{ "metadata": { "name": "", "signature": "sha256:a84d51472594c75f9afdf6cd721b95cb9d112fa36b409d534c3bc68aa928266a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 5 : Heat Transfer" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.1 page number 171" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "A=5.*4 #in m2\n", "T1=100.; #in K\n", "T2=30.; #in K\n", "\n", "# Calculations\n", "delta_T=T1-T2;\n", "\n", "x=0.25 #in m\n", "k=0.70 #in W/mK\n", "Q=k*A*(delta_T/x);\n", "\n", "# Results\n", "print \"rate of heat loss = %f W\"%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "rate of heat loss = 3920.000000 W\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.2 page number 171\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "d1=0.15 #in m\n", "d2=0.16 #in m\n", "l=1. #in m\n", "\n", "# Calculations\n", "A1=3.14*d1*l;\n", "A2=3.14*d2*l\n", "Am=(A1-A2)/math.log (A1/A2);\n", "\n", "T1=120.; #in K\n", "T2=119.8; #in K\n", "\n", "delta_T=T1-T2;\n", "x=(d2-d1)/2;\n", "k=50. #in W/mK\n", "Q=k*Am*(delta_T/x);\n", "\n", "# Results\n", "print \"rate of heat loss per unit length = %f W/m\"%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "rate of heat loss per unit length = 973.062272 W/m\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.3 page number 172\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "ri=0.5 #in m\n", "ro=0.6; #in m\n", "A1=4*3.14*ri**2;\n", "A2=4*3.14*ro**2;\n", "\n", "# Calculations\n", "Am=(A1*A2)**0.5;\n", "\n", "Ti=140.; #in K\n", "To=50.; #in K\n", "delta_T=Ti-To;\n", "x=0.1 #in m\n", "k=0.12 #in W/mK\n", "\n", "Q=k*Am*(delta_T/x);\n", "\n", "# Results\n", "print \"Heat loss through sphere = %f W\"%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat loss through sphere = 406.944000 W\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.4 page number 173\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "x1=0.250; #in m\n", "k1=0.7; #in W/mK\n", "A1=1.; #in m2\n", "R1=x1/(k1*A1); #in K/W\n", "\n", "# Calculations and Results\n", "#for the felt layer\n", "x2=0.020; #in m\n", "k2=0.046; #in W/mK\n", "A2=1.; #in m2\n", "R2=x2/(k2*A2); #in K/W\n", "R=R1+R2;\n", "print \"Total resistance = %f K/W\"%(R)\n", "\n", "T1=110.; #in K\n", "T2=25. #in K\n", "delta_T=T1-T2;\n", "Q=delta_T/R;\n", "print \"heat loss through wall = %f W/square m\"%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total resistance = 0.791925 K/W\n", "heat loss through wall = 107.333333 W/square m\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.5 page number 173\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "d1=0.15 #in m\n", "d2=0.16 #in m\n", "l=1. #in m\n", "A1=3.14*d1*l;\n", "A2=3.14*d2*l\n", "Am1=(A2-A1)/math.log (A2/A1);\n", "x1=(d2-d1)/2.;\n", "k1=50. #in W/mK\n", "R1=x1/(k1*Am1);\n", "\n", "# Calculations and Results\n", "#resistance by insulation\n", "d2=0.16 #in m\n", "d3=0.26 #in m\n", "l=1. #in m\n", "A2=3.14*d2*l;\n", "A3=3.14*d3*l\n", "Am2=(A3-A2)/math.log (A3/A2);\n", "x2=(d3-d2)/2.;\n", "k2=0.08 #in W/mK\n", "R2=x2/(k2*Am2);\n", "R=R1+R2;\n", "\n", "print \"total resistance = %f K/W\"%(R)\n", "\n", "T1=120.; #in K\n", "T2=40.; #in K\n", "delta_T=T1-T2;\n", "Q=delta_T/R;\n", "\n", "print \"heat loss = %f W/m\"%(Q)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total resistance = 0.966583 K/W\n", "heat loss = 82.765822 W/m\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.6 page number 174\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "x1=0.1; #in m\n", "x2= 0.25; #in m\n", "k_rb=0.93; #in W/mK\n", "k_ib=0.116 #in W/mK\n", "k_al=203.6 #in W/mK\n", "A=0.1 #in m2\n", "\n", "# Calculations and Results\n", "#to find resistance without rivets\n", "R=(1/A)*((x1/k_rb)+(x2/k_ib));\n", "T1=225 #in K\n", "T2=37 #in K\n", "delta_T=T1-T2;\n", "Q=delta_T/R;\n", "print \"heat transfer rate = %f W\"%(Q)\n", "\n", "#to find resistance with rivet\n", "d=0.03 #in m\n", "rivet_area= (3.14/4)*d**2;\n", "R_r=(x1+x2)/(k_al*rivet_area);\n", "area_norivet=A-rivet_area;\n", "R_cl=(A/area_norivet)*R;\n", "R_eq=1/(1/R_r+1/R_cl);\n", "Q_new=delta_T/R_eq;\n", "\n", "print \"Rate of heat transfer with rivet = %f W\"%(Q_new)\n", "increase=((Q_new-Q)/Q)*100;\n", "print \"percentage increase in heat transfer rate = %f\"%(increase)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "heat transfer rate = 8.308660 W\n", "Rate of heat transfer with rivet = 85.514415 W\n", "percentage increase in heat transfer rate = 929.220242\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.7 page number 187" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math\n", "\n", "# variables\n", "Cp = 4.178 # kJ/kg K for water\n", "q = 1838. # rate at which heat is transfered\n", "A = .1005 # heat transfer area\n", "dt1 = 80. - 24 # temperature diffference at hot end\n", "dt2 = 36.-24 # temperature difference at cold end\n", "\n", "# Calculations and Results\n", "dtm = (56 + 12)/2.0\n", "h = q/(A*dtm)\n", "print \"Heat transfer coefficient, h = %.0f W/m**2 K\"%h\n", "\n", "dtm = (56 - 12)/math.log(56/12.)\n", "h = q/(A*dtm)\n", "print \"h = %.0f W/m**2 K\"%h\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat transfer coefficient, h = 538 W/m**2 K\n", "h = 640 W/m**2 K\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.8 page number 188\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "\n", "# Variables\n", "density=984.1 #in kg/cubic meter\n", "v=3. #in m/s\n", "viscosity=485*10**-6; #in Pa-s\n", "k=0.657 #in W/mK\n", "cp=4178. #in J/kg K\n", "d=0.016 #in m\n", "\n", "# Calculations and Results\n", "Re=(density*v*d)/viscosity;\n", "Pr=(cp*viscosity)/k;\n", "\n", "#dittus boelter equation\n", "h=0.023*Re**0.8*Pr**0.3*(k/d);\n", "print \"heat transfer coefficient = %f W/sq meter K\"%(h)\n", "\n", "#Sieder Tate equation\n", "viscosity_w=920*10**-6.\n", "h1=0.023*Re**0.8*Pr**(1./3)*(k/d)*(viscosity/viscosity_w)**0.14;\n", "print \"heat transfer coefficient = %f W/sq meter K\"%(h1)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "heat transfer coefficient = 12964.257508 W/sq meter K\n", "heat transfer coefficient = 12306.258209 W/sq meter K\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.9 page number 191\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "T_sun = 5973 #in degree C\n", "d = 1.5*10**13 #in cm\n", "R = 7.1*10**10; #in cm\n", "\n", "# Calculations\n", "T_earth = ((R/(2*d))**0.5)*T_sun;\n", "\n", "# Results\n", "print \"Temperature of earth = %f C\"%(T_earth-273) \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature of earth = 17.576884 C\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.10 page number 191\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "R=7*10**10; #in cm\n", "Ts=6000; #in K\n", "\n", "# Calculations\n", "l=1.5*10**13; #in m\n", "To=((R**2/(4*l**2))**0.25)*Ts;\n", "\n", "# Results\n", "print \"temperature of earth = %f K\"%(To)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "temperature of earth = 289.827535 K\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.11 page number 192\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "R=6.92*10**5 #in km\n", "l=14.97*10**7 #in km\n", "Ts=6200; #in K\n", "\n", "# Calculations\n", "To=(R**2/l**2)**0.25*Ts;\n", "\n", "# Results\n", "print \"Equilibrium temperature = %f K\"%(To)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Equilibrium temperature = 421.535191 K\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.12 page number 192\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "view_factor=0.5;\n", "R=6.92*10**5 #in km\n", "l=14.97*10**7 #in km\n", "Ts=6200; #in K\n", "\n", "# Calculations\n", "To=(view_factor*(R**2/l**2))**0.25*Ts;\n", "\n", "# Results\n", "print \"Equilibrium temperature = %f K\"%(To)\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Equilibrium temperature = 354.467431 K\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.13 page number 193\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "view_factor=0.25;\n", "R=7.1*10**10 #in cm\n", "l=1.5*10**13 #in cm\n", "Ts=5973; #in K\n", "alpha=0.2;\n", "epsilon=0.1;\n", "\n", "# Calculations\n", "ratio=alpha/epsilon;\n", "To=(ratio*view_factor*(R**2/l**2))**0.25*Ts;\n", "\n", "\n", "# Results\n", "print \"Equilibrium temperature = %f K\"%(To)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Equilibrium temperature = 345.556097 K\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.14 page number 193\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "R=7*10**10; #in cm\n", "l=1.5*10**13; #in cm\n", "sigma=5.3*10**-5; #in erd/s(cm2)(K)4\n", "T=6000; #in K\n", "\n", "# Calculations\n", "S=(R/l)**2*(sigma)*(T**4)*60;\n", "\n", "# Results\n", "print \"solar constant = %f J/sq cm min\"%(S/10**7)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "solar constant = 8.975232 J/sq cm min\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.15 page number 207\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "F = 5000. #in kg/hr\n", "xF = 0.01\n", "xL = 0.02;\n", "\n", "# Calculations and Results\n", "L = F*xF/xL;\n", "V = F-L;\n", "print \"L = %f Kg/hr V = %f kg/hr\"%(L,V)\n", "\n", "TF= 303 #in K\n", "hF = 125.9 #in KJ/kg\n", "T1 = 373.2 #in K\n", "Hv = 2676.1 #in kJ/kg\n", "hL = 419.04; #in kJ/kg\n", "Ts = 383.2 #in K\n", "Hs = 2691.5 #in kJ/kg\n", "hs = 461.30 #in kJ/kg\n", "\n", "S = (F*hF-L*hL-V*Hv)/(hs-Hs);\n", "print \"amount of steam = %f kg steam/h\"%(S)\n", "\n", "q = S*(Hs - hs);\n", "q = q*1000/3600 #conversion to Watt\n", "U = q/(69.9*10);\n", "print \"heat transfer coefficient = %f W/sq m K\"%(U)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "L = 2500.000000 Kg/hr V = 2500.000000 kg/hr\n", "amount of steam = 3187.315039 kg steam/h\n", "heat transfer coefficient = 2824.809251 W/sq m K\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.16 page number 208\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "from numpy import *\n", "# Variables\n", "b1 = 6000*125.79+3187.56*2691.5-3187.56*461.30; #data from previous problem\n", "b2 = 6000;\n", "A = array([[419.04, 2676.1],[1, 1]])\n", "\n", "# Calculations and Results\n", "b = array([[b1],[b2]]);\n", "x = linalg.solve(A,b)\n", "#x = x*b\n", "L = x[0];\n", "V = x[1];\n", "\n", "print \"L = %f kg/hrV = %f kg/hr\"%(L,V)\n", "\n", "F = 6000 #in kg/hr\n", "xF = 0.01;\n", "xL = F*xF/L;\n", "print \"percentage increase in outlet concentration = %f\"%(xL*100)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "L = 3629.927289 kg/hrV = 2370.072711 kg/hr\n", "percentage increase in outlet concentration = 1.652926\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "example 5.17 page number 209\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ " \n", "import math \n", "# Variables\n", "Hv=2635.3 #kJ/kg\n", "hL=313.93 #in kJ/kg\n", "\n", "# Calculations and Results\n", "S=(2500*313.93+2500*2635.3-5000*125.79)/(2691.5-461.30);\n", "print \"steam flow rate = %f kg steam/hr\"%(S)\n", "\n", "q = S*(2691.5 - 461.30);\n", "q = q*1000./3600 #in W\n", "U = 2833.13; #in W/m2 K\n", "delta_T = 383.2-348.2; #in K\n", "A = q/(U*delta_T);\n", "\n", "print \"Area = %f sq meter\"%(A)\n", "print \"in this case a condensor and vaccum pump should be used\"\n", "\n", "# Note : there is mistake in calculation in Book. Please calculate manually." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "steam flow rate = 3024.000090 kg steam/hr\n", "Area = 18.892462 sq meter\n", "in this case a condensor and vaccum pump should be used\n" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }