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Diffstat (limited to 'Textbook_Of_Heat_Transfer/Chapter_2_Heat_Conduction.ipynb')
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diff --git a/Textbook_Of_Heat_Transfer/Chapter_2_Heat_Conduction.ipynb b/Textbook_Of_Heat_Transfer/Chapter_2_Heat_Conduction.ipynb new file mode 100755 index 00000000..8e524b2c --- /dev/null +++ b/Textbook_Of_Heat_Transfer/Chapter_2_Heat_Conduction.ipynb @@ -0,0 +1,1017 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:a3257cf5589919f02234d6cf7ed2bf5fce234214f8f5ed548e011fbbc2b55a9f"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 2:Heat Conduction in Solids"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1 , Page no:27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "di=0.02; #inner radius m\n",
+ "do=0.04; #inner radius m\n",
+ "ri=di/2; #inner radius m\n",
+ "ro=do/2; #inner radius m\n",
+ "k=0.58; #thermal conductivity of tube material w/m K\n",
+ "ti=70; #degree C\n",
+ "to=100; #degree C\n",
+ "l=1; #per unit length m\n",
+ "\n",
+ "#calculations\n",
+ "q=l*2*(3.14)*k*(ti-to)/math.log(ro/ri);\n",
+ "\n",
+ "#result\n",
+ "print\"Heat flow per unit length is\",round(q,4),\"W/m\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Heat flow per unit length is -157.6462 W/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2 , Page no:31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "di=0.02; #inner radius\n",
+ "do=0.04; #outer radius\n",
+ "ri=di/2; #inner radius\n",
+ "ro=do/2; #outer radius\n",
+ "k=0.58; #thermal conductivity of tube material\n",
+ "ti=70; #degree C\n",
+ "to=100; #degree C\n",
+ "l=1; #per unit length\n",
+ "h=5000; #W/m^2 K\n",
+ "\n",
+ "#calculations\n",
+ "Rthtube=(math.log(ro/ri))/(2*3.14*k*l); #thermal resistance of tube per unit length\n",
+ "Rthcond=1/(3.14*do*l*h); #thermal resistance of condensing steam per unit length\n",
+ "q=l*2*(3.14)*k*(ti-100)/math.log(ro/ri); #heat flow rate per unit meter \n",
+ "\n",
+ "#result\n",
+ "print\"Thermal resistance of tube per unit length is\",round(Rthtube,4),\"K/W\";\n",
+ "print\"Thermal resistance of condensing steam perunit length is\",round(Rthcond,5),\"K/W\";\n",
+ "print\"Heat flow per unit length is\",round(q,4),\"K/W\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thermal resistance of tube per unit length is 0.1903 K/W\n",
+ "Thermal resistance of condensing steam perunit length is 0.00159 K/W\n",
+ "Heat flow per unit length is -157.6462 K/W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 , Page no:31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "hw=140; #heat transfer coefficient on water side\n",
+ "ho=150; #heat transfer coefficient on oil side\n",
+ "k=30; #thermal conductivity\n",
+ "ro=0.1; #inner diameter of GI pipe on inside\n",
+ "ri=0.008; #outer diameter of GI pipe on inside\n",
+ "l=1; #per unit length\n",
+ "\n",
+ "#calculations\n",
+ "RinnerGI=math.log((ro/ri))/(2*3.14*k*l); #Thermal resistance of inner GI pipe\n",
+ "Roilside=1/(ho*3.14*2*ri*l); #Thermal resistanceon the oil side per unit length\n",
+ "Rwaterside=1/(hw*3.14*2*ro*l); #Thermal resistanceon the water side per unit length\n",
+ "\n",
+ "#result\n",
+ "print\"Thermal resistance of inner GI pipe =\",round(RinnerGI,5),\"K/W\";\n",
+ "print\"Thermal resistance on the oil side perunit length =\",round(Roilside,5),\"K/W\";\n",
+ "print\"Thermal resistance on cold water side per unit length =\",round(Rwaterside,5),\"K/W\";\n",
+ "print\"So,Engineer in-charge has made a bad decision\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thermal resistance of inner GI pipe = 0.01341 K/W\n",
+ "Thermal resistance on the oil side perunit length = 0.1327 K/W\n",
+ "Thermal resistance on cold water side per unit length = 0.01137 K/W\n",
+ "So,Engineer in-charge has made a bad decision\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4 , Page no:32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ti=300; #Internal temp of hot gas in degree Celsius\n",
+ "od=0.1; #Outer diameter of long metal pipe in meters\n",
+ "i_d=0.04; #Internal diamtere of long metal pipe in meters\n",
+ "ki=0.052; #thermal conductivity of mineral wood in W/mK\n",
+ "to=50; #Outer surface temperature in degree celsius\n",
+ "hi=29; #heat transfer coefficient in the inner side in W/m^2 K\n",
+ "ho=12; #heat transfer coefficient in the outer pipe W/m^2 K\n",
+ "t=25; # Surrounding temperature in degree celsius\n",
+ "\n",
+ "#Calculation\n",
+ "#Determination of thickness of insulation\n",
+ "#By solving the following two equations by trial and error method for r3\n",
+ "#q_L=2*3.14*0.047*(t1-t)/(1/hi+(0.047/ki)*2.303*math.log(r3/od/2)+(0.047/h0*r3));\n",
+ "#q_L=2*3.14*h0*(to-t);\n",
+ "#By trial and error we get\n",
+ "r3=0.082; #in m\n",
+ "t=r3-(od/2);\n",
+ "#Heat loss per unit length\n",
+ "q=600*(22/7)*r3;\n",
+ "\n",
+ "#Result\n",
+ "print\"Thickness of insulation =\",t*100,\"cm\";\n",
+ "print\"Heat loss per unit length =\",round(q,1),\"W/m\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Thickness of insulation = 3.2 cm\n",
+ "Heat loss per unit length = 154.6 W/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.5 , Page no:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "\n",
+ "#Variable declaration\n",
+ "ti=90; #Temp on inner side in degree celsius\n",
+ "to=30; #Temp on outer side in degree celsius\n",
+ "hi=500; #heat transfer coeffcient in W/m^2 K\n",
+ "ho=10; #heat transfer coeffcient in W/m^2 K\n",
+ "i_d=0.016; #Internal diameter in meters\n",
+ "od=0.02; #Outer diameter in meters\n",
+ "from pylab import *\n",
+ "%matplotlib inline\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "r3=np.linspace (0.01,0.06,12);\n",
+ "t=[0,0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5]\n",
+ "q_L=(2*(3.14)*(i_d/2)*(ti-to))/((1/hi)+(0.008/0.2)*np.log(r3/0.01) + (0.008/r3*(1/ho)));\n",
+ "\n",
+ "#Result\n",
+ "print \"Insulaion thickness (cm)\", \" r3 (m)\",\" Heat loss rate per meter (W/m) \" \n",
+ "print \" \",t[0],\" \",0.01,\" \",round(q_L[0],1),\"(roundoff error)\"\n",
+ "print \" \",t[1],\" \",0.015,\" \", round(q_L[1],1),\"(roundoff error)\"\n",
+ "print \" \",t[2],\" \",0.02,\" \",round(q_L[2],1),\"(roundoff error)\"\n",
+ "print \" \",t[4],\" \",0.03,\" \",round(q_L[4],1),\"(roundoff error)\"\n",
+ "print \" \",t[6],\" \",0.04,\" \",round(q_L[6],1),\"(roundoff error)\"\n",
+ "print \" \",t[8],\" \",0.05,\" \",round(q_L[8],1),\"(roundoff error)\"\n",
+ "print \" \",t[10],\" \",0.06,\" \",round(q_L[10],1),\"(roundoff error)\"\n",
+ "plt.plot (t,q_L);\n",
+ "plt.title (\"Variation of heat loss rate with insulation thickness\");\n",
+ "plt.xlabel(\" Insulation thickness in cm\");\n",
+ "plt.ylabel(\" Heat Loss in W/m \");\n",
+ "plt.show();"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Insulaion thickness (cm) r3 (m) Heat loss rate per meter (W/m) \n",
+ " 0 0.01 36.8 (roundoff error)\n",
+ " 0.5 0.015 41.9 (roundoff error)\n",
+ " 1 0.02 43.2 (roundoff error)\n",
+ " 2 0.03 42.0 (roundoff error)\n",
+ " 3 0.04 39.6 (roundoff error)\n",
+ " 4 0.05 37.4 (roundoff error)\n",
+ " 5 0.06 35.5 (roundoff error)\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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hRqMBhISQhdqGDwe4eZMs04wQ4g+x697Bi7h9w5IlAD/9RPbxJyVRHQ1CokOs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\nAxLp4OAIwDpgAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x4db9850>"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.6 , Page no:34"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "hnatural = 10; #heat transfer coefficient for natural \n",
+ "hforced = 50; #heat transfer coefficient for forced\n",
+ "k1 = 0.2; #thermal conductivity\n",
+ "k2 = 0.05; #thermal conductivity\n",
+ "\n",
+ "#result\n",
+ "print\"critical radius of insulation in cm\";\n",
+ "print\"\\n h=10 h=50\";\n",
+ "print\"\\nAsbestos \",k1 *100/ hnatural,\" \", k1*100/ hforced;\n",
+ "print\"\\nMineral wool \",k2 *100/ hnatural,\" \", k2*100/ hforced;"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "critical radius of insulation in cm\n",
+ "\n",
+ " h=10 h=50\n",
+ "\n",
+ "Asbestos 2.0 0.4\n",
+ "\n",
+ "Mineral wool 0.5 0.1\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.7 , Page no:43"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=5; #Height\n",
+ "l=10; #Length\n",
+ "t=1; #thickness\n",
+ "k=1.05; #W/m K\n",
+ "q=58; #W/m^3\n",
+ "t1=35; #c\n",
+ "h=11.6; #Heat transfer coefficient\n",
+ "\n",
+ "#calculations\n",
+ "b=t/2;\n",
+ "tmax=t1+q*b*(b/(2*k)+1/h);\n",
+ "\n",
+ "#result\n",
+ "print\"Maximum Temperature =\",round(tmax,3),\"degree c\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum Temperature = 44.405 degree c\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.8 , Page no:47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#The bar will have two dimensional variation in temperature\n",
+ "#the differential equation is subject to boundary conditions\n",
+ "x1 = 0; #cm\n",
+ "Tx1 = 30; #C\n",
+ "x2 = 5; #cm\n",
+ "Tx2 = 30; #C\n",
+ "y1 = 0; #cm\n",
+ "Ty1 = 30; #C\n",
+ "y2 = 10; #cm\n",
+ "Ty2 = 130; #C\n",
+ "\n",
+ "#substituting theta = T-30 and using eqn 2.6.11\n",
+ "#putting x = 2.5cm and y = 5cm in infinite summation series\n",
+ "n = 1;\n",
+ "x1 = (1- math.cos ( 3.14*3.14/180 *n))/( math.sinh (2*3.14* 3.14/180 *n))*math.sin(n**(3.14*3.14/180 /2))*math.sinh (n*3.14*3.14/180);\n",
+ "\n",
+ "n = 3;\n",
+ "x2 = (1- math.cos ( 3.14*3.14/180 *n))/( math.sinh (2*3.14* 3.14/180 *n))*math.sin(n**(3.14*3.14/180 /2))*math.sinh (n*3.14*3.14/180);\n",
+ "\n",
+ "n = 5;\n",
+ "x3 = (1- math.cos ( 3.14*3.14/180 *n))/( math.sinh (2*3.14* 3.14/180 *n))*math.sin(n**(3.14*3.14/180 /2))*math.sinh (n*3.14*3.14/180);\n",
+ "\n",
+ "x = x1+x3+x3;\n",
+ "T = x *100+30;\n",
+ "\n",
+ "#result\n",
+ "print \"Steady statetemper a ture= \",T,\"c (roundoff error)\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Steady statetemper a ture= 33.1695223665 c (roundoff error)\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.9 , Page no:51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "k = 330; #thermal conductivity\n",
+ "a = 95*10**(-6); #thermal expansion coefficient\n",
+ "R = 0.01; #radius in meters\n",
+ "To = 77; #temperature in kelvins\n",
+ "Tf = 273+50; #temperature in kelvins\n",
+ "theta1 = To - Tf; \n",
+ "T = 273+10; ##temperature in kelvins\n",
+ "theta = T - Tf;\n",
+ "h = 20; #heat transfer coefficient in W/m^2 K\n",
+ "\n",
+ "print\"Theta1 =\",theta1,\"K\";\n",
+ "print\"Theta =\",theta,\"K\";\n",
+ "print\"v/A =\",R/2,\"m\";\n",
+ "print\"k/a =\",round((k/a)*10**(-6),4),\"*10^(6)J/m^3 K\";\n",
+ "\n",
+ "time =(k/a)*(R/2)/h*math.log(theta1/theta);\n",
+ "\n",
+ "print\"Time taken by the rod to heat up =\",round(time,1),\"secs\";\n",
+ "\n",
+ "Bi = h*R/k;\n",
+ "\n",
+ "#result\n",
+ "print\"Biot number Bi =\",round(Bi*10**4,2),\"*10^(-4)\";\n",
+ "print\"Since Biot number is much less than 0.1,therefore assumption that internal temper a ture gradients are negligible is a good one\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Theta1 = -246 K\n",
+ "Theta = -40 K\n",
+ "v/A = 0.005 m\n",
+ "k/a = 3.4737 *10^(6)J/m^3 K\n",
+ "Time taken by the rod to heat up = 1577.4 secs\n",
+ "Biot number Bi = 6.06 *10^(-4)\n",
+ "Since Biot number is much less than 0.1,therefore assumption that internal temper a ture gradients are negligible is a good one\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.10(1) , Page no:58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "b = 0.005; #m\n",
+ "t = 5*60; #time, [sec]\n",
+ "Th = 200; #C\n",
+ "Tw = 20 ; #C\n",
+ "h = 150; #W/m^2 K\n",
+ "rho = 2200; #kg/m^3\n",
+ "Cp = 1050; #J/kg K\n",
+ "k = 0.4; #W/m K\n",
+ "ratiob0 = 0.12; \n",
+ "ratiob1 = 0.48; \n",
+ "lambda1b = 1.0498; \n",
+ "\n",
+ "#calculations\n",
+ "theta = Th - Tw;\n",
+ "Biotno = h*b/k;\n",
+ "a = k/( rho*Cp); #alpha\n",
+ "Fourierno = a*t/b**2;\n",
+ "thetaxb0 = theta*ratiob0;\n",
+ "Txb0 = thetaxb0+Tw;\n",
+ "thetaxb1 = theta*ratiob1 ;\n",
+ "Txb1 = thetaxb1+Tw ;\n",
+ "\n",
+ "x = (2*math.sin((lambda1b)))/(lambda1b+((math.sin((lambda1b)))*(math.cos((lambda1b)))));\n",
+ "thetaxb0 = theta*x*(math.exp((-lambda1b**2)*Fourierno));\n",
+ "Txb0 = thetaxb0+Tw;\n",
+ "\n",
+ "#result\n",
+ "print\"Temperature at b=0 is\",round(Txb0,4),\"degree\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Temperature at b=0 is 41.3418 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.10(2) , Page no:58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "b = 0.005; #m\n",
+ "t = 5*60; #time, [sec]\n",
+ "Th = 200; #C\n",
+ "Tw = 20; #C\n",
+ "h = 150; #W/m^2 K\n",
+ "rho = 2200; #kg/m^3\n",
+ "Cp = 1050; #J/kg K\n",
+ "k = 0.4; #W/m K\n",
+ "ratiob0 = 0.12;\n",
+ "ratiob1 = 0.48;\n",
+ "lambda1b = 1.0498;\n",
+ "\n",
+ "#calculations\n",
+ "theta = Th - Tw;\n",
+ "Biotno = h*b/k;\n",
+ "a = k/( rho *Cp);\n",
+ "Fourierno = a*t/b**2;\n",
+ "thetaxb0 = theta * ratiob0;\n",
+ "Txb0 = thetaxb0 + Tw;\n",
+ "thetaxb1 = theta * ratiob1;\n",
+ "Txb1 = thetaxb1 + Tw;\n",
+ "x = 2*math.sin(((lambda1b)))/(lambda1b + (math.sin(((lambda1b))))*(math.cos((lambda1b))));\n",
+ "thetaxb1 = thetaxb0*(math.cos (lambda1b *1));\n",
+ "Txb1 = thetaxb1+Tw;\n",
+ "\n",
+ "#result\n",
+ "print\"Temperature at b=1 is\",round(Txb1,3),\"degree C\\n\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Temperature at b=1 is 30.751 degree C\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.11(1) , Page no:65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "D = 0.05 ; #m\n",
+ "To = 450 ; #degree C\n",
+ "Tf = 90 ; #degree C\n",
+ "T = 150 ; #degree C\n",
+ "h = 115 ; #W/m^2 K\n",
+ "rho = 8000 ; #kg/m^3\n",
+ "Cp = 0.42*1000 ; #kg/m^3\n",
+ "k = 46 ; #W/m K\n",
+ "R = D/2; \n",
+ "\n",
+ "#calculations\n",
+ "t1 = rho*Cp*R /(3* h)* math.log ((To -Tf)/(T-Tf)); #sec\n",
+ "t1min = t1 /60 ; #min\n",
+ "\n",
+ "#result\n",
+ "print\"Time taken by the centre of the ball to reach 150 degree C if internal gradients are neglected is\",round(t1,4),\"seconds i.e.\",round(t1min,4),\"minutes\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time taken by the centre of the ball to reach 150 degree C if internal gradients are neglected is 436.2545 seconds i.e. 7.2709 minutes\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.11(2) , Page no:65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "D = 0.05 ; #m\n",
+ "To = 450 ; #degree C\n",
+ "Tf = 90 ; #degree C\n",
+ "T = 150 ; #degree C\n",
+ "h = 115 ; #W/m^2 K\n",
+ "rho = 8000 ; #kg/m^3\n",
+ "Cp = 0.42*1000 ; #kg/m^3\n",
+ "k = 46 ; #W/m K\n",
+ "R = D/2;\n",
+ "lambda1R = 0.430;\n",
+ "y = 5;\n",
+ "\n",
+ "#calculations\n",
+ "ratio = (T-Tf)/( To - Tf);\n",
+ "Bi = h*R/k;\n",
+ "x = 2* (math.sin(lambda1R)- lambda1R * math.cos(lambda1R))/ (lambda1R - math.sin ( lambda1R)*math.cos( lambda1R));\n",
+ "t=(math.log (ratio/x))/(-1*(k/(Cp*rho*R**2))*lambda1R**2);\n",
+ "tmin = t /60;\n",
+ "\n",
+ "#result\n",
+ "print\"Time taken by the centre of the ball to reach 150 degree\" \n",
+ "print \"C if internal temperature gradients are not neglected is\",round(t,3),\"seconds i.e\",round(tmin,3),\"min (roundoff error)\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time taken by the centre of the ball to reach 150 degree\n",
+ "C if internal temperature gradients are not neglected is 446.95 seconds i.e 7.449 min (roundoff error)\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.12 , Page no:67"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a = 0.12 ; #m\n",
+ "T = 400 ; #C\n",
+ "To = 25 ; #C\n",
+ "t = 100/60 ; #hour\n",
+ "h = 10 ; #W/m^2 K\n",
+ "k = 1.0 ; #W/m K\n",
+ "alpha = 3.33*10** -3 ; #m^2/h\n",
+ "ratiox = 0.82 ;\n",
+ "ratioy = 0.41;\n",
+ "ratioz = 0.30;\n",
+ "\n",
+ "#calculations\n",
+ "x1 = h*a/k ;\n",
+ "x2 = k/(h*a);\n",
+ "x3 = alpha *t/a**2;\n",
+ "totalratio = ratiox * ratioy * ratioz ;\n",
+ "Tcentre = To + totalratio *(T-To) ;\n",
+ "ratiox = 1.1310* math.exp ( -(0.9036**2) *0.385) ;\n",
+ "ratioy = 1.0701* math.exp ( -(0.6533**2) *2.220) ;\n",
+ "ratioz = 1.0580* math.exp ( -(0.5932**2) *3.469) ;\n",
+ "ratio = ratiox * ratioy * ratioz ;\n",
+ "Tcentre = To + totalratio *(T-To) ;\n",
+ "\n",
+ "#result\n",
+ "print\"Temperature at the centre of the brick =\",round(Tcentre,3),\"degree c\";\n",
+ "print\"Alternatively, obtaining Biot number and values of lambda1b and using eqn 2.7.20, we get\";\n",
+ "print\"Temperature at the centre of the brick =\",round(Tcentre,3),\"degree c\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Temperature at the centre of the brick = 62.822 degree c\n",
+ "Alternatively, obtaining Biot number and values of lambda1b and using eqn 2.7.20, we get\n",
+ "Temperature at the centre of the brick = 62.822 degree c\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.13(1) , Page no:73"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "D = 0.003 ; #m\n",
+ "L = 0.03 ; #m\n",
+ "h = 10 ; #W/m^2\n",
+ "Tf = 20 ; #C\n",
+ "T1 = 120 ; #C\n",
+ "k = 350 ; #W/m K\n",
+ "\n",
+ "#calculations\n",
+ "m = (4* h/(k*D)) **(1/2) ;\n",
+ "ml = m *0.03 ;\n",
+ "T = Tf + (T1 -Tf)/ math.cosh (m*L);\n",
+ "\n",
+ "#result\n",
+ "print\"ml=\",round(ml,4);\n",
+ "print\"Temperature at the tip of fin made of copper is\",round(T,4),\"degree c\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ml= 0.1852\n",
+ "Temperature at the tip of fin made of copper is 118.3099 degree c\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.13(2) , Page no:73"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "D = 0.003 ; #m\n",
+ "l = 0.03 ; #m\n",
+ "h = 10 ; #W/m^2\n",
+ "Tf = 20 ; #C\n",
+ "T1 = 120 ; #C\n",
+ "k = 15 ; #W/m K\n",
+ "\n",
+ "#calculations\n",
+ "m = (4*h/(k*D)) **(1/2) ;\n",
+ "ml = m *0.03 ;\n",
+ "T = Tf + (T1 -Tf)/ math.cosh (m*l);\n",
+ "\n",
+ "#result\n",
+ "print\"ml=\",round(ml,4);\n",
+ "print\"Temperature at the tip of fin made of steel is\",round(T,4),\"degree c\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ml= 0.8944\n",
+ "Temperature at the tip of fin made of steel is 90.058 degree c\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.13(3) , Page no:73"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "D = 0.003 ; #m\n",
+ "L = 0.03 ; #m\n",
+ "h = 10 ; #W/m^2\n",
+ "Tf = 20 ; #C\n",
+ "T1 = 120 ; #C\n",
+ "k = 0.35 ; #W/m K\n",
+ "\n",
+ "#calculations\n",
+ "m = (4* h/(k*D)) **(1/2) ;\n",
+ "mL = m *0.03 ;\n",
+ "T = Tf + (T1 -Tf)/ math.cosh (m*L);\n",
+ "\n",
+ "#result\n",
+ "print\"ml=\",round(mL,4);\n",
+ "print\"Temperature at the tip of fin made of teflon is\",round(T,4),\"degree c\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ml= 5.8554\n",
+ "Temperature at the tip of fin made of teflon is 20.5729 degree c\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.14 , Page no:74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "L = 0.02 ; #M\n",
+ "t = 0.002 ; #M\n",
+ "b = 0.2 ; #M\n",
+ "theta1 = 200 ; #C\n",
+ "h = 15 ; #W/m^2 K\n",
+ "k = 45 ; #W/m K\n",
+ "\n",
+ "#calculations\n",
+ "Bi = h*(t /2) /k ;\n",
+ "P = 2*( b+t); #m\n",
+ "A = b*t ;\n",
+ "mL = math.sqrt((h*P)/(A*k))*L;\n",
+ "n = math.tanh(mL)/mL;\n",
+ "qloss = n*h *40.4*2*10**-4*200;\n",
+ "\n",
+ "#result\n",
+ "print\"Fin Effectiveness =\",round(n,3);\n",
+ "print\"Heat loss rate from fin surface =\",round(qloss,3);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Fin Effectiveness = 0.957\n",
+ "Heat loss rate from fin surface = 23.207\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.15 , Page no:74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h = 15 ; #W/m^2 .K\n",
+ "k = 300; #W/m.K\n",
+ "T = 200; #C\n",
+ "Tsurr = 30; #C\n",
+ "d = .01; #M\n",
+ "L = .1; #M #\n",
+ "A = .5*.5; #M^2\n",
+ "n = 100; #Number of Pins\n",
+ "\n",
+ "#calculations\n",
+ "Bi = h*d /2/ k; #Biot Number\n",
+ "mL = (h *4/ k/d) **.5* L; \n",
+ "zi = math.tanh (mL)/mL;\n",
+ "Res1 = 1/h/A; #Thermal resistance without fins\n",
+ "Res2 = 1/(h*(A - n*3.14 /4* d**2 + zi *(n* 3.14 *d*L))); #Thermal resistance with fins\n",
+ "delRes = Res1 - Res2 ; #heat transfer rate\n",
+ "q = (T- Tsurr )/ Res2 - (T- Tsurr )/ Res1 ;\n",
+ "\n",
+ "#result\n",
+ "print\"Decrease in thermal resistaneat surface\",round(delRes,4),\"k/w\",\"\\nIncrease in heattransfer rate\",round(q,1);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Decrease in thermal resistaneat surface 0.1425 k/w \n",
+ "Increase in heattransfer rate 731.3\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |