfer is 13.4 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "L = 1.6 \t\t\t#m,height of enclosure\n", + "w = 0.04 \t\t\t#m, width of enclosure\n", + "b = 0.8 \t\t\t#m, breath\n", + "T1 = 22. \t\t\t#C,surface temp.\n", + "T2 = 30. \t\t\t#C, wall temp.\n", + "Tm = (T1+T2)/2 \t\t\t#C, Mean air temp.\n", + "Pr = 0.7 \t\t\t#Prandtl no.\n", + "\n", + "# Calculations\n", + "#fpr air at 26 C\n", + "beeta = 1./(Tm+273) \t\t\t#K**-1. coefficient of volumetric expension\n", + "mu = 1.684*10**-5 \t\t\t#m**2/s, vismath.cosity\n", + "k = 0.026 \t\t\t#W/m C, thermal conductivity\n", + "alpha = 2.21*10**-5 \t\t\t#m**2/s, thermal diffusity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "Raw = g*beeta*(T2-T1)*w**3/(mu*alpha) \t\t\t#Rayleigh no.\n", + "Nuw = 0.42*(Raw)**0.25*Pr**0.012*(L/w)**-0.3 \t\t\t#Nusslet no.\n", + "h = Nuw*k/w \t\t\t#kcal/h m**2 C, heat transfer coefficient\n", + "q = h*(T2-T1)*(L*b) \t\t\t#W,the rate of heat transfer\n", + "\n", + "# Results\n", + "print \"the rate of heat transfer is %.1f W\"%(q)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7 Page No : 163" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the rate of heat loss per meter length is 39.7 kcal/h\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "Ts = 60. \t\t\t#C, surface temp\n", + "To = 30. \t\t\t#C, bulk temp.\n", + "d = 0.06 \t\t\t#m, diameter of pipe\n", + "l = 1. \t\t\t#m, length\n", + "Tm = (Ts+To)/2\n", + "#for air at Tm\n", + "rho = 1.105 \t\t\t#kg/m**3, density\n", + "cp = 0.24 \t\t\t#kcal/kg C. specific heat\n", + "mu = 1.95*10**-5 \t\t\t#kg/m s. vismath.cosity\n", + "P = 0.7 \t\t\t#Prandtl no. \n", + "kv = 1.85*10**-5 \t\t\t#m**2/s, kinetic vismath.cosity\n", + "k = 0.0241 \t\t\t#kcal/f m C, thermal conductivity\n", + "beeta = (1./(Tm+273)) \t\t\t#K**-1. coefficient of volumetric expension\n", + "V = 0.3 \t\t\t#m/s, velocity\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "#Calculation\n", + "Rad = g*beeta*(Ts-To)*d**3*P/(kv**2) \t\t\t#Rayleigh no.\n", + "#from eq. 5.9\n", + "Nufree = (0.60+(0.387*Rad**(1./6))/(1+(0.559/P)**(9./16))**(8./27))**2\n", + "#calculation of forced convection nusslet no.\n", + "#from eq. 4.19\n", + "Re = d*V/(kv)\n", + "Nuforced = 0.3+(0.62*Re**(1./2)*P**(1./3)/(1+(0.4/P)**(2./3))**(1./4))*(1.+(Re/(2.82*10**5))**(5./8))**(4./5)\n", + "Nu = (Nuforced**3+Nufree**3)**(1./3) \t\t\t#nusslet no. for mixed convection\n", + "#Nu = h*d/k\n", + "h = Nu*k/d \t\t\t#kcal/h m**2 C, heat transfer corfficient\n", + "q = h*math.pi*d*l*(Ts-To)\n", + "\n", + "# Results\n", + "print \"the rate of heat loss per meter length is %.1f kcal/h\"%(q)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch6.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch6.ipynb new file mode 100644 index 00000000..362c8be7 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch6.ipynb @@ -0,0 +1,560 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 : Boiling and condensation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1 Page No : 177" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "So a bubble nucleus that has been detached from a cavity will not collapse in the liquid if it is larger than 1.89 micrometer \n", + "The superheat of the liquid is 9 C\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "import warnings\n", + "warnings.filterwarnings('ignore', 'The iteration is not making good progress')\n", + "# Variables\n", + "#(a)\n", + "Tsat = 350 \t\t\t#K, saturated temp.\n", + "Tl = Tsat+5 \t\t\t#K, liquid temp.\n", + "#By antoine eqn.\n", + "T = Tl-273 \t\t\t#C, \n", + "\n", + "# Calculations and Results\n", + "pl = math.exp(4.22658-(1244.95/(T+217.88)))\n", + "ST = 26.29-0.1161*T \t\t\t#dyne/cm, Surface tension of liquid\n", + "ST_ = ST*10**-3 \t\t\t#N/m Surface tension of liquid\n", + "Lv = 33605 \t\t\t#kj/kgmol, molar heat of vaporization\n", + "R = 0.08314 \t\t\t#m**3 bar/kgmol K, gas math.cosmath.tant\n", + "r = (2*ST_*R*Tsat**2)/((Tl-Tsat)*pl*(Lv*10**3))\n", + "print \"So a bubble nucleus that has been detached from a cavity will not collapse in \\\n", + "the liquid if it is larger than %.2f micrometer \"%(r*10**6)\n", + "\n", + "#(b)\n", + "r1 = 10**-6 \t\t\t#m\n", + "#pl1 = exp(4.22658-(1244.95/(Tl_-273+217.88))) \t\t\t#vapour pressure\n", + "#ST1 = 0.02629-1.161*10**-4(Tl_-273) \t\t\t#surface tension\n", + "\n", + "def f(Tl): \n", + " return (Tl-Tsat)-2*(0.02629-1.161*10**-4*(Tl-273))*R*Tsat**2/(r1*Lv*10**3)\n", + "Tl = fsolve(f,0.1)\n", + "T_ = (Tl-273.5)-(Tsat-273)\n", + "print \"The superheat of the liquid is %d C\"%(T_)\n", + "\n", + "# note : answers are slightly different because of rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2 Page No : 180" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "total rate of boiling of water is 69 kg/h \n", + "Qs2 compares reasonably well with the Qs1\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "d = 0.35 \t\t\t#m, diameter of pan\n", + "p = 1.013 \t\t\t#bar, pressure\n", + "T1 = 115. \t\t\t#C, bottom temp.\n", + "T2 = 100. \t\t\t#C, boiling temp.\n", + "Te = T1-T2 \t\t\t#C, excess temp.\n", + "#For Water\n", + "mu1 = 2.70*10**-4 \t\t\t#Ns/m**2, vismath.cosity\n", + "cp1 = 4.22 \t\t\t#kj/kg C, specific heat\n", + "rho1 = 958. \t\t\t#kg/m63. density\n", + "Lv1 = 2257. \t\t\t#kj/kg, enthalpy of vaporization \n", + "s1 = 0.059 \t\t\t#N/m , surface tension\n", + "Pr1 = 1.76 \t\t\t#Prandtl no.\n", + "#For saturated steam\n", + "rho2 = 0.5955\n", + "#For the pan\n", + "Csf = 0.013 \t\t\t#consmath.tant\n", + "n = 1. \t\t\t#exponent\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "# Calculations and Results\n", + "#from eq. 6.6 \t\t\t#heat flux\n", + "Qs1 = mu1*Lv1*(g*(rho1-rho2)/s1)**(1./2)*(cp1*Te/(Csf*Lv1*(Pr1)**n))**3\n", + "Rate = Qs1/Lv1 \t\t\t#kg/m**2 s. rate of boiling\n", + "Ap = math.pi/4*d**2 \t\t\t#m**2, pan area\n", + "Trate = Rate*Ap \t\t\t#kg/s, Total rate of boiling\n", + "Trate_ = Trate*3600.5 \t\t\t#kg/h. Total rate of boiling\n", + "print \"total rate of boiling of water is %.0f kg/h \"%(Trate_)\n", + "\n", + "#umath.sing Lienhard's eq., \t\t\t#critical heat flux\n", + "Qmax = 0.149*Lv1*rho2*(s1*g*(rho1-rho2)/(rho2)**2)**(1/4)\n", + "#by Mostinski eq.\n", + "Pc = 221.2 \t\t\t#critical pressure\n", + "Pr = p/Pc \t\t\t#reduced pressure\n", + "hb = 0.00341*(Pc)**(2.3)*Te**(2.33)*Pr**(0.566) \t\t\t#boiling heat transfer coefficient\n", + "hb_ = hb/1000 \t\t\t#kW/m**2 C boiling heat transfer coefficient\n", + "Qs2 = hb_*(Te)\n", + "print \"Qs2 compares reasonably well with the Qs1\"\n", + "\n", + "# note: rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3 Page No : 181" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The boilins rate is 63 kg/m**2 h\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "A = 12.5673\n", + "B = 4234.6\n", + "pv = 1.813\n", + "T1 = 200. \t\t\t#C, tube wall temp.\n", + "#For methanol\n", + "Tc = 512.6 \t\t\t#K, critical temp.\n", + "w = 0.556 \t\t\t#acentric factor\n", + "Zra = 0.29056-0.08775*w\n", + "R = 0.08314 \t\t\t#m**3bar/gmol K, universal gas consmath.tant\n", + "Pc = 80.9 \t\t\t#bar, critical temp.\n", + "Mw = 32. \t\t\t#g, molecular wt\n", + "\n", + "#Calculation\n", + "#Estimation of liquid and vapour properties \n", + "#from antoine eq.\n", + "T = B/(A-math.log(pv)) \t\t\t#K, boiling point\n", + "Te = (T1+273)-T \t\t\t#K, excess temp.\n", + "Tm = ((T1+273)+T)/2 \t\t\t#K, mean temp.\n", + "#Liquid properties\n", + "#(a)\n", + "Tr = T/Tc \t\t\t#K, reduced temp.\n", + "#from Rackett technique\n", + "Vm = R*Tc*(Zra)**(1+(1-Tr)**(2/7))/Pc \t\t\t#m**3/kg mol, molar volume\n", + "rhol = Mw/Vm \t\t\t#kg/m**3, density of satorated liquid density\n", + "#(b)\n", + "#from Missenard technique\n", + "T2 = 348. \t\t\t#K,given data temp.\n", + "T3 = 373. \t\t\t#K,given data temp.\n", + "Cp2 = 107.5 \t\t\t#j/g mol K specific heat at T2\n", + "Cp3 = 119.4 \t\t\t#j/g mol K specific heat at T3\n", + "#By linear interpolation at T = 353.7 K\n", + "Cp = Cp2+(Cp3-Cp2)*((T-T2)/(T3-T2)) \t\t\t#kj/kg mol C, specific heat at T = 353.7 K\n", + "Cp_ = Cp*0.03125 \t\t\t#kj/kg C\n", + "#(c)Surface tension at given temp.(K)\n", + "T4 = 313.\n", + "St4 = 20.96\n", + "T5 = 333.\n", + "St5 = 19.4\n", + "#By linear interpolation at T = 353.7 K\n", + "S = 17.8 \t\t\t#dyne/cm, surface temp.\n", + "#(d) liquid vismath.cosity\n", + "T6 = 298. \n", + "MUt6 = 0.55 \t\t\t#cP, liquid vismath.cosity at temp = 298\n", + "MU = ((MUt6)**-0.2661+((T-T6)/233))**(-1/0.2661) \t\t\t#cP\n", + "#(e)Prandtl no. a,b,c are consmath.tant\n", + "a = 0.3225\n", + "b = -4.785*10**-4\n", + "c = 1.168*10**-7\n", + "kl = a+b*T+c*T**2 \t\t\t#W/m C, thermal conductivity\n", + "Prl = Cp_*1000*MU*10**-3/kl \t\t\t#Prandtl no.\n", + "#(f)heat of vaporization at 337.5 K\n", + "Lv = 1100. \t\t\t#kj/kg, enthalpy of vaporization\n", + "\n", + "#Properties of methanol vapour at Tm\n", + "#(a)\n", + "Vm1 = R*Tm/pv \t\t\t#m**3/kg mol, molar volume\n", + "rhov = Mw/Vm1 \t\t\t#kg/m**3, density of vapour\n", + "#(b) a1,b1,c1,d1 are math.cosmath.tants\n", + "a1 = -7.797*10**-3\n", + "b1 = 4.167*10**-5\n", + "c1 = 1.214*10**-7\n", + "d1 = -5.184*10**-11\n", + "#thermal conductivity of vapour\n", + "kv = a1+b1*Tm+c1*Tm**2+d1*Tm**3 \t\t\t#W/m C\n", + "#(c)heat capacity of vapour, a2,b2,c2,d2 are math.cosmath.tants\n", + "a2 = 21.15\n", + "b2 = 7.092*10**-2\n", + "c2 = 2.589*10**-5\n", + "d2 = -2.852*10**-8\n", + "#heat capacity of vapour, in kj/kh mol K\n", + "Cpv = a2+b2*Tm+c2*Tm**2+d2*Tm**3\n", + "\n", + "#(d)vismath.cosity of vapour\n", + "T7 = 67.\n", + "MUt7 = 112.\n", + "T8 = 127.\n", + "MUt8 = 132.\n", + "#from linear inter polation at Tm\n", + "MUv = 1.364*10**-5 \t\t\t#kg/m s\n", + "\n", + "#from Rohsenow's eq.\n", + "Csf = 0.027 \t\t\t#consmath.tant\n", + "n = 1.7 \t\t\t#exponent value\n", + "#from eq. 6.6\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "#heat flux \t\t\t#kW/m**2\n", + "Q = MU*10**-3*Lv*(g*(rhol-rhov)/S*10**-3)**(1./2)*(Cp_*Te/(Csf*Lv*(Prl)**n))**3\n", + "#from eq. 6.11\n", + "#from eq 6.11, critical heat flux\n", + "Qmax = 0.131*Lv*(rhov)**(1./2)*(S*10**-3*g*(rhol-rhov))**(1./4)\n", + "#dimensionless radius r_\n", + "r = 0.016\n", + "r_ = r*(g*(rhol-rhov)/(S*10**-3))**(1./2)\n", + "#peak heat flux\n", + "Qmax1 = Qmax*(0.89+2.27*math.exp(-3.44*math.sqrt(r_)))\n", + "#from eq. 6.12\n", + "#heat transfer coefficient hb\n", + "d = 0.032 \t\t\t#m, tube diameter\n", + "hb = 0.62*((kv**3)*rhov*(694-rhov)*g*(Lv*10**3+0.4*Cpv*Te)/(d*MUv*Te))**(1./4)\n", + "Qb = hb*Te \t\t\t#kw/m**2, heat flux\n", + "BR = Qb*10**-3/Lv \t\t\t#kg/m**2s, boilng rate \n", + "\n", + "# Results\n", + "print \"The boilins rate is %.0f kg/m**2 h\"%(BR*3600)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4 Page No : 188" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total tube length is 0.393 m\n" + ] + } + ], + "source": [ + "import math \n", + "\n", + "# Variables\n", + "W1 = 200. \t\t\t#kg/h, rate of entering toluene\n", + "muv = 10.**-5 \t\t\t#kg/m s, vismath.cosity of toluene vapour\n", + "mul = 2.31*10**-4 \t\t\t#kg/m s, vismath.cosity of benzene\n", + "rhol = 753. \t\t\t#kg/m**3, density of benzene\n", + "rhov = 3.7 \t\t\t#kg/m**3, density of toluene vapour\n", + "Cpl = 1968. \t\t\t#j/kg C, specific heat of benzene\n", + "kl = 0.112 \t\t\t#W/m C, thermal conductivity of benzene\n", + "T1 = 160. \t\t\t#C tube wall temp.\n", + "T2 = 120. \t\t\t#C , saturated temp.\n", + "Te = T1-T2 \t\t\t#C, excess temp.\n", + "Lv = 3.63*10**5 \t\t\t#j/kg, enthalpy of vaporization\n", + "s = 1.66*10**-2 \t\t\t#N/m, surface tension\n", + "\n", + "#Calculation of hc & hb\n", + "w = 0.125 \t\t\t#m, mean step size\n", + "d = 0.0211 \t\t\t#, internal diameter of tube\n", + "G = W1/(3600*math.pi/4*(d**2)) \t\t\t#kg/m**2 s, mass flow rate\n", + "Re1 = G*(1-w)*d/mul \t\t\t#Reynold no. \n", + "Prl = Cpl*mul/kl \t\t\t#Prandtl no.\n", + "#from eq. 6.23\n", + "x = (w/(1-w))**(0.9)*(rhol/rhov)**(0.5)*(muv/mul)**0.1 \t\t\t#let x = 1/succepsibility\n", + "#from eq. 6.22 \n", + "F = 2.35*(x+0.231)**0.736 \t\t\t#factor signifies 'liquid only reynold no.' to a two phase reynold no.\n", + "#from eq. 7.21\n", + "Re2 = 10**-4*Re1*F**1.25 \t\t\t#Reynold no.\n", + "#from eq. 6.18\n", + "S = (1+0.12*Re2**1.14)**-1 \t\t\t#boiling supression factor\n", + "#from eq. 6.15\n", + "hc = 0.023*Re1**(0.8)*Prl**(0.4)*(kl/d)*F \t\t\t#W/m**2 C, forced convection boiling part\n", + "#from eq. 6.16\n", + "mulv = (1/rhov)-(1/rhol) \t\t\t#m**3/kg, kinetic vismath.cosity of liquid vpaour\n", + "dpsat = Te*Lv/((T2+273)*mulv) \t\t\t#N/m**2, change in saturated presssure \n", + "#nucleate boiling part hb\n", + "hb = 1.218*10**-3*(kl**0.79*Cpl**0.45*rhol**0.49*Te**0.24*dpsat**0.75*S/(s**0.5*mul**0.29*Lv**0.24*rhov**0.24))\n", + "h = hc+hb \t\t\t#W/m**2 C, total heat transfer coefficient\n", + "\n", + "#calculation of required heat transfer area\n", + "a = 5. \t\t\t#%, persentage change in rate of vaporization\n", + "W2 = W1*a/100 \t\t\t#kg/h, rate of vaporization\n", + "W2_ = W2/3600 \t\t\t#kg/s\n", + "Q = W2_*Lv \t\t\t#W,heat load\n", + "A = Q/(h*Te) \t\t\t#m**2, area of heat transfer\n", + "l = A/(math.pi*d) \t\t\t#m, required length of tube\n", + "#from table 6.2\n", + "Tl = 0.393\n", + "\n", + "# Results\n", + "print \"The total tube length is %.3f m\"%(Tl)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5 Page No : 195" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total rate of condensation is 33.08 kg/h\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "# Variables\n", + "rhol = 483. \t\t\t#kg/m**3, density of liquid propane\n", + "mul = 9.1*10**-5 \t\t\t#P ,vismath.cosity of liquid propane\n", + "kl = 0.09 \t\t\t#W/m K, thermal conductivity of liquid propane\n", + "Lv = 326. \t\t\t#kj/kg. enthalpy of vaporization\n", + "Cpl = 2.61 \t\t\t#kj/kg K, specific heat of liquid propane\n", + "T1 = 32.\n", + "T2 = 25. \t\t\t#C, surface temp.\n", + "p1 = 11.2\n", + "rhov = 24.7 \t\t\t#kg/m**3, density of vapour\n", + "g = 9.8\n", + "h = 0.3\n", + "\n", + "#Calculation\n", + "Lv1 = Lv+0.68*Cpl*(T1-T2)\n", + "#h = 0.943*(g*Lv1*10**3*rhol*(rhol-rhov)*kl**3/(mul*L*(T1-T2)))**(1/4)\n", + "#Q = h*(L*1)*(T1-T2)\n", + "#m = Q/(Lv1*10**3) = 1.867*10**-2*L**(3/4)\n", + "Ref = 30.\n", + "#from the relation 4*m/mu = Re\n", + "L = (Ref*mul/(4*1.867*10**-2))**(4./3)\n", + "m = 1.867*10**-2*L**(3./4) \t\t\t#rate of condensation for laminar flow\n", + "#from eq. 6.32\n", + "#Nu1 = h_/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1/3) = Ref/(1.08*(Ref)**(1.22)-5.2)\n", + "Lp = h-L \t\t\t#length of plate over which flow is wavy\n", + "A = Lp*1 \t\t\t#m**2 area of condensation\n", + "\n", + "\n", + "def f(h1): \n", + " return h1/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1./3)-(29.76+0.262*h1)/(1.08*(29.76+0.262*h1)**(1.22)-5.2)\n", + "h1 = fsolve(f,1000)\n", + "m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n", + "Ref1 = 4*m2/mul\n", + "m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n", + "\n", + "# Results\n", + "print \"Total rate of condensation is %.2f kg/h\"%(m2*3600)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6 Page No : 199" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rate of condensation is 45.7 kg/h \n", + "Rate of condensation is 1052 kg/h \n", + "thus there will be increase in the calculated rate of heat transfer and in rate of condensation as 1.188 percent\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "#data fot TCE\n", + "T1 = 87.4 \t\t\t#C, normal boiling point\n", + "T2 = 25. \t\t\t#C, surface temp.\n", + "Lv = 320.8 \t\t\t#kj/kg, heat of vaporization\n", + "cp = 1.105 \t\t\t#kj/kg C, specific heat\n", + "mu = 0.45*10**-3 \t\t\t#P. liquid vismath.cosity\n", + "k = 0.1064 \t\t\t#W/m C, thermal conductivity\n", + "rhol = 1375. \t\t\t#kg/m**3, liquid density\n", + "rhov = 4.44 \t\t\t#kg/m**3, density of vapour\n", + "Tm = (T1+T2)/2. \t\t\t#C, mean film temp.\n", + "d = 0.0254 \t\t\t#m, outside diameter of tube\n", + "l = 0.7 \t\t\t#m, length\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "\n", + "# Calculations and Results\n", + "#(a) from eq. 6.34\n", + "Lv1 = Lv+0.68*cp*(T1-T2)\n", + "h = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(mu*d*(T1-T2)))**(1./4)\n", + "A = math.pi*d*l \t\t\t#m**2, area of tube\n", + "Q = h*A*(T1-T2) \t\t\t#W, rate of heat transfer\n", + "m = (Q/Lv1)/1000 \t\t\t#kg/s rate of condensation\n", + "print \"Rate of condensation is %.1f kg/h \"%(m*3600)\n", + "\n", + "#(b) from eq. 6.35\n", + "N = 6. \t\t\t#No. of tubes in vertical tire\n", + "h1 = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(N*mu*d*(T1-T2)))**(1./4)\n", + "TN = 36. \t\t\t#total no. of tubes\n", + "TA = TN*math.pi*d*l \t\t\t#m**2, total area\n", + "Q1 = h1*TA*(T1-T2) \t\t\t#W, rate of heat transfer\n", + "m1 = (Q1/Lv1)/1000. \t\t\t#kg/s rate of condensation\n", + "print \"Rate of condensation is %.0f kg/h \"%(m1*3600)\n", + "#from chail's corelation\n", + "h2 = (1+0.2*cp*(T1-T2)*(N-1)/(Lv1))\n", + "print \"thus there will be increase in the calculated rate of\\\n", + " heat transfer and in rate of condensation as %.3f percent\"%(h2)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7 Page No : 201" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fraction of input vapour condensed is 52.7\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "Gv = 20. \t\t\t#kg/m**2 s, mass flow rate of benzene\n", + "di = 0.016 \t\t\t#m, tube diameter\n", + "muv = 8.9*(10**-6) \t\t\t#P, vismath.cosity\n", + "Lv = 391. \t\t\t#kj/kg., enthalpy of vaporization\n", + "cpl = 1.94 \t\t\t#kj/kg C, specific heat\n", + "Tv = 80. \t\t\t#C, normal boiling point of benzene\n", + "Tw = 55. \t\t\t#C, wall temp.\n", + "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", + "rhol = 815. \t\t\t#kg/m**3, density of benzene\n", + "rhov = 2.7 \t\t\t#kg/m**3, density of benzene vapour\n", + "kl = 0.13 \t\t\t#W/m C, thermal conductivity\n", + "mu = 3.81*10**-4 \t\t\t#P, vismath.cosity of benzene\n", + "l = 0.5 \t\t\t#m, length of tube\n", + "\n", + "#calculation\n", + "Rev = di*Gv/muv \t\t\t#Reynold no. of vapour\n", + "#from eq. 6.38\n", + "Lv1 = Lv+(3./8)*cpl*(Tv-Tw)\n", + "#heat transfer corfficient , h\n", + "h = 0.555*(g*rhol*(rhol-rhov)*kl**3*Lv1*10**3/(di*mu*(Tv-Tw)))**(1./4)\n", + "Aavl = math.pi*di*l \t\t\t#m**2, available area\n", + "Q = Aavl*h*(Tv-Tw) \t\t\t#W, rate of heat transfer\n", + "m = Q/(Lv1*10**3) \t\t\t#kg/s, rate of condensation of benzene\n", + "Ratei = Gv*(math.pi/4)*di**2 \t\t\t#kg/s rate of input of benzene vapour\n", + "n = m/Ratei \n", + "\n", + "# Results\n", + "print \"fraction of input vapour condensed is %.1f\"%(n*100)\n", + "\n", + "# note : rouding off error." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch7.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch7.ipynb new file mode 100644 index 00000000..19ff7097 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch7.ipynb @@ -0,0 +1,996 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7 : radiation heat transfer" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3 Page No : 215" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the fraction of radiation falls in visible range is 0.366 \n", + "the fraction of radiation on the left of visible range is 0.1229 \n", + "the fraction in right of visible range is 0.5111 \n", + "The maximum wavelength is 0.5014 micrometer is\n", + "The frequency is 5.98e+08 s**-1\n", + "the maximum spectral emissive power is 8.298e+13 W/m**2\n", + "the hemispherical total emissive power is 6.326e+07 W/m**2\n" + ] + } + ], + "source": [ + "import math \n", + "# Variables\n", + "Ts = 5780. \t\t\t#K, surface temp.\n", + "\n", + "# Calculations and Results\n", + "#(a)\n", + "lamda1 = 0.4 \t\t\t#micrometer, starting visible spectrum range \n", + "lamda2 = 0.7 \t\t\t#micrometer,ending visible spectrum range\n", + "E1 = lamda1*Ts \t\t\t#micrometer K, \n", + "E2 = lamda2*Ts \t\t\t#micrometer K, \n", + "#from table 7.2\n", + "#fraction of radiation lying between 0 and lamda1\n", + "F1 = 0.1229\n", + "#fraction of radiation lying between 0 and lamda2\n", + "F2 = 0.4889\n", + "#the fraction of radiation falls betweem lamda1 & lamda 2\n", + "F3 = F2-F1\n", + "print \"the fraction of radiation falls in visible range is %.3f \"%(F3)\n", + "#(b)\n", + "F4 = F1\n", + "print \"the fraction of radiation on the left of visible range is %.4f \"%(F4)\n", + "#(c)\n", + "F5 = 1-F2\n", + "print \"the fraction in right of visible range is %.4f \"%(F5)\n", + "#(d)\n", + "#from wein's print lacement law\n", + "lmax = 2898/Ts\n", + "print \"The maximum wavelength is %.4f micrometer is\"%(lmax)\n", + "c = 2.998*10**8 \t\t\t#m/s, speed of light\n", + "mu = c/lmax\n", + "print \"The frequency is %1.2e s**-1\"%(mu)\n", + "#(e)\n", + "#from eq. 7.4\n", + "h = 6.6256*10**-34 \t\t\t#Js planck's consmath.tant\n", + "k = 1.3805*10**-23 \t\t\t#J/K, boltzman consmath.tant\n", + "Eblmax = (2*math.pi*h*c**2*(lmax*10**-6)**-5)/((math.exp(h*c/(lmax*10**-6*k*Ts)))-1)\n", + "print \"the maximum spectral emissive power is %1.3e W/m**2\"%(Eblmax)\n", + "#(f)\n", + "s = 5.668*10**-8 \t\t\t#stephen math.cosmath.tant\n", + "Eb = s*Ts**4\n", + "print \"the hemispherical total emissive power is %1.3e W/m**2\"%(Eb)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4 Page No : 216" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Surface temp. is 515 C\n", + "wavength is 5.62 micrometer \n", + " from fig 7.1 it falls in the infrared region of spectrum.\n" + ] + } + ], + "source": [ + "#Variables\n", + "Eb = 4000. \t\t\t#W/m sq, Total emmisive power\n", + "s = 5.669*10**-8 \t\t\t#Stephen boltzman consmath.tant\n", + "\n", + "#Calculation\n", + "T = (Eb/s)**0.25 \t\t\t#k, surface temp. of black body\n", + "ym = 2898./T \t\t\t#micro meter,\n", + "#By weins law : Max. wavelength of emmision is inversaly proportional \n", + "#to temprature. and consmath.tant is 2898 micrometer.\n", + "\n", + "#Result\n", + "print \"Surface temp. is %.0f C\"%(T)\n", + "print \"wavength is %.2f micrometer \"%(ym)\n", + "print \" from fig 7.1 it falls in the infrared region of spectrum.\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5 Page No : 219" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "total hemispherical) emissive power is 1.241e+05 W/m**2\n", + "total hemispherical) emissivity of the surface is 0.4326\n" + ] + } + ], + "source": [ + "# Variables\n", + "T = 1500. \t\t\t#K, surface temprature\n", + "#from fig 7.7\n", + "e1 = 0.2 \t\t\t#emissivity ,when wavelength(l1) is 0<l1<2 micrometer\n", + "e2 = 0.6 \t\t\t#emissivity ,when wavelength(l2) is 2<l2<6 micrometer\n", + "e3 = 0.1 \t\t\t#emissivity ,when wavelength(l3) is 6<l3<10 micrometer\n", + "e4 = 0 \t\t\t#emissivity ,when wavelength(l4) is l4>10 micrometer\n", + "#from table 7.2\n", + "F1 = 0.2733 \t\t\t#fraction of energy in wavelength (l1)\n", + "F2 = 0.89-F1 \t\t\t#fraction of energy in wavelength (l2)\n", + "F3 = 0.9689-0.89 \t\t\t#fraction of energy in wavelength (l3)\n", + "\n", + "#Calculation and Result\n", + "s = 5.669*10**-8 \t\t\t#stephen's consmath.tant\n", + "Eb = s*T**4 \t\t\t#emissive power \n", + "E = (e1*F1+e2*F2+e3*F3)*Eb\n", + "print \"total hemispherical) emissive power is %1.3e W/m**2\"%(E)\n", + "#(b)\n", + "e = E/(s*T**4)\n", + "print \"total hemispherical) emissivity of the surface is %.4f\"%(e)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6 Page No : 226" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fraction of radiation passes through hole 0.0588 \n", + "fraction of radiation intercepted by the ring 0.0791 \n" + ] + } + ], + "source": [ + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "ri = 5. \t\t\t#cm ,inside radius of ring\n", + "w = 3. \t\t\t#cm, width\n", + "ro = ri+w \t\t\t#cm, outside radius \n", + "L = 20. \t\t\t#cm, surface dismath.tance\n", + "\n", + "# Calculations\n", + "def f4(r): \n", + " return 20.**2*r/(20.**2+r**2)**2\n", + "\n", + "F1 = 2* quad(f4,0,ri)[0]\n", + "\n", + "#view factor along surface dA1-A2\"\n", + "\n", + "def f5(r): \n", + " return 20**2*r/(20**2+r**2)**2\n", + "\n", + "F2 = 2* quad(f5,ri,ro)[0]\n", + "\n", + "# Results\n", + "print \"fraction of radiation passes through hole %.4f \"%(F1)\n", + "print \"fraction of radiation intercepted by the ring %.4f \"%(F2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8 Page No : 232" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "view factor F11 = 0\n", + "view factor F22 = 1\n", + "view factor F21 = 0.5\n", + "view factor = 0.5\n" + ] + } + ], + "source": [ + "import math\n", + "#Variables\n", + "F11 = 0 \t\t\t#view factor\n", + "d = 1. \t\t\t#let it be\n", + "print \"view factor F11 = %.0f\" %(F11)\n", + "\n", + "#Calculation and Result\n", + "F12 = 1-F11 \t\t\t#view factor\n", + "print \"view factor F22 = %.0f\"%(F12)\n", + "\n", + "A1 = ((math.pi)*d**2)/4 \t\t\t#sq m, area\n", + "A2 = ((math.pi)*d**2)/2 \t\t\t#sq m, area\n", + "F21 = A1/A2 \t\t\t#from eq . 7.26\n", + "print \"view factor F21 = %.1f\"%( F21)\n", + "F22 = 1-F21 \n", + "#Results\n", + "print \"view factor = %.1f\"%(F22)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9 Page No : 233" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "view factor F11 = 0\n", + "view factor F33 = 0.5\n", + "view factor F14 = 0.056\n", + "view factor F13 = 0.056\n", + "view factor F12 = 0.944\n", + "view factor F31 = 0.028\n", + "view factor F32 = 0.472\n", + "view factor F21 = 0.118\n", + "view factor F23 = 0.118\n", + "view factor F22 = 0.764\n" + ] + } + ], + "source": [ + "import math\n", + "#Variable\n", + "s = 3. \t\t\t#no. of surface\n", + "tvf = s**2 \t\t\t#total view factor\n", + "\n", + "#using the result of example 7.8\n", + "F11 = 0 \n", + "F33 = 0.5\n", + "print \"view factor F11 = %.0f\"%(F11)\n", + "print \"view factor F33 = %.1f\"%(F33)\n", + "\n", + "#Calculation & Results\n", + "R1 = 0.25 \t\t\t#R = d/2*h &h = 2d\n", + "R2 = 0.25\n", + "X = 1+((1+R2**2)/(R1**2))\n", + "F14 = (0.5)*(X-math.sqrt((X**2)-4*(R2/R1)**2))\n", + "print \"view factor F14 = %.3f\"%(F14)\n", + "F13 = F14\n", + "print \"view factor F13 = %.3f\"%(F13)\n", + "F12 = 1-F11-F13 \t\t\t# from eq. 7.31 for surface 1\n", + "print \"view factor F12 = %.3f\"%(F12)\n", + "\n", + "d = 1. \t\t\t#say\n", + "A1 = (math.pi*(d**2))/4.\n", + "A3 = (math.pi*(d**2))/2.\n", + "F31 = A1*F13/(A3)\n", + "print \"view factor F31 = %.3f\"%(F31)\n", + "\n", + "# from eq. 7.31 for surface 3\n", + "F33 = 0.5\n", + "F32 = 1-F31-F33\n", + "print \"view factor F32 = %.3f\"%(F32)\n", + "\n", + "#for surface 2\n", + "A2 = 2*math.pi*d**2\n", + "F21 = A1*F12/A2\n", + "print \"view factor F21 = %.3f\"%(F21)\n", + "F23 = A3*F32/A2\n", + "print \"view factor F23 = %.3f\"%(F23)\n", + "F22 = 1-F21-F23\n", + "print \"view factor F22 = %.3f\"%(F22)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10 Page No : 235" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The view factor from surface 1 to 2 is 1\n", + "The view factor from surface 2 to 1 is 0.167\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "ds = 0.3 \t\t\t#m, diameter of shell\n", + "r1 = 0.1 \t\t\t#m, dismath.tance from the centre\n", + "\n", + "#Calculation and Results\n", + "#by the defination of view factor\n", + "F12 = 1.\n", + "print \"The view factor from surface 1 to 2 is %.0f\"%(F12)\n", + "#F21\n", + "R = ds/2. \t\t\t#m, radius of sphere\n", + "r2 = math.sqrt(R**2-r1**2)\n", + "A1 = math.pi*r2**2 \t\t\t#m**2 area\n", + "A2 = 2*math.pi*R**2+2*math.pi*R*math.sqrt(R**2-r2**2)\n", + "#from reciprocity relation\n", + "F21 = (A1/A2)*F12\n", + "print \"The view factor from surface 2 to 1 is %.3f\"%(F21)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.12 Page No : 237" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The time required for the ball to cool is 10.3 h\n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "# Variables\n", + "d = 0.3 \t\t\t#m, diameter of steel sphere\n", + "Ti = 800. \t\t\t#K, initial temp. of sphere\n", + "T2 = 303. \t\t\t#C,ambient temp.\n", + "T1 = 343. \t\t\t#C, final tempreture\n", + "rho = 7801. \t\t\t#kg/m**3, density of steel\n", + "cp = 0.473 \t\t\t#kj/kg C, specific heat of steel\n", + "#calculation\n", + "R = d/2 \t\t\t#m, radius of sphere\n", + "A1 = 4*math.pi*R**2 \t\t\t#m**2, area of sphere\n", + "m = 4./3*math.pi*R**3*rho \t\t\t#m**3, mass of sphere\n", + "F12 = 1. \t\t\t#view factor\n", + "s = 5.669*10**-8 \t\t\t#stephen Boltzman's consmath.tant\n", + "#-dT1/dt = A1*F12*s*(T**4-T2**4)/(m*cp)\n", + "\n", + "def f1(T1): \n", + " return (1/(T1**4-T2**4))\n", + "\n", + "I = quad(f1,343,800)[0]\n", + "\n", + "t = I/(A1*F12*s/(m*cp*10**3))\n", + "\n", + "# Results\n", + "print \"The time required for the ball to cool is %.1f h\"%(t/3600)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.13 Page No : 247" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) Net rate of radiative heat loss Q12 = 596.6 W \n", + "b) Net rate of radiative heat loss Q12 = 441.5 W\n" + ] + } + ], + "source": [ + "import math\n", + "#Variables\n", + "d = 0.114 \t\t\t#m, dia.o f pipe\n", + "l = 1. \t\t\t#m, length of pipe\n", + "A = (math.pi)*d*l \t\t\t#m sq, area\n", + "e1 = 1. \t\t\t#emmisivity of black body\n", + "F12 = 1. \t\t\t#view factor, 1:pipe surface, 2:room walls\n", + "s = 5.67*10**-8 \t\t\t#stephen boltzman consmath.tant\n", + "T1 = 440. \t\t\t#K, steam temp.\n", + "T2 = 300. \t\t\t#K, wall temp.\n", + "#Caluclation\n", + "Q12 = A*e1*F12*s*(T1**4-T2**4) \t\t\t#net rate of radiative heat loss\n", + "\n", + "#Results\n", + "print \"a) Net rate of radiative heat loss Q12 = %.1f W \"%(Q12)\n", + "#Part-b\n", + "e2 = 0.74\n", + "Q12 = A*e2*F12*s*(T1**4-T2**4) \t\t\t#net rate of radiative heat loss\n", + "print \"b) Net rate of radiative heat loss Q12 = %.1f W\"%(Q12)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.14 Page No : 247" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a-i) View factor F12 = 1\n", + "view factor F21 = 0.937\n", + "ii) The net rate of heat gain Q1net = 4.0 J/s\n", + "b) Rate of nitrogen loss = 72 g/h\n" + ] + } + ], + "source": [ + "import math\n", + "#Variable declaration\n", + "F12 = 1. \t\t\t#view factor\n", + "r1 = 0.15 \t\t\t#m inner radius of phere\n", + "r2 = 0.155 \t\t\t#m , outer radius\n", + "\n", + "#Calculation\n", + "A1 = 4.*(math.pi)*r1**2 \t\t\t#sq m inner area\n", + "A2 = 4.*(math.pi)*r2**2 \t\t\t#sq m,outer area \n", + "F21 = A1/A2\n", + "h = 200. \t\t\t#J/g, heat of vaporization of nitrogen\n", + "s = 5.669*10**-8 \t\t\t# boltzman consmath.tant\n", + "T2 = 298. \t\t\t#K, temp. of outer wall\n", + "T1 = 77. \t\t\t#K, Temp. of inner wall\n", + "e1 = 0.06 \t\t\t#emmisivity\n", + "e2 = 0.06 \t\t\t#emmisivity\n", + "x = ((1-e1)/(e1*A1))+(1/(A1*F12))+((1-e2)/(e2*A2))\n", + "Q1net = (s*(T2**4-T1**4))/(x)\n", + "\n", + "#Result-a-i\n", + "print \"a-i) View factor F12 = %.0f\"%(F12)\n", + "print \"view factor F21 = %.3f\"%(F21)\n", + "#Result- b\n", + "print \"ii) The net rate of heat gain Q1net = %.1f J/s\"%(Q1net)\n", + "nl = Q1net/h\n", + "nl = nl*3600 \t\t\t#g/h\n", + "print \"b) Rate of nitrogen loss = %.0f g/h\"%(nl)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.15 Page No : 248" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the net rate of radiant heat transfer to the wall is 2900 W\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "x = 0.15 \t\t\t#m, length of opening on a furnace\n", + "y = 0.12 \t\t\t#m, width of opening on a furnace\n", + "x1 = 6. \t\t\t#m, width of wall\n", + "y1 = 5. \t\t\t#m, height of wall\n", + "e2 = 0.8 \t\t\t#emissivity of wall\n", + "T1 = 1400. \t\t\t#C, furnace temp.\n", + "T2 = 35. \t\t\t#C, wall temp.\n", + "T3 = 273. \t\t\t#C, smath.radians(numpy.arcmath.tan(ard temp.\n", + "s = 5.669*10**-8 \t\t\t#stephen boltzman's consmath.tant\n", + "#in fig. 7.29\n", + "l1 = 2. \t\t\t#m, l1 = AF\n", + "l2 = 1.5 \t\t\t#m, l2 = AH\n", + "h = 3. \t\t\t#m, E = dA1\n", + "\n", + "# Calculations\n", + "F1 = (1./(2*math.pi))*((l2/(math.sqrt(l2**2+h**2)))*math.tanh(l1/(math.sqrt(l2**2+h**2)))+(l1/(math.sqrt(l1**2+h**2)))*math.tan(l2/(math.sqrt(l1**2+h**2))))\n", + "#Similarly\n", + "#for the dA1-A3 pair the equation is\n", + "F2 = 0.1175\n", + "#for the dA1-A4 pair the equation is\n", + "F3 = 0.1641\n", + "#for the dA1-A5 pair the equation is\n", + "F4 = 0.0992\n", + "#view factor b/w the opening (dA1)and the wall (W) is \n", + "F5 = F1+F2+F3+F4\n", + "#Calculation of radient heat exchange\n", + "dA1 = x*y\n", + "Aw = x1*y1\n", + "Eb1 = s*(T1+T3)**4\n", + "Ebw = s*(T2+T3)**4\n", + "F6 = dA1*F5/Aw\n", + "Q = dA1*F5*e2*(Eb1*(1-(1-e2)*F6)-Ebw)\n", + "\n", + "# Results\n", + "print \"the net rate of radiant heat transfer to the wall is %.0f W\"%(round(Q,-2))\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.16 Page No : 250" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the net rate of radiant heat loss = 17.1 kW \n", + "convective heat transfer coeff. = 90 W/sq m C\n" + ] + } + ], + "source": [ + "#Variable declaration\n", + "l = 3. \t\t\t#m, length of wall\n", + "w = 2. \t\t\t#m, width of, wall\n", + "d = 3. \t\t\t#m\n", + "R1 = l/d\n", + "A1 = l*w \t\t\t#sq m,area 1: front part\n", + "A2 = A1 \t\t\t#sq m , area, 2\"back part\n", + "e1 = 0.7 \t\t\t#emmisivity\n", + "e2 = 0.7 \t\t\t#emmisivity\n", + "T1 = 673. \t\t\t#k\n", + "T2 = 523. \t\t\t#k\n", + "s = 5.669*10**-8 \t\t\t#stephen boltzman consmath.tant\n", + "\n", + "#Calculation\n", + "F12 = 0.148 \t\t\t#view factor ,from fig. 7.12\n", + "x = (A1+A2-2*A1*F12)/(A2-(A1*(F12**2)))+((1/e1)-1)+(A1/A2)*((1/e2)-1)\n", + "\n", + "#Results\n", + "Q1net = -1*A1*(s*(T2**4-T1**4))/(x)\n", + "print \"the net rate of radiant heat loss = %.1f kW \"%(Q1net/1000)\n", + "# (b)\n", + "F24 = 1. \t\t\t#from fig 7.12\n", + "T20 = 333. \t\t\t#K, outer surface temp. of surface 2\n", + "T4 = 303. \t\t\t#K, ambient temp\n", + "Q2rad = A2*e2*F24*s*(T20**4-T4**4)\n", + "q = Q1net-Q2rad\n", + "q1 = q/1000 \t\t\t# Kw\n", + "h = q/(A2*(T20-T4))\n", + "print \"convective heat transfer coeff. = %.0f W/sq m C\"%(h)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.17 Page No : 251" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "net rate of radiation exchange b/w disk 1 and 2 is 2286 W/m**2\n" + ] + } + ], + "source": [ + "from numpy import array, linalg\n", + "import math\n", + "\n", + "# Variables\n", + "r1i = 0.1 \t\t\t#m, inner radius of disk 1\n", + "r1o = 0.2 \t\t\t#m, outer radius of disk 1\n", + "r2i = 0.12 \t\t\t#m, inner radius of disk 2\n", + "r2o = 0.25 \t\t\t#m, outer radius of disk 2\n", + "h = 0.08 \t\t\t#m, dismath.tance between the disks\n", + "R2 = r2o/h\n", + "R1 = r1o/h\n", + "X = 1+(1+R1**2)/R2**2\n", + "F23_14 = 1./2*(X-math.sqrt(X**2-4*(R1/R2)**2))\n", + "\n", + "#calculation\n", + "R2_ = r2o/h\n", + "R1_ = r1i/h\n", + "X_ = 1+(1+R1_**2)/R2_**2\n", + "F23_4 = 1/2*(X_-math.sqrt(X_**2-4*(R1_/R2_)**2)) \t\t\t#view factor\n", + "#similarly\n", + "F3_14 = 0.815 \t\t\t#view factor\n", + "F34 = 0.4 \t\t\t#view factor\n", + "A23 = math.pi*r2o**2 \t\t\t#area\n", + "A3 = math.pi*r2i**2\n", + "A1 = math.pi*(r1o**2-r1i**2)\n", + "#from eq. 1\n", + "F12 = A23*(F23_14-F23_4)/A1-(A3*(F3_14-F34))/A1\n", + "\n", + "#calculation of the rate of radiative heat exchange\n", + "# Variables\n", + "T1 = 1000. \t\t\t#K, temprature of disk 1\n", + "T2 = 300. \t\t\t#K, temprature of disk 2\n", + "s = 5.669*10**-8 \t\t\t#stephen's Boltzman consmath.tant\n", + "e1 = 0.8 \t\t\t#emissivity\n", + "e2 = 0.7\n", + "A2 = math.pi*(r2o**2-r2i**2)\n", + "F1s = 1-F12\n", + "F2s = 1-(A1*F12/A2)\n", + "#calculation\n", + "#let some quantities equal to \n", + "a = (1-e1)/(e1*A1)\n", + "b = 1/(A1*F12)\n", + "c = (1-e2)/(e2*A2)\n", + "d = 1/(A1*F1s)\n", + "e = 1/(A2*F2s)\n", + "f = s*T1**4\n", + "g = s*T2**4\n", + "#from eq. 7.42(a)\n", + "#(f-J1)/a = (J1-J2)/b+J1/d\n", + "#(g-J2)/c = (J2-J1)/b+J1/e\n", + "#solving two eqns by matrix\n", + "A = array([[-0.0564,0.5036],[0.4712,-0.0564]])\n", + "B = array([[161.847],[21376.31]])\n", + "X = linalg.solve(A,B)\n", + "J1 = X[0]\n", + "J2 = X[1]\n", + "\n", + "#net rate of radiation exchange \n", + "Q12net = (J1-J2)/17.73\n", + "\n", + "# Results\n", + "print \"net rate of radiation exchange b/w disk 1 and 2 is %d W/m**2\"%(Q12net)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.18 Page No : 255" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The net rate of heat gain of tube is 0.30 W\n" + ] + } + ], + "source": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "# Variables\n", + "di = 0.0254 \t\t\t#m, inner diameter of tube\n", + "Ti = 77. \t\t\t#K, liquid temprature\n", + "do = 52.5*10**-3 \t\t\t#m, pipe internal diameter\n", + "To = 270. \t\t\t#K, wall temprature\n", + "l = 1. \t\t\t#m, length of tube\n", + "e1 = 0.05 \t\t\t#emissivity of tube wall\n", + "e2 = 0.1 \t\t\t#emissivity of pipe wall\n", + "e3 = 0.02 \t\t\t#emissivity for inner surface of radiation field\n", + "e4 = 0.03 \t\t\t#emissivity for outer surface of radiation field\n", + "s = 5.669*10**-8 \t\t\t#stephen boltzman math.cosmath.tantl\n", + "\n", + "#Calculation\n", + "ds = (do+di)/2 \t\t\t#m, diameter of radiation shield\n", + "Ao = math.pi*do*l \t\t\t#m**2, outer pipe area\n", + "As = math.pi*ds*l \t\t\t#m**2, shield area\n", + "Ai = math.pi*di*l \t\t\t#m**2, inner pipe area\n", + "#View factors\n", + "#for the long cylindrical enclosure made up of the outer pipe and the shield\n", + "Fso = 1. \t\t\t#because outer surface of shield cant see itself\n", + "Fos = As/Ao \n", + "Fsi = Ai/As\n", + "#now assume \n", + "#(1-e2)/e2+ 1/Fos +Ao*(1-e4)/(As*e4) = x\n", + "#(1-e3)/e3 +1/Fsi +(1/Fsi)*(1-e1)/e1 = y\n", + "x = (1-e2)/e2+ 1/Fos +Ao*(1-e4)/(As*e4)\n", + "y = (1-e3)/e3 +1/Fsi +(1/Fsi)*(1-e1)/e1\n", + "#solving the equations for heat transfer from the outer pipe and inner pipe\n", + "def f(Ts): \n", + " return (Ao*(To**4-Ts**4)/x)-(Ai*(Ts**4-Ti**4)/x)\n", + "Ts = fsolve(f,1)\n", + "Qos = (Ao*s*(To**4-Ts**4))/x\n", + "\n", + "# Results\n", + "print \"The net rate of heat gain of tube is %.2f W\"%(Qos)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.19 Page No : 258" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rate of heat loss from the top surface : 403 W\n", + "Rate of heat loss from the side walls : 1271 W\n", + "Total rate of heat loss : 1674 W\n" + ] + } + ], + "source": [ + "# Variables\n", + "T1 = 300 + 273. #K\n", + "Ta = 30. + 273. # K\n", + "w = 0.075 # m\n", + "k = 0.08 # W/m c\n", + "l = 1.075 # m\n", + "delta = 5.669 * 10**-8 # W/m**2 K**4\n", + "A1 = 1 * 1.5 # M**2\n", + "A2 = A1\n", + "A2m = (1.5 + 1.9)/2 # m**2\n", + "A3m = (5. + 6.02)/2 # m**2 \n", + "\n", + "# Calculations\n", + "T2 = 545.1 # k\n", + "T2_ = 322.6\n", + "T3 = 544.7\n", + "T3_ = 328.4\n", + "rate_of_heatloss1 = int(A2m*k/w*(T2-T2_))\n", + "rate_of_heatloss2 = int(A3m*k/w*(T3-T3_))\n", + "total = rate_of_heatloss1 + rate_of_heatloss2\n", + "\n", + "# results\n", + "print \"Rate of heat loss from the top surface : %d W\"%rate_of_heatloss1\n", + "print \"Rate of heat loss from the side walls : %d W\"%rate_of_heatloss2\n", + "print \"Total rate of heat loss : %d W\"%total" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.20 Page No : 264" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the spectral extinction coefficient is 24.08 m**-1\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "T = 300. \t\t\t#K, temprature\n", + "per = 91. \t\t\t#percent, adsorbed radiation\n", + "lam = 4.2 \t\t\t#micrometer, wavelength radiation\n", + "L = 0.1 \t\t\t#m, path length\n", + "\n", + "#calculation\n", + "# I2/I1 = f\n", + "f = 1-per/100. \t\t\t#fraction of incident radiation transmitted\n", + "#from eq. 7.69\n", + "a = -math.log(f)/L\n", + "\n", + "# Results\n", + "print \"the spectral extinction coefficient is %.2f m**-1\"%(a)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.21 Page No : 265" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total rate of heat transfer from the gas to the wall is 22.5 kW\n" + ] + } + ], + "source": [ + "# Variables\n", + "Ts = 800. \t\t\t#C, wall temp.\n", + "Tg = 1100. \t\t\t#C. burner temprature\n", + "CO2 = 8. \t\t\t#percent, composition of CO2 in flue gas\n", + "M = 15.2 \t\t\t#percent, composition of moisture in flue gas\n", + "a = 0.4 \t\t\t#m, length of duct\n", + "b = 0.4 \t\t\t#width of duct\n", + "h = 15. \t\t\t#W/m**2 C, heat transfer coefficient\n", + "P = 1. \t\t\t#atm pressure\n", + "#CAlCULATION of Eg(Tg)\n", + "pc = CO2/100.*P \t\t\t#atm, partial pressure of CO2\n", + "pw = M/100.*P \t\t\t#atm, partial pressure of moisture\n", + "l = 1. \t\t\t#m, length of duct\n", + "V = a*b*l \t\t\t#m**3, volume of duct\n", + "A = 1.6*l \t\t\t#m**2 area of duct\n", + "Le = 3.6*(V/A) \t\t\t#m, mean beam length\n", + "\n", + "pc*Le\n", + "pw*Le\n", + "Tg_ = Tg+273.\n", + "Ts_ = Ts+273.\n", + "#from fig 7.38\n", + "Ec = 0.06\n", + "Eg = 0.048 \t\t\t#from fig 7.39\n", + "#a correction dE need to be calculated\n", + "#pw/(pc+pw)\n", + "#pc*Le+pw*Le\n", + "#from fig. 7.39\n", + "dE = 0.003\n", + "Eg_Tg = Ec+Eg-dE \t\t\t#emissivity at temp. Tg\n", + "\n", + "#Calculation of alpha\n", + "#pc*Le*Ts/Tg\n", + "#from fig. 7.37\n", + "Ec1 = 0.068\n", + "#from fig. 7.38\n", + "Ew1 = 0.069\n", + "Cc = 1 \t\t\t#correction factor\n", + "Cw = 1 \t\t\t#correction factor\n", + "d_alpha = dE \t\t\t#AT 1 ATM TOTAL PRESSURE\n", + "alpha = Cc*Ec1*(Tg_/Ts_)**0.65+Cw*Ew1*(Tg_/Ts_)**0.45-dE\n", + "#radiant heat ransfer rate\n", + "s = 5.669*10**-8 \t\t\t#stephen's boltzman consmath.tant\n", + "Qrad = A*s*(Eg_Tg*Tg_**4-alpha*Ts_**4) \t\t\t#kW\n", + "Qconv = h*A*(Tg-Ts) \t\t\t#kW, convective heat transfer rate\n", + "Q = Qrad+Qconv\n", + "\n", + "# Results\n", + "print \"The total rate of heat transfer from the gas to the wall is %.1f kW\"%(Q/1000)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb new file mode 100644 index 00000000..ff0dc69f --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb @@ -0,0 +1,494 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8 : Heat Exchanger" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1 Page No : 303" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the heat duty of the exchanger is 47000 kj/h\n", + "the water flow rate is 1122 kg/h\n", + "heat transfer coefficient based on inside area is 3560 W/m**2 C \n", + "heat transfer coefficient based on outside area is 880.3 W/m**2 C \n", + "overall heat transfer coefficient outside area basis is 663.1 W/m**2 C \n", + "overall heat transfer coefficient inside area basis is 802.0 W/m**2 C \n", + "The fouling factor is 0.000949 m**2 C/W\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "#for Benzene\n", + "Mb = 1000. \t\t\t#Kg, mass of benzene\n", + "T1 = 75. \t\t\t#C initial temp. of benzene\n", + "T2 = 50. \t\t\t#C final temp. of benzene\n", + "Cp1 = 1.88 \t\t\t#Kj/Kg C. specific heat of benzene\n", + "mu1 = 0.37 \t\t\t#cP. vismath.cosity of benzene\n", + "rho1 = 860. \t\t\t#kg/m**3, density\n", + "k1 = 0.154 \t\t\t#W/m K. thermal conductivity\n", + "\n", + "#for water\n", + "Tav = 35. \t\t\t#C av, temp.\n", + "Cp2 = 4.187 \t\t\t#specific heat\n", + "mu2 = 0.8 \t\t\t#cP. vismath.cosity\n", + "k2 = 0.623 \t\t\t#W/m K. thermal conductivity\n", + "T3 = 30. \t\t\t#C. initial temp.\n", + "T4 = 40. \t\t\t#C final temp.\n", + "\n", + "#Calculation and Results\n", + "#(a)\n", + "HD = Mb*Cp1*(T1-T2) \t\t\t#Kj/h, heat duty\n", + "WR = HD/(Cp2*(T4-T3)) \t\t\t#kg/h Water rate\n", + "print \"the heat duty of the exchanger is %.0f kj/h\"%(HD)\n", + "print \"the water flow rate is %d kg/h\"%(WR)\n", + "\n", + "#(b)\n", + "#tube side (water) calculations\n", + "# Variables\n", + "di1 = 21. \t\t\t#mm, inner diameter of inner tube \n", + "do1 = 25.4 \t\t\t#mm, outer dia. of inner tube\n", + "t = 2.2 \t\t\t#mm/ wall thickness\n", + "kw = 74.5 \t\t\t#W/m K. thermal conductivity of the wall\n", + "di2 = 41. \t\t\t#mm, inner diameter of outer pipe\n", + "do2 = 48. \t\t\t#mm, outer diameter of outer pipe\n", + "\n", + "FA1 = (math.pi/4)*(di1*10**-3)**2 \t\t\t#m**2, flow area\n", + "FR1 = WR/1000.\n", + "v1 = FR1/(FA1*3600) \t\t\t#m/s, velocity\n", + "Re1 = (di1*10**-3)*v1*1000/(mu2*10**-3) \t\t\t#Reynold no.\n", + "Pr1 = Cp2*1000*(mu2*10**-3)/k2 \t\t\t#Prandtl no.\n", + "#umath.sing dittus boelter eq.\n", + "Nu1 = 0.023*(Re1)**(0.8)*(Pr1)**(0.3) \t\t\t#nusslet no.\n", + "h1 = round(Nu1*k2/(di1*10**-3),-1) \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "#Outer side (benzene) calculation\n", + "FA2 = (math.pi/4)*(di2*10**-3)**2-(math.pi/4)*(do1*10**-3)**2 \t\t\t#flow area\n", + "wp = math.pi*(di2*10**-3+do1*10**-3) \t\t\t#wettwd perimeter\n", + "dh = 4*FA2/wp \t\t\t#hydrolic diameter\n", + "bfr = Mb/rho1 \t\t\t#m**3/h benzene flow rate\n", + "v2 = bfr/(FA2*3600) \t\t\t#m/s, velocity\n", + "Re2 = dh*v2*rho1/(mu1*10**-3) \t\t\t#Reynold no\n", + "Pr2 = Cp1*10**3*(mu1*10**-3)/k1 \t\t\t#Prandtl no.\n", + "Nu2 = 0.023*(Re2)**(0.8)*(Pr2)**(0.4) \t\t\t#nusslet no.\n", + "h2 = Nu2*k1/(dh) \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "print \"heat transfer coefficient based on inside area is %.0f W/m**2 C \"%(h1)\n", + "print \"heat transfer coefficient based on outside area is %.1f W/m**2 C \"%(h2)\n", + "\n", + "#Calculation of clean overall heat transfer coefficient, outside area basis\n", + "#from eq. 8.28\n", + "# Variables\n", + "l = 1. \t\t\t#assume , length\n", + "Ao = math.pi*do1*10**-3*l\n", + "Ai = math.pi*di1*10**-3*l\n", + "Am = (do1*10**-3-di1*10**-3)*math.pi*l/(math.log(do1*10**-3/(di1*10**-3)))\n", + "\n", + "#overall heat transfer coefficient\n", + "Uo = 1/((1/h2)+(Ao/Am)*((do1*10**-3-di1*10**-3)/(2*kw))+(Ao/Ai)*(1/h1))\n", + "Ui = Uo*Ao/Ai\n", + "\n", + "#Calculation of LMTD\n", + "dt1 = T1-T4\n", + "dt2 = T2-T3\n", + "LMTD = (dt1-dt2)/math.log(dt1/dt2) \t\t\t#math.log mean temp. difference correction factor\n", + "Q = HD*1000/3600 \t\t\t#W, heat required\n", + "Ao_ = Q/(Uo*LMTD) \t\t\t#m**@, required area\n", + "len = Ao_/(math.pi*do1*10**(-3)) \t\t\t#m, tube length necessary\n", + "\n", + "#(c)\n", + "la = 15. \t\t\t#m ,actual length\n", + "Aht = (math.pi*do1*10**(-3)*la)\n", + "Udo = Q/(Aht*LMTD) \t\t\t#W/m**2 C, overall heat transfer coefficient with dirt factor\n", + "#from eq. 8.2\n", + "Rdo = (1/Udo)-(1/Uo) \t\t\t#m**2 C/W\n", + "print \"overall heat transfer coefficient outside area basis is %.1f W/m**2 C \"%(Uo)\n", + "print \"overall heat transfer coefficient inside area basis is %.1f W/m**2 C \"%(Ui)\n", + "print \"The fouling factor is %f m**2 C/W\"%(Rdo)\n", + "\n", + "# note : rounding off error. please check." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2 Page No : 309" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tube side Pressure drop is 1.118e+04 N/m**2 \n", + "Shell side Pressure drop is 120 N/m**2 \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "Cp = 50. \t\t\t#tpd, plant capacity\n", + "T1 = 135. \t\t\t#C, Temp.\n", + "T2 = 40. \t\t\t#C temp.\n", + "T3 = 30. \t\t\t#C temp.\n", + "dt1 = (T1-T2) \t\t\t#C hot end temp. \n", + "dt2 = (T2-T3) \t\t\t#C cold end temp.\n", + "#Properties of ethylbenzene\n", + "rho1 = 840. \t\t\t#kg/m**3, density\n", + "cp1 = 2.093 \t\t\t#kj/kg K , specific heat\n", + "T = 87.5 \t\t\t#C\n", + "mu1 = math.exp(-6.106+1353/(T+273)+5.112*10**-3*(T+273)-4.552*10**-6*((T+273)**2))\n", + "k1 = 0.2142-(3.44*10**-4)*(T+273)+(1.947*10**-7)*(T+273)**2\n", + "k1_ = k1*0.86 \t\t\t#kcal/h m K\n", + "#properties of water\n", + "rho2 = 993. \t\t\t#kg/m**3, density\n", + "mu2 = 8*10.**-4 \t\t\t#kg/m s , vismath.cosity \n", + "cp2 = 4.175 \t\t\t#kj/kg K , specific heat\n", + "k2 = 0.623 \t\t\t#W/m K, thermal conductivity\n", + "k2_ = k2*0.8603 \t\t\t#kcal/h m**2 K\n", + "#Calculation\n", + "#(i) Energy balance\n", + "Cp = Cp*1000./24 \t\t\t#kg/h, plant capacity\n", + "Cp = 2083. \t\t\t#approx.\n", + "HD = Cp*cp1*dt1 \t\t\t#kj/h, Heat duty \n", + "HD_ = HD*0.238837 \t\t\t#kcal/h\n", + "wfr = HD/(cp2*dt2)\n", + "\n", + "#(ii)\n", + "mu1 = mu1 \t\t\t#cP, vismath.cosity of ethylbenzene\n", + "k1 = k1 \t\t\t#W/m K, thermal conductivity of ethylbenzene\n", + "\n", + "#(iii)\n", + "#LMTD calculation\n", + "LMTD = (dt1-dt2)/math.log(dt1/dt2)\n", + "#assume\n", + "Udo = 350. \t\t\t#kcal/h m**2 C, overall coefficient\n", + "A = HD_/(Udo*LMTD) \t\t\t#m**2, area required\n", + "\n", + "#(iv)\n", + "id_ = 15.7 \t\t\t#mm, internal diameter of tube\n", + "od = 19. \t\t\t#mm, outer diameter of tube\n", + "l = 3000. \t\t\t#mm, length\n", + "OSA = math.pi*(od*10**-3)*(l*10**-3) \t\t\t#m**2. outer surface area\n", + "n = A/OSA \t\t\t#no. of tubes required\n", + "fa = n*(math.pi/4)*(id_*10**-3)**2 \t\t\t#m**2, flow arae\n", + "lv = (wfr/1000)/(3600*fa) \t\t\t#m/s, linear velocity\n", + "\n", + "#(v)\n", + "n1 = 44. \t\t\t#total no. of tubes that can be accomodated in a 10 inch shell\n", + "np = 11. \t\t\t#no. of tubes in each pass\n", + "#(vi)\n", + "bf = 0.15 \t\t\t#m, baffel spacing\n", + "#(vii)\n", + "#estimation of heat transfer coefficient\n", + "#Tube side (water)\n", + "fa1 = (math.pi/4)*(id_*10**-3)**2*np \t\t\t#m**2, flow area\n", + "v1 = (wfr/1000.)/(3600*fa1) \t\t\t#m/s, velocity\n", + "Re = (id_*10**-3)*v1*rho2/mu2 \t\t\t#Reynold no.\n", + "#from fig . 8.11(a)\n", + "jh = 85. \t\t\t#colburn factor\n", + "#jh = (hi*di)/k*(cp*mu/k)**-1/3 \n", + "#assume, (cp*mu/k) = x\n", + "hi = jh*(k2_/(id_*10**-3))*(cp2*1000*mu2/k2)**(1/3) \t\t\t#kcal/h m**2 C\n", + "\n", + "#shell side(organic)\n", + "B = bf \t\t\t#m, baffel spacing\n", + "p = 0.0254 \t\t\t#m,radius of 1 tube\n", + "Ds = 0.254 \t\t\t#m, inside diameter of shell\n", + "c = 0.0064 \n", + "#from eq. 8.32\n", + "As = c*B*Ds/p \t\t\t#m**2, flow area\n", + "Gs = Cp/As \t\t\t#kg/m**2 h, mass flow rate of shell fluid\n", + "do = od/10 \t\t\t#cm, outside diameter of shell\n", + "#from eq. 8.31\n", + "Dh = 4*((0.5*p*100)*(0.86*p*100)-((math.pi*(do)**2)/8))/((math.pi*do)/2)\n", + "Dh_ = Dh*10**-2 \t\t\t#m, hydrolic diameter\n", + "Re1 = (Dh_*Gs)/(3600*(mu1*10**-3)) \t\t\t#Reynold no.\n", + "#from fig 8.11(b)\n", + "jh1 = 32 \t\t\t#colburn factor\n", + "ho = jh1*(k1_/Dh_)*((6)**(1./3))\n", + "#from eq. 8.28\n", + "ratio = od/id_ \t\t\t#ratio = Ao/Ai\n", + "Rdo = 0.21*10**-3 \t\t\t#outside dirt factor\n", + "Rdi = 0.35*10**-3 \t\t\t#inside dirt factor\n", + "Udo = 1/((1/ho)+Rdo+(ratio)*Rdi+(ratio)*(1/hi))\n", + "\n", + "#SECOND TRIAL\n", + "#estimation of heat transfer coefficient\n", + "#Tube side (water)\n", + "np1 = 12 \t\t\t#\n", + "fa2 = (math.pi/4)*(id_*10**-3)**2*np1 \t\t\t#m**2, flow area\n", + "v2 = (wfr/1000)/(3600*fa2) \t\t\t#m/s, velocity\n", + "Re2 = (id_*10**-3)*v2*rho2/mu2 \t\t\t#Reynold no.\n", + "#from fig . 8.11(a)\n", + "jht = 83. \t\t\t#colburn factor\n", + "#jh = (hi*di)/k*(cp*mu/k)**-1/3 \n", + "#assume, (cp*mu/k) = x\n", + "hit = jht*(k2_/(id_*10**-3))*(cp2*1000*mu2/k2)**(1./3) \t\t\t#kcal/h m**2 C\n", + "\n", + "#shell side\n", + "B2 = 0.1 \t\t\t#m, baffel spacing\n", + "p2 = 0.0254 \t\t\t#m,radius of 1 tube\n", + "Ds2 = 0.254 \t\t\t#m, inside diameter of shell\n", + "c2 = .0064\n", + "#from eq. 8.32\n", + "As2 = c2*B2*Ds2/p2 \t\t\t#m**2, flow area\n", + "Gs2 = Cp/As2 \t\t\t#kg/m**2 h, mass flow rate of shell fluid\n", + "do2 = od/10 \t\t\t#cm, outside diameter of shell\n", + "#from eq. 8.30\n", + "Dh2 = 4*((p2*100)**2-((math.pi*(do2)**2)/4))/((math.pi*do2))\n", + "Dh2_ = Dh2*10**-2 \t\t\t#m, hydrolic diameter\n", + "Re2 = (Dh2_*Gs2)/(3600*(mu1*10**-3))\n", + "#from fig 8.11(b)\n", + "jh2 = 48 \t\t\t#colburn factor\n", + "ho2 = jh2*(k1_/Dh2_)*((6)**(1./3))\n", + "#from eq. 8.28\n", + "ratio = od/id_ \t\t\t#ratio = Ao/Ai\n", + "Rdo2 = 0.21*10**-3 \t\t\t#outside dirt factor\n", + "Rdi2 = 0.35*10**-3 \t\t\t#inside dirt factor\n", + "Udo2 = 1/((1/ho2)+Rdo+(ratio)*Rdi+(ratio)*(1/hit))\n", + "\n", + "#from eq. 8.10(a)\n", + "tauc = (T2-T3)/(T1-T3) \t\t\t#Temprature ratio\n", + "R = (T1-T2)/(T2-T3) \t\t\t#Temprature ratio\n", + "Ft = 0.8 \t\t\t#LMTD correction ftor\n", + "Areq = HD_/(Udo2*Ft*LMTD) \t\t\t#area required\n", + "tubes = 48. \t\t\t#no. of tubes\n", + "lnt = 4.5 \t\t\t#length of 1 tube\n", + "Aavl = (math.pi*od*10**-3)*tubes*lnt \t\t\t#available area\n", + "excA = ((Aavl-Areq)/Areq)*100 \t\t\t#% excess area\n", + "\n", + "#Pressure drop calculation\n", + "#Tube side\n", + "#from eq. 8.33\n", + "Gt = wfr/(3600*fa2) \t\t\t#kg/m**2 s, mass flow rate of tube fluid\n", + "n2 = 4. \t\t\t#tube passes\n", + "fit = 1. \t\t\t#dimensionless vismath.cosity ratio\n", + "g = 9.8 \t\t\t#gravitational consmath.tant\n", + "f = 0.0037 \t\t\t#friction factor\n", + "dpt = f*Gt**2*lnt*n2/(2*g*rho2*id_*10**-3*fit) \t\t\t#kg/m**2, tube side pressure drop\n", + "\n", + "#eq.8.35\n", + "dpr = 4*n2*v2**2*rho2/(2*g) \t\t\t#kg/m**2, return tube pressure loss\n", + "dpr_ = dpr*9.801 \t\t\t#N/m**2\n", + "tpr = dpt+dpr \t\t\t#kg/m**2, total pressure drop\n", + "#shell side\n", + "fs = 0.052 \t\t\t#friction factor for shell\n", + "bf1 = 0.1 \t\t\t#m, baffel spacing\n", + "Nb = lnt/bf1-1 \t\t\t#no. of baffles\n", + "dps = fs*(Gs2/3600)**2*Ds*(Nb+1)/(2*g*rho1*Dh2_*fit) \t\t\t#kg/m**2, shell side pressure drop\n", + "dps_ = dps*9.81 \t\t\t#N/m**2, shell side pressure drop\n", + "print \"Tube side Pressure drop is %1.3e N/m**2 \"%(dpr_)\n", + "print \"Shell side Pressure drop is %.0f N/m**2 \"%(round(dps_,-1))\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3 Page No : 320" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Th2 = 49.5 C\n", + "The new rate of heat transfer : 161003 kcal/h\n", + "the heat teansfer rate will be affected by 1.3 percent \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "#for hot stream\n", + "Wh = 10000. \t\t\t#kg/h, Rate of leaving a hydrolic system by the oil\n", + "Cph = 0.454 \t\t\t#Kcal/Kg C, specific heat of oil\n", + "Th1 = 85. \t\t\t#C initial temp. of oil\n", + "Th2 = 50. \t\t\t#C final temp. of oil \n", + "\n", + "#For cold stream\n", + "Cpc = 1. \t\t\t#Kcal/Kg C, specific heat of water\n", + "Tc2 = 30. \t\t\t#C final temp. of water\n", + "Tc1 = 38. \t\t\t#C initial temp. of water\n", + "\n", + "# Calculations\n", + "#from heat balance eq.\n", + "#kg/h, Rate of leaving a hydrolic system by the water\n", + "Wc = Wh*Cph*(Th1-Th2)/(Cpc*(Tc1-Tc2))\n", + "#For the hot stream\n", + "Cmin = Wh*Cph \t\t\t#Kcal/h C.Taking hot stream as min. stream\n", + "#For cold stream\n", + "Cmax = Wc*Cpc \t\t\t#Kcal/h C.Taking cold stream as max. stream\n", + "Cr = Cmin/Cmax \t\t\t#Capacity ratio\n", + "n = (Th1-Th2)/(Th1-Tc2) \t\t\t#effectiveness factor\n", + "#From eq. 8.57\n", + "#No. of transfer units\n", + "NTU = -(1+(Cr)**2)**-(1./2)*math.log(((2/n)-(1+Cr)-(1+(Cr)**2)**(1./2))/((2./n)-(1+Cr)+(1+(Cr)**2)**(1./2)))\n", + "Ud = 400. \t\t\t#kcal/h m**2C , overall dirty heat transfer coefficient\n", + "#from eq. 8.53\n", + "A = (NTU*Cmin)/Ud \t\t\t#Area required\n", + "#if the water rate is increased by 20 %,\n", + "a = 20.\n", + "Wc_ = Wc+(Wc*(a/100))\n", + "Cmax_ = Wc_*Cpc\n", + "Cr_ = Cmin/Cmax_\n", + "#From eq. 8.56\n", + "n_ = 2*((1+Cr_)+(1+(Cr_)**2)**(1./2)*(1+math.exp(-(1+(Cr_)**2)**(1./2)*NTU))/(1-math.exp(-(1+(Cr_)**2)**(1./2)*NTU)))**(-1)\n", + "Th2_ = Th1-(n_*(Th1-Tc2))\n", + "q1 = Wh*Cph*(Th1-Th2) \t\t\t#kcal/h previous rate of heat transfer\n", + "q2 = Wh*Cph*(Th1-Th2_) \t\t\t#kcal/h new rate of heat transfer\n", + "#increase in rate of heat transfer\n", + "dq = (q2-q1)/q1 \n", + "\n", + "# Results\n", + "print \"Th2 = %.1f C\"%Th2_\n", + "print \"The new rate of heat transfer : %d kcal/h\"%q2\n", + "print \"the heat teansfer rate will be affected by %.1f percent \"%(dq*100 )\n", + "\n", + "# note : rounding off error would be there." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4 Page No : 337" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the time required to heat the charge 22 min\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "p = 0.0795 \t\t\t#m. pitch of the coil\n", + "d1 = 0.0525 \t\t\t#m,coil diameter\n", + "h = 1.464 \t\t\t#m,height of the limpetted section\n", + "d2 = 1.5 \t\t\t#m,diameter of batch polymerization reactor\n", + "d3 = 0.5 \t\t\t#m,diameter of agitator\n", + "rpm = 150. \t\t\t#speed of agitator\n", + "rho = 850. \t\t\t#kg/m3,density of monomer\n", + "rho1 = 900. \t\t\t#kg/m3,density of fluid\n", + "mu = 0.7*10**-3 \t\t\t#poise, vismath.cosity of monomer\n", + "mu1 = 4*10.**-3 \t\t\t#poise, vismath.cosity of fluid\n", + "cp = 0.45 \t\t\t#kcal/kg C, specific heat of monomer\n", + "cp1 = 0.5 \t\t\t#kcal/kg C, specific heat of fluid\n", + "k = 0.15 \t\t\t#kcal/h mC, thermal conductivity of monomer\n", + "k1 = 0.28 \t\t\t#kcal/h mC, thermal conductivity of fluid\n", + "Rdi = 0.0002 \t\t\t#h m2 C/kcal, fouling factor for vessel\n", + "Rdc = 0.0002 \t\t\t#h m2 C/kcal, fouling factor for coil\n", + "Tci = 120. \t\t\t#C, initial temp. of coil liquid\n", + "Tvi = 25. \t\t\t#C, initial temp. of vessel liquid\n", + "Tvf = 80. \t\t\t#C, final temp. of vessel liquid\n", + "\n", + "#calculation\n", + "a = math.pi*d2*h \t\t\t#outside area of the vessel\n", + "x = 60. \t\t\t#%. added of the unwetted area to the wetted area\n", + "ao = ((d1+(x/100)*(p-d1))/p)*a \t\t\t#m**2,effective outside heat transfer area of vessel\n", + "ai = 6.9 \t\t\t#m**2,inside heat transfer area of vessel\n", + "#same as outside area , if thickness is very small\n", + "#vessel side heat transfer coefficient\n", + "Re = (d3**2*(rpm/60)*rho)/mu \t\t\t#reynold no.\n", + "Pr = ((cp*3600)*(mu))/k\n", + "#from eq. 8.66\n", + "y = 1 \t\t\t#x = mu/muw = 1\n", + "Nu = 0.74*(Re**(0.67))*(Pr**(0.33))*(y**(0.14)) \t\t\t#Nusslet no\n", + "hi = Nu*(k/d2) \t\t\t#heat transfer coefficient\n", + "\n", + "#coil side heat transfer coefficient\n", + "v = 1.5 \t\t\t#m/s, linear velocity of fluid\n", + "fa = ((math.pi/4)*d1**2) \t\t\t#m2, flow area of coil\n", + "fr = v*fa*3600 \t\t\t#m3/h , flow rate of the fluid\n", + "Wc = fr*rho \t\t\t#kg/h , flow rate\n", + "dh = (4*(math.pi/8)*d1**2)/(d1+(math.pi/2)*d1) \t\t\t#m,hydrolic diameter of limpet coil\n", + "Re1 = v*rho1*dh/mu1 \t\t\t#coil reynold no.\n", + "Pr1 = cp1*mu1*3600/k1 \t\t\t#prandtl no. of the coil fluid\n", + "#from eq. 8.68\n", + "d4 = 0.0321 \t\t\t#m, inside diameter of the tube\n", + "Nu1 = 0.021*(Re1**(0.85)*Pr1**(0.4)*(d4/d2)**(0.1)*y**0.14) \n", + "hc = Nu1*(k1/dh) \t\t\t#coil side coefficient\n", + "\n", + "U = 1/((1/hi)+(ai/(hc*ao))+Rdi+Rdc) \t\t\t#overall heat transfer corfficient\n", + "#from eq. 8.63\n", + "beeta = math.exp(U*ai/(Wc*cp1))\n", + "Wv = 2200. \t\t\t#kg, mass of fluid vessel\n", + "t = (beeta/(beeta-1))*((Wv*cp)/(Wc*cp1))*math.log((Tci-Tvi)/(Tci-Tvf)) \n", + "\n", + "# Results\n", + "print \"the time required to heat the charge %.0f min\"%(t*60)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch9.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch9.ipynb new file mode 100644 index 00000000..6a4e4ff0 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch9.ipynb @@ -0,0 +1,692 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9 : Evaporation and Evaporators" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1 Page No : 391" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rate at which heat must be supplied at 1 atm pressure is 2.441e+08 kj/ day\n", + "The rate at which heat must be supplied at a pressure of 600 mm Hg is 2.373e+08 kj/day \n" + ] + } + ], + "source": [ + "# Variables\n", + "ro = 1020. \t\t\t# kg/m**3, density of feed\n", + "sf = 4.1 \t\t\t#kj/kg C,specific heat of the feed\n", + "sp = 3.9 \t\t\t#kj/kg C,specific heat of the product\n", + "ci = 5. \t\t\t#initial concentration\n", + "cw = 100.-ci \t\t\t#conc. of water\n", + "cf = 40. \t\t\t#final conc.\n", + "rate = 100. \t\t\t#m**3/day, rate of conc. of aq. solution\n", + "ft = 25. \t\t\t# C, feed temp.\n", + "\n", + "#calculation and results\n", + "#materiel balance\n", + "Wf = rate*ro \t\t\t#Kg. feed entering\n", + "Ms = ro*ci \t\t\t#Kg mass of solute\n", + "Mw = ro*cw \t\t\t#kg,mass of water\n", + "fc = cw/ci \t\t\t#kg,feed concentration\n", + "pc = (100-cf)/cf \t\t\t# kg,product concentration\n", + "wlwp = Ms*pc \t\t\t#Kg, water leaving with the product\n", + "Ws = Mw-wlwp \t\t\t#kg,water evaporated\n", + "Wp = wlwp+Ms \t\t\t# kg, product\n", + "#energy balance\n", + "rt = 0. \t\t\t#C reference temp.\n", + "ef = sf*(ft-rt) \t\t\t#kj/kg,enthlpy of the feed\n", + "#case i\n", + "Tp = 100. \t\t\t#temp. of the product (because the solute has a 'high molecular wt' the boiling pt elevation is neglected)\n", + "ip = sp*(Tp-rt) \t\t\t#kj/kg, enthalpy of the product\n", + "iv = 2680. \t\t\t#kj/kg, enthalpy of the vapour generated at 100 C and 1 atm pr. from the steam table\n", + "#refer to fig. 9.23\n", + "#from energy balance eq. (Wf*if+qs = Wv*iv+Wp*ip)\n", + "qs = Ws*iv+Wp*ip-Wf-ef \t\t\t#Wv = Ws\n", + "print \"The rate at which heat must be supplied at 1 atm pressure is %1.3e kj/ day\"%(qs)\n", + "\n", + "#case ii\n", + "#650 mm Hg vaccum = 110 mmHg pressure\n", + "bp = 53.5 \t\t\t#C, boiling point of water\n", + "ip2 = sp*(bp-rt) \t\t\t#kj/kg, enthalpy of the product\n", + "es = 2604. \t\t\t#kj/kg, enthalpy of the saturated steam (from steam table)\n", + "#from energy balnce eq.\n", + "qs2 = Wp*ip+Ws*es-Wf-ef\n", + "print \"The rate at which heat must be supplied at a pressure of 600 mm Hg is %1.3e kj/day \"%(qs2)\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2 Page No : 393" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The steam required is 1737 kg/h\n", + "No. of tube are 102\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "ci = 10. \t\t\t#%,initial concentration\n", + "cf = 40. \t\t\t#%, final conc\n", + "Wf = 2000. \t\t\t#kg/h, feed rate\n", + "ft = 30. \t\t\t#C feed temp.\n", + "rp = 0.33 \t\t\t#kg/cm**2, reduced pressure\n", + "bt1 = 75. \t\t\t#C,boiling point temp.\n", + "sst = 115. \t\t\t#C, saturated steam temp.\n", + "l = 1.5 \t\t\t# m,height of calandria\n", + "sh = 0.946 \t\t\t#kcal/kg C, specific heat of liquir\n", + "lh = 556.5 \t\t\t#kcal/kg latent heat of steam\n", + "bt2 = 345. \t\t\t#K, boiling point of water \n", + "h = 2150. \t\t\t#kcal/h m**2 C, overall heat transfer coefficient\n", + "si = 2000.*(ci/100) \t\t\t#kg/h, solids in\n", + "wi = 1800. \t\t\t#kg/h,wate in\n", + "\n", + "# Calculations\n", + "Wp = si/(cf/100) \t\t\t#kg/h, product out\n", + "Wv = Wf-Wp \t\t\t#evaporation rate\n", + "ef = sh*(ft-bt1)\n", + "ip = 0\n", + "lamda_s = 529.5 \t\t\t#kcal/kg, lamda_s = is-il\n", + "bpe = (273+bt1)-345 \t\t\t#boiling point elevation.\n", + "#from eergy balance eq.\n", + "Ws = (Wp*ip+Wv*lh-Wf*ef)/lamda_s\n", + "q = Ws*lamda_s \t\t\t#kcal/h,rate of heat transfer\n", + "A = q/(h*(sst-bt1)) \t\t\t# m**2\n", + "di = 0.0221 \t\t\t#m,inside diameter\n", + "At = math.pi*l*di \t\t\t#m**2, area of a math.single tube\n", + "N = A/At \t\t\t#no. of tubes\n", + "\n", + "# Results\n", + "print \"The steam required is %.0f kg/h\"%(Ws)\n", + "print \"No. of tube are %d\"%(N)\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3 Page No : 393" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The steam pressure to be used in the calandria is 2.15 barabs)\n", + "The heat transfer rate required is 4.01e+06 Kj/h\n", + "Rate of steam supply is 1833 kg/h\n" + ] + } + ], + "source": [ + "# Variables\n", + "Wf = 2000. \t\t\t#kg/h, feed rate\n", + "ci = 8. \t\t\t#% initial conc.\n", + "cf = 40. \t\t\t#% final conc.\n", + "ft = 30. \t\t\t#C, feed temp.\n", + "vp = 660. \t\t\t#mm Hg, vaccum pressure\n", + "ssp = 8. \t\t\t# bar absolute, saturated steam pr.\n", + "\n", + "#calculation\n", + "sr = Wf*(ci/100) \t\t\t#kg/h, solid rate\n", + "Wp = sr/(cf/100) \t\t\t#kg/h,concentrated product rate\n", + "ap = 760-vp \t\t\t#mm Hg, absolute pressure in the evaporator\n", + "bt = 325. \t\t\t#K,boiling temp. of water\n", + "l_s = 2380. \t\t\t#kj/kg, latent heat\n", + "R = 8.303 \t\t\t#gas consmath.tant\n", + "w = 40. \t\t\t#g,mass of solute\n", + "M = 18. \t\t\t#g,molecular wt of solvent\n", + "W = 60. \t\t\t#g,mass of the solvent\n", + "m = 2000. \t\t\t#g,molecular wt of solute\n", + "dtb = (R*bt**2*w*M)/(l_s*W*m) \t\t\t#C, boiling point elevation\n", + "bp = bt+dtb \t\t\t#k,boiling point of 40% solution\n", + "dt = 70. \t\t\t#C, from given data flux becomes maximum at a temp. drop = 70 C\n", + "st = bp+dt \t\t\t#K,saturation temp. of steam in the steam chest\n", + "Sp = 2.15 \t\t\t# bar, from steam table, saturation lr. of steam at this temp.\n", + "\n", + "sh = 4.2 \t\t\t#kj/kg C, specific heat of product\n", + "rt = 0. \t\t\t#C reference teml.\n", + "ef = sh*(ft-rt) \t\t\t# kj/kg, enthalpy of the feed\n", + "ip = sh*(54-rt) \t\t\t#kj/kg, enthalpy of the product\n", + "iv = 2607. \t\t\t#kj/kg, enthalpy of vapour produced\n", + "#from eq 9.6\n", + "Wv = 1600. \t\t\t#enthalpy of evaporation\n", + "q = Wp*ip+Wv*iv-Wf*ef \t\t\t#kj/h, heat transfe rate required\n", + "hvp = 2188. \t\t\t#kj/kg, heat of vaporization of saturated steam at 397 K\n", + "rs = q/hvp \t\t\t#kg/h, rate of steam supply\n", + "\n", + "# Results\n", + "print \"The steam pressure to be used in the calandria is %.2f barabs)\"%(Sp);\n", + "print \"The heat transfer rate required is %.2e Kj/h\"%(q);\n", + "print \"Rate of steam supply is %.0f kg/h\"%(rs);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4 Page No : 402" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The evaporator area is 72 square metre \n", + "Steam economy is 1.79\n" + ] + } + ], + "source": [ + "import math \n", + "\n", + "from numpy import array, linalg\n", + "# Variables\n", + "Wf = 6000. \t\t\t#kg/h, feed rate\n", + "ci = 2. \t\t\t#%, initial concentration\n", + "cf = 35. \t\t\t#%, final conc.\n", + "ft = 50. \t\t\t#C,feed temp.\n", + "ssp = 2. \t\t\t#bar abs, saturated steaam pr.\n", + "sep = 0.0139 \t\t\t#bar abs, maintained temp. in second effect\n", + "h1 = 2000. \t\t\t#W/m**2 K,overall heat transfer coeffcient in 1st effect\n", + "h2 = 1500. \t\t\t#W/m**2 K, overall heat transfer coefficient in 2nd effect\n", + "cp = 4.1 \t\t\t#kj/kg k,specific heat\n", + "\n", + "#calculation\n", + "si = Wf*(ci/100) \t\t\t#kg/h, solid in\n", + "wi = 5880. \t\t\t#kg/h, water in\n", + "Wp = si/(cf/100) \t\t\t#kg/h product out\n", + "wo = Wp*(1-cf/100) \t\t\t#kg/h, water out with the product\n", + "ter = wi-wo \t\t\t#kg/h, total evaporation rate\n", + "\n", + "#boiling temp. in the first effect\n", + "T1 = 120. \t\t\t#C,Temprature\n", + "l_s1 = 2200. \t\t\t#kj/kg, latent heat\n", + "T2 = 12. \t\t\t#C,boiling point in second effect\n", + "l_s2 = 2470. \t\t\t# kj/kg in second effect\n", + "tatd = T1-T2 \t\t\t# C,tatd = dt1+dt2 = T1-T2 , total available temp. drop\n", + "#from eq. 9.20\n", + "#h1*dt1 = h2*dt2\n", + "#solving above two equations by matrix\n", + "A = array([[1,1],[2000,-1500]])\n", + "C = array([108,0])\n", + "X = linalg.solve(A,C)\n", + "#X = inv(A)*C\n", + "\n", + "dt1 = X[0]\n", + "dt2 = X[1]\n", + "t1 = T1-dt1 \t\t\t#temp. of steam leaving the first effect\n", + "t2 = T2-dt2 \t\t\t#temp. of steam leaving second effect\n", + "#energy balance over the 1st effect, from eq.9.14\n", + "rt1 = t1\n", + "ef = cp*(ft-t1) \t\t\t#kj/kg,enthalpy of feed\n", + "i1 = 0\n", + "lam_s1 = 2330. \t\t\t#kj/kg\n", + "is1 = lam_s1\n", + "#Wf*ef+Ws*l_s = (Wf-Ws1)*i1+Ws1*is1\n", + "#substituting we get,\n", + "#Ws1 = 0.9442*Ws-253.4..........(1)\n", + "#energy balance over second effect\n", + "#from eq 9.15\n", + "#(Wf-Ws1)*i1+Ws1*lam_s1 = (Wf-Ws1-Ws2)*i2+Ws2*is2\n", + "rt2 = t2\n", + "lam_s2 = 2470.\n", + "is2 = lam_s2\n", + "i2 = 0\n", + "# substituting we get\n", + "#Ws2 = 0.8404*Ws1+617.5............(2)\n", + "#ter,Ws1+Ws2 = 5657...............(3)\n", + "#solving by matrix method\n", + "A = array([[0.9442,-1,0],[0,0.8404,-1],[0,1,1]])\n", + "B = array([253.4,-617.5,5657])\n", + "X = linalg.solve(A,B)\n", + "#X = inv(A)*B\n", + "Ws = X[0]\n", + "Ws1 = X[1]\n", + "Ws2 = X[2]\n", + "\n", + "#evaporator area\n", + "A1 = Ws*l_s1/(h1*dt1) \t\t\t#for 1st effect\n", + "A2 = Ws1*lam_s1/(h2*dt2) \t\t\t#for second effect\n", + "\n", + "#revised calculation\n", + "#taking\n", + "dt1_ = 48.\n", + "dt2_ = 60.\n", + "T1_ = T1-dt1_\n", + "T2_ = T2-dt2_\n", + "ls1_ = 2335.\n", + "ls2_ = 2470.\n", + "# energy balance over first effect gives\n", + "#Ws1 = 0.9422Ws-231.8.........(4)\n", + "#energy balance over second effect gives\n", + "#Ws2 = 0.8457Ws1+579.5......(5)\n", + "#solving eq 3,4,5\n", + "P = array([[0.9422,-1,0],[0,0.8457,-1],[0,1,1]])\n", + "Q = array([231.8,-579.5,5657])\n", + "Y = linalg.solve(P,Q)\n", + "#Y = inv(P)*Q\n", + "Ws_ = Y[0]\n", + "Ws1_ = Y[1]\n", + "Ws2_ = Y[2]\n", + "\n", + "#eveporator area for 1st & 2nd effect in m**2\n", + "A1_ = Ws_*l_s1/(h1*dt1_)\n", + "A2_ = Ws1_*ls1_/(h2*dt2_)\n", + "EA = (A1_+A2_)/2\n", + "SE = (Ws1_+Ws2_)/Ws_\n", + "\n", + "# Results\n", + "print \"The evaporator area is %.0f square metre \"%(EA);\n", + "print \"Steam economy is %.2f\"%(SE);\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5 Page No : 404" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum no. of effects are 4\n" + ] + } + ], + "source": [ + "# Variables\n", + "ssp = 3.32 \t\t\t#bar abs, saturated steam pr.\n", + "rp = 0.195 \t\t\t# bar abs, residual pr. in the condenser\n", + "tl = 41. \t\t\t#K, sun of temp. losses because of BPE\n", + "mt = 8. \t\t\t#k,minimum available temp. driving force\n", + "#calculation\n", + "sst = 410. \t\t\t#K,saturated steam temp.\n", + "st = 333. \t\t\t#K,corresponding saturation temp. when pressure in the last effect is 0.195 bar\n", + "ttd = sst-st \t\t\t#K,total temp. difference\n", + "atd = ttd-tl \t\t\t# K,available temp. drop across the unit\n", + "n = atd/mt \t\t\t#maximum no. of effect\n", + "\n", + "# Results\n", + "print \"Maximum no. of effects are %.0f\"%(n);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6 Page No : 405" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The areas are now reasonably close \n", + "Steam Rate is 8854 Kg/h \n", + "Steam economy is 1.93\n" + ] + } + ], + "source": [ + "# Variables\n", + "fc = 9.5 \t\t\t#%,feed concentration\n", + "pc = 50. \t\t\t#%, product conc.\n", + "ft = 40. \t\t\t# C,feed temp.\n", + "er = 2000. \t\t\t#kg NaOH/h, evaporation rate\n", + "vp = 714. \t\t\t#mm Hg, vaccum pr. in last effect\n", + "#heat transfer coefficients, W/m**2 C\n", + "h1 = 6000. \t\t\t#for first effect\n", + "h2 = 3500. \t\t\t#for second effect\n", + "h3 = 2500. \t\t\t#for third effect\n", + "\n", + "#calculatiin\n", + "Wf = er/(fc/100) \t\t\t#kg/h, 2 tons NaOH per hour, feed rate\n", + "Wp = er/(pc/100) \t\t\t#kg/h, product rate\n", + "ter = Wf-Wp \t\t\t#kg/h, total evaporation rate\n", + "#steam\n", + "p = 3.3 \t\t\t#bar,assumed saturated\n", + "#from steam table\n", + "Ts = 137. \t\t\t#C,temp.\n", + "l_s = 2153. \t\t\t#kj/kg, latent heat\n", + "pl = 760.-vp \t\t\t#mm Hg,pressure in the last effect\n", + "bp = 37. \t\t\t#C,boiling point of water\n", + "#refer to fig. 9.24\n", + "attd = Ts-bp \t\t\t#C,apparent total temp. drop\n", + "#let assume the following evaporation rate for three effects in kg/h\n", + "ev1 = 5600.\n", + "ev2 = 5680.\n", + "ev3 = 5773.\n", + "#conc. in three effects\n", + "c1 = er/(Wf-ev1)\n", + "c2 = er/(Wf-ev1-ev2)\n", + "c3 = 0.5 \t\t\t# Variables\n", + "#boiling point elevations in three effects in C\n", + "bpe1 = 3.5\n", + "bpe2 = 8.\n", + "bpe3 = 39.\n", + "attda = attd-(bpe1+bpe2+bpe3) \t\t\t#actual total temp. drop available\n", + "#temp. drop in three effects\n", + "#from eq. 9.23\n", + "dt1 = attda*((1/h1)/((1/h1)+(1/h2)+(1/h3)))\n", + "dt2 = attda*((1/h2)/((1/h1)+(1/h2)+(1/h3)))\n", + "dt3 = attda*((1/h3)/((1/h1)+(1/h2)+(1/h3)))\n", + "\n", + "#from table 9.4\n", + "#enthalpy of solution in three effects in kj/kg\n", + "i1 = 486.\n", + "i2 = 385.\n", + "i3 = 460.\n", + "#enthalpy of vapour generated for three effects in kj/kg\n", + "is1 = 2729.\n", + "is2 = 2691.\n", + "is3 = 2646.\n", + "#Enthalpy of condensate over effect 1,2,3 in kj/kg\n", + "il1 = 0.\n", + "il2 = 519.\n", + "il3 = 418.\n", + "#Enthalpy balance over effect 1\n", + "ef = 145. \t\t\t#kj/kg,enthalpy of feed\n", + "#from energy balance eq.\n", + "#Ws1 = 0.96Ws-3200......(1)\n", + "#enthalpy balanc over effect 2\n", + "#Ws2 = 0.9146Ws1+922...........(2)\n", + "#enthalpy balanc over effet 3\n", + "#Ws3 = 1.073Ws2+0.0343Ws1-722........(3)\n", + "#ter = Ws1+Ws2+Ws3 = 17053..........(4)\n", + "\n", + "#Solving above four eqns by matrix\n", + "A = array([[0.96,-1,0,0],[0,0.9146,-1,0],[0,0.0343,1.073,-1],[0,1,1,1]])\n", + "B = array([3200,-922,722,17053])\n", + "X = linalg.solve(A,B)\n", + "#X = inv(A)*B\n", + "Ws = X[0]\n", + "Ws1 = X[1]\n", + "Ws2 = X[2]\n", + "Ws3 = X[3]\n", + "\n", + "#calculation of heat transfer areas iver effect 1, 2 ,3\n", + "A1 = Ws*l_s*10**3/(h1*dt1*3600)\n", + "A2 = Ws1*(is1-il2)*10**3/(h2*dt2*3600)\n", + "A3 = Ws2*(is2-il3)*10**3/(h3*dt3*3600)\n", + "\n", + "#Revised dt\n", + "avar = (A1+A2+A3)/3\n", + "dt1_ = (A1/avar)*dt1\n", + "dt2_ = (A2/avar)*dt2\n", + "dt3_ = attda-dt1_-dt2_\n", + "\n", + "#from table 9.5\n", + "#enthalpy of vapour generated over effect 1,2,3 in kj/kg\n", + "is1_ = 2720.\n", + "is2_ = 2685.\n", + "is3_ = 2646.\n", + "#enthalpy of soln on 1,2,3 in kj/kg\n", + "i1_ = 470.\n", + "i2_ = 380.\n", + "i3_ = 460.\n", + "#enthalpy of condensate over effect 1 ,2,3 in kj/kg\n", + "il1_ = 0.\n", + "il2_ = 513.\n", + "il3_ = 412.\n", + "#enthalpy balance ove effect 1,2,3 gives\n", + "Ws_ = 8854.\n", + "Ws1_ = 5432.\n", + "Ws2_ = 5812.\n", + "Ws3_ = 5809.\n", + "#revised heat transfer areas for effect 1 ,2,3 in m**2\n", + "A1_ = Ws_*l_s*1000/(h1*dt1_*3600)\n", + "A2_ = Ws1_*(is1_-il2_)*10**3/(h2*dt2_*3600)\n", + "A3_ = Ws2_*(is2_-il3_)*10**3/(h3*22.5*3600)\n", + "avar_ = (A1_+A2_+A3_)/3\n", + "SE = ter/Ws_\n", + "\n", + "# Results\n", + "print \"The areas are now reasonably close \"\n", + "print \"Steam Rate is %.0f Kg/h \"%(Ws_)\n", + "print \"Steam economy is %.2f\"%(SE)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7 Page No : 409" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The increase in evaporation capacity ic 113 percentage \n", + " The percentage change in the math.cost of concentrating a ton of feed is 15 percentage\n" + ] + } + ], + "source": [ + "from numpy import array, linalg\n", + "\n", + "# Variables\n", + "Wf = 3000. \t\t\t#kg/h,feed\n", + "fc = 8. \t\t\t#%, feed concentration\n", + "pc = 40. \t\t\t#% product concentration\n", + "si = Wf*(fc/100) \t\t\t#kg,solid in\n", + "pr = si/(40./100) \t\t\t#g/h, product rate\n", + "ft = 60. \t\t\t#C,feed temp.\n", + "er = Wf-pr \t\t\t#kg/h, evaporation rate\n", + "math.cost = 120000. \t\t\t#total math.cost per year\n", + "p1 = 4.5 \t\t\t#bar, low pressure steam\n", + "scpt = 700. \t\t\t#per ton. math.cost of steam\n", + "cp = 0.764 \t\t\t# kcal/kg, specific heat\n", + "\n", + "#from table 9.6\n", + "eep = 1. \t\t\t#atm existing evaporator pressure \n", + "oop = 400000. \t\t\t# peryear ,other operatingmath.cost\n", + "oop_ = 600000. \t\t\t#per yr, for proposed condition\n", + "wd = 300. \t\t\t#days per year.working days\n", + "wh = wd*24. \t\t\t#working hr\n", + "\n", + "# Calculations\n", + "#EXISTING OPERATING CONDITION \n", + "rt = 0 \t\t\t#C,reference temp.\n", + "ef = eep*(ft-rt) \t\t\t#kcal/kg, enthalpy of feed\n", + "pt = 100. \t\t\t#C,product temp.\n", + "i1 = cp*(pt-rt) \t\t\t#kcal/kg, enthalpy of soln\n", + "is1 = 639. \t\t\t#kcal/kg,enthalpy of vapour generated at 1 atm (from steam table)\n", + "l_s = 496. \t\t\t#kcal/kg,latent heat of steam at 4.5 bar\n", + "T = 425. \t\t\t#K\n", + "#heat balance\n", + "Ws = (er*is1+pr*i1-Wf*ef)/l_s \t\t\t#kg/h, steam required\n", + "q = Ws*l_s \t\t\t#ton/ hr,heat supplied\n", + "x = q/(T-(pt+273)) \t\t\t#x = Ud*A\n", + "#hourly math.cost\n", + "sc = Ws/1000*(scpt) \t\t\t# /perh, steam math.cost\n", + "lc = 100. \t\t\t#per h,labour math.cost\n", + "oc = oop/(wh) \t\t\t# per h,othe math.cost\n", + "tc = sc+lc+oc \t\t\t#total math.cost\n", + "C = tc/(Wf/1000) \t\t\t# per ton,math.cost per ton of feed\n", + "\n", + "#PROPOSED OPERATING CONDITION\n", + "bpl = 320. \t\t\t#K,boiling point of liquid\n", + "dt = T-bpl\n", + "q_ = x*dt \t\t\t#kcal/h,rate of heat supply\n", + "sr = q_/l_s \t\t\t#steam rate ton per hr\n", + "pt_ = 47. \t\t\t#C,product temp .\n", + "ep = cp*(pt_-rt) \t\t\t#kcal/kg. enthalpy of product\n", + "ev = 618. \t\t\t#kcal/kg, enthalpy of vapour generated\n", + "#heat balance\n", + "#24Wf_-582Ws1_ = 2825000 ..........(1)\n", + "#material balance\n", + "# 4Wf_-5Ws1_ = 0 .............(2)\n", + "#solving by matrix method\n", + "a = array([[24,-582],[4,-5]])\n", + "b = array([-2825000,0])\n", + "x_ = linalg.solve(a,b)\n", + "#x_ = inv(a)*b\n", + "Wf_ = x_[0]\n", + "Ws1_ = x_[1]\n", + "ic = (Wf_-Wf)/Wf\n", + "print \"The increase in evaporation capacity ic %d percentage \"%(ic*100)\n", + "sr_ = Ws1_/1000 \t\t\t#ton per hr ,steam rate \n", + "#hourly math.cost\n", + "sc_ = Ws1_*scpt \t\t\t#steam math.cost\n", + "lc_ = 200. \t\t\t#labour math.cost rs.200/ h\n", + "oc_ = oop_/wh \t\t\t# other math.cost\n", + "tc_ = sc_/1000+lc_+oc_\n", + "C_ = tc_/(Wf_/1000) \t\t\t#math.cost per ton of feed\n", + "ps = (C-C_)/C\n", + "print \" The percentage change in the math.cost of concentrating a ton of feed is %.0f percentage\"%(ps*100)\n", + "\n", + "# rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.8 Page No : 415" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Make up steam required is 1.302e+04 kg/day\n" + ] + } + ], + "source": [ + "# Variables\n", + "q = 2200. \t\t\t#kj/kg heat of condensation of steam \n", + "#from example 9.1\n", + "Qr = 2.337*10**8 \t\t\t#kj/day rate of heat supply\n", + "\n", + "#calculation\n", + "Rate = Qr/q \t\t\t#kg/day steam supply rate\n", + "Rate_ = 1.062*10**5 \t\t\t#approximate value\n", + "E = 2800. \t\t\t#kj/kg enthalpy of compressed vapour\n", + "T = 175.7 \t\t\t#C, temprature\n", + "Ts = 121. \t\t\t#C Saturation temprature\n", + "E1 = 2700. \t\t\t#enthalpy at saturation temprature\n", + "q1 = T-Ts \t\t\t#Superheat of vapour\n", + "T1 = 100. \t\t\t#C hot water temprature\n", + "E2 = 419. \t\t\t#Enthalpy at hot water temp.\n", + "x = (E-E1)/(E1-E2) \t\t\t#water supplied per kg of superheated steam\n", + "S = 1.044 \t\t\t#steam obtained after desuperheating\n", + "R1 = 8.925*10**4 \t\t\t#kg/day rate of vapour generation \n", + "R2 = S*R1 \t\t\t#Rate of recompressed sat. steam\n", + "R2_ = 9.318*10**4 \t\t\t#approximate value\n", + "SR = Rate_-R2_ \n", + "\n", + "# Results\n", + "print \"Make up steam required is %.3e kg/day\"%(SR)\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/screenshots/10.png b/Heat_Transfer_Principles_And_Applications_by_Dutta/screenshots/10.png Binary files differnew file mode 100644 index 00000000..291f94e6 --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/screenshots/10.png diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/screenshots/5.png 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