From 206d0358703aa05d5d7315900fe1d054c2817ddc Mon Sep 17 00:00:00 2001 From: Jovina Dsouza Date: Wed, 18 Jun 2014 12:43:07 +0530 Subject: adding book --- .../Chapter_4.ipynb | 277 +++++++++++++++++++++ 1 file changed, 277 insertions(+) create mode 100644 Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb (limited to 'Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb') diff --git a/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb new file mode 100644 index 00000000..70b74f06 --- /dev/null +++ b/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_4.ipynb @@ -0,0 +1,277 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Two dimensional, Steady State Conduction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1 Page 211 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Thermal resistance of wire coating associated with peripheral variations in coating thickness\n", + "import math\n", + "d = .005; \t\t\t\t\t\t\t\t\t\t#[m] Diameter of wire\n", + "k = .35; \t\t\t\t\t\t\t\t\t\t#[W/m.K] Thermal Conductivity\n", + "h = 15; \t\t\t\t\t\t\t\t\t\t#[W/m^2.K] Total coeff with Convection n Radiation\n", + "#calculations\n", + "\n", + "rcr = k/h; \t\t\t\t\t\t\t\t\t\t# [m] critical insulation radius\n", + "tcr = rcr - d/2.; \t\t\t\t\t\t\t\t\t\t# [m] critical insulation Thickness\n", + "\n", + "Rtcond = 2.302*math.log10(rcr/(d/2.))/(2*math.pi*k); #[K/W] Thermal resistance \n", + "\n", + "#Using Table 4.1 Case 7\n", + "z = .5*tcr;\n", + "D=2*rcr;\n", + "Rtcond2D = (math.acosh((D*D + d*d - 4*z*z)/(2*D*d)))/(2*math.pi*k);\n", + "#results\n", + "\n", + "print '%s %.2f %s' %(\"\\n\\n The reduction in thermal resistance of the insulation is\", Rtcond-Rtcond2D,\" K/W \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + " The reduction in thermal resistance of the insulation is 0.10 K/W \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3 Page 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature Distribution and Heat rate per unit length\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "Ts = 500.; \t#[K] Temp of surface\n", + "Tsurr = 300.; \t#[K] Temp of surrounding Air\n", + "h = 10.; \t#[W/m^2.K] Heat Convection soefficient\n", + "#Support Column\n", + "delx = .25; \t#[m]\n", + "dely = .25; \t#[m]\n", + "k = 1.; \t#[W/m.K] From Table A.3, Fireclay Brick at T = 478K\n", + "#calculations\n", + "\n", + "#Applying Eqn 4.42 and 4.48\n", + "A = numpy.array([[-4, 1, 1, 0, 0, 0, 0, 0],\n", + "\t\t[2, -4, 0, 1, 0, 0, 0, 0],\n", + "\t\t[1, 0, -4, 1, 1, 0, 0, 0],\n", + "\t\t[0, 1, 2, -4, 0, 1, 0, 0],\n", + "\t\t[0,0, 1, 0, -4, 1, 1, 0],\n", + "\t\t[0, 0, 0, 1, 2, -4, 0, 1],\n", + "\t\t[0, 0, 0, 0, 2, 0, -9, 1],\n", + "\t\t[0, 0, 0, 0, 0, 2, 2, -9]]);\n", + " \n", + "C = numpy.array([[-1000], [-500], [-500], [0], [-500], [0], [-2000], [-1500]]);\n", + "\n", + "T = numpy.linalg.solve (A,C);\n", + "#results\n", + "\n", + "print '%s' %(\"\\n Temp Distribution in K = \");\n", + "print (T);\n", + "\n", + "q = 2*h*((delx/2.)*(Ts-Tsurr)+delx*(T[6]-Tsurr)+delx*(T[7]-Tsurr)/2.);\n", + "print '%s %.2f %s' %(\"\\n\\n Heat rate from column to the airstream\",q,\" W/m \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Temp Distribution in K = \n", + "[[ 489.30472333]\n", + " [ 485.15381783]\n", + " [ 472.06507549]\n", + " [ 462.00582466]\n", + " [ 436.94975396]\n", + " [ 418.73932983]\n", + " [ 356.99461052]\n", + " [ 339.05198674]]" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + "\n", + " Heat rate from column to the airstream 882.60 W/m \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4 Page 230" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable Initialization\n", + "\n", + "# Temperature Field and Rate of Heat Transfer\n", + "import math\n", + "import numpy\n", + "from numpy import linalg\n", + "#Operating Conditions\n", + "\n", + "ho = 1000; #[W/m^2.K] Heat Convection coefficient\n", + "hi = 200; #[W/m^2.K] Heat Convection coefficient\n", + "Ti = 400; #[K] Temp of Air\n", + "Tg = 1700; #[K] Temp of Gas\n", + "h = 10 ; #[W/m^2.K] Heat Convection coefficient\n", + "\n", + "A = 2*6*math.pow(10,-6) ;#[m^2] Cross section of each Channel\n", + "x = .004 ; #[m] Spacing between joints\n", + "t = .006; #[m] Thickness\n", + "k = 25; #[W/m.K] Thermal Conductivity of Blade\n", + "delx = .001 ; #[m]\n", + "dely = .001 ; #[m]\n", + "#calculations and results\n", + "\n", + "#Applying Eqn 4.42 and 4.48\n", + "A = numpy.array([[-(2+ho*delx/k), 1, 0,0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", + " [1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,0,1,-2*(2+ho*delx/k),1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],\n", + " [0,0,0,0,1,-(2+ho*delx/k),0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],\n", + " [1,0,0,0,0,0,-4,2,0,0,0,0,1,0,0,0,0,0,0,0,0],\n", + " [0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0,0,0],\n", + " [0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0,0],\n", + " [0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0,0],\n", + " [0,0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0,0,0,0],\n", + " [0,0,0,0,0,1,0,0,0,0,2,-4,0,0,0,0,0,1,0,0,0],\n", + " [0,0,0,0,0,0,1,0,0,0,0,0,-4,2,0,0,0,0,1,0,0],\n", + " [0,0,0,0,0,0,0,1,0,0,0,0,1,-4,1,0,0,0,0,1,0],\n", + " [0,0,0,0,0,0,0,0,2,0,0,0,0,2,-2*(3+hi*delx/k),1,0,0,0,0,1],\n", + " [0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-2*(2+hi*delx/k),1,0,0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-2*(2+hi*delx/k),1,0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,-(2+hi*delx/k),0,0,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-2,1,0],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,1,-4,1],\n", + " [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,-(2+hi*delx/k)]]);\n", + " \n", + "C = numpy.array([[-ho*delx*Tg/k], \n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-2*ho*delx*Tg/k],\n", + " [-ho*delx*Tg/k],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [-2*hi*delx*Ti/k],\n", + " [-2*hi*delx*Ti/k],\n", + " [-2*hi*delx*Ti/k],\n", + " [-hi*delx*Ti/k],\n", + " [0],\n", + " [0],\n", + " [-hi*delx*Ti/k]]);\n", + "\n", + "T = numpy.linalg.solve (A,C);\n", + "print '%s' %(\"\\n Temp Distribution in K = \");\n", + "print (T);\n", + "q = 4*ho*((delx/2.)*(Tg-T[0])+delx*(Tg-T[1])+delx*(Tg-T[2])+ delx*(Tg-T[3])+delx*(Tg-T[4])+delx*(Tg-T[5])/2.);\n", + "print '%s %.1f %s' %(\"\\n\\n Heat rate Transfer = \" ,q,\"W/m \");\n", + "#END" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + " Temp Distribution in K = \n", + "[[ 1525.95413813]\n", + " [ 1525.27944565]\n", + " [ 1523.59609075]\n", + " [ 1521.93574674]\n", + " [ 1520.83066847]\n", + " [ 1520.45069026]\n", + " [ 1519.66699612]\n", + " [ 1518.7949547 ]\n", + " [ 1516.52842892]\n", + " [ 1514.53554374]\n", + " [ 1513.30134519]\n", + " [ 1512.88873965]\n", + " [ 1515.12393697]\n", + " [ 1513.70494809]\n", + " [ 1509.18712651]\n", + " [ 1506.37665411]\n", + " [ 1504.9504289 ]\n", + " [ 1504.50157796]\n", + " [ 1513.41885557]\n", + " [ 1511.71377418]\n", + " [ 1506.02634497]]\n", + "\n", + "\n", + " Heat rate Transfer = 3540.6 W/m \n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit