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diff --git a/Transport_Phenomena:_A_Unified_Approach/ch4.ipynb b/Transport_Phenomena:_A_Unified_Approach/ch4.ipynb new file mode 100755 index 00000000..dbef3bc2 --- /dev/null +++ b/Transport_Phenomena:_A_Unified_Approach/ch4.ipynb @@ -0,0 +1,342 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4 : molecular transport and the general property balance" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.1 - Page No :99\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "# Variables\n", + "# given\n", + "id_ = 2.067; \t\t\t #[in] - inside diameter\n", + "t = 0.154; \t\t\t #[in] - wall thickness\n", + "od = id_+2*t; \t\t\t #[in] - outer diameter\n", + "a = 1.075; \t\t\t #[in**2] - wall sectional area of metal\n", + "A = a*(1./144); \t\t #[ft**2] - wall sectional area of metal in ft**2\n", + "deltaz = 5./12; \t\t #[ft] - length of transfer in z direction\n", + "T2 = 10+273.15; \t\t #[K] - temperature at the top\n", + "T1 = 0+273.15; \t\t #[K] - temperature at the bottom\n", + "q = -3.2; \t\t\t #[Btu/hr] - heat transferred\n", + "\n", + "# Calculations\n", + "deltaT = (T2-T1)+8; \t\t\t #[degF]\n", + "k = round(-(q/A)/(deltaT/deltaz),2);\n", + "\n", + "# Results\n", + "print \"Thermal conductivity = %.2f Btu h**-1 ft**-1 degF**-1\"%(k);\n", + "Alm = round((2*math.pi*deltaz*((od-id_)/(2*12)))/math.log(od/id_),3); \t\t\t #[ft**2] log-mean area\n", + "kincorrect = round(k*(A/Alm),3);\n", + "print \"kincorrect = %.3f Btu h**-1 ft**-1 degF**-1 \"%(kincorrect);\n", + "print \"The error is a factor of %.1f\"%(32.4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thermal conductivity = 9.92 Btu h**-1 ft**-1 degF**-1\n", + "kincorrect = 0.306 Btu h**-1 ft**-1 degF**-1 \n", + "The error is a factor of 32.4\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.2 - Page No :100\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "\n", + "# Variables\n", + "# given\n", + "T1 = 0.; \t\t\t #[degC]\n", + "T2 = 10.; \t \t\t #[degC]\n", + "km = 17.17; \t\t\t #[W/m*K]\n", + "l = 1.; \t\t \t #[m]\n", + "r2 = 1.1875;\n", + "r1 = 1.0335;\n", + "deltaT = T1-T2;\n", + "\n", + "# Calculations\n", + "# umath.sing the formula Qr = -km*((2*pi*l)/ln(r2/r1))*deltaT;\n", + "Qr = -km*((2*math.pi*l)/math.log(r2/r1))*deltaT;\n", + "\n", + "# Results\n", + "print \"Heat loss = %.0f W \\nThe plus sign indicates that the heat flow is radially out from the center\"%(Qr);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Heat loss = 7767 W \n", + "The plus sign indicates that the heat flow is radially out from the center\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.3 - Page No :100\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "# given\n", + "km = 9.92; \t \t\t #[Btu/h*ft*degF]\n", + "Alm = round(0.242*(12./5),3); \t\t\t #[ft**2]\n", + "T1 = 0.; \t\t\t #[degC]\n", + "T2 = 10.; \t\t\t #[degC]\n", + "deltaT = (T1-T2)*1.8; \t\t\t #[degF]\n", + "r2 = 1.1875;\n", + "r1 = 1.0335;\n", + "deltar = round((r2-r1)/12,3); \t\t\t #[ft]\n", + "\n", + "# Calculations\n", + "# using the formula Qr/Alm = -km*(deltaT/deltar)\n", + "Qr = (-km*Alm*(deltaT/deltar));\n", + "\n", + "# Results\n", + "print \" qr by log-mean area method = %.0f Btu/h\"%(Qr);\n", + "\n", + "\n", + "# in SI units \n", + "Alm = 0.177; \t\t\t #[m**2]\n", + "T1 = 0; \t\t\t #[degC]\n", + "T2 = 10; \t\t\t #[degC]\n", + "km = 17.17; \t\t\t #[W/m*K]\n", + "r2 = 1.1875;\n", + "r1 = 1.0335;\n", + "deltaT = T1-T2;\n", + "deltar = (r2-r1)*0.0254; \t\t\t #[m]\n", + "\n", + "# umath.sing the same formula\n", + "Qr = (-km*(deltaT/deltar))*Alm;\n", + "print \" qr in SI units = %.0f W\"%(Qr);\n", + "\n", + "# Note : Answers are wrong in book. Please calculate manually." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " qr by log-mean area method = 7980 Btu/h\n", + " qr in SI units = 7769 W\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.4 - Page No :101\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "# given\n", + "x1 = 0; \t\t\t #[cm]\n", + "x2 = 30; \t\t\t #[cm]\n", + "p1 = 0.3; \t\t\t #[atm]\n", + "p2 = 0.03; \t\t\t #[atm]\n", + "D = 0.164; \t\t\t #[am**2/sec]\n", + "R = 82.057; \t\t\t #[cm**3*atm/mol*K]\n", + "T = 298.15; \t\t\t #[K]\n", + "\n", + "# Calculations\n", + "# using the formula Nax*int(dx/Ax) = -(D/RT)*int(1*dpa)\n", + "def f4(x): \n", + "\t return 1./((math.pi/4)*(10-(x/6))**2)\n", + "\n", + "a = quad(f4,x1,x2)[0]\n", + "\n", + "def f5(p): \n", + "\t return 1\n", + "\n", + "b = quad(f5,p1,p2)[0]\n", + "Nax = -((D/(R*T))*b)/a;\n", + "\n", + "# Results\n", + "print \"Mass transfer rate = %.2e mol/sec = %.2e mol/h \\nthe plus sign indicates diffusion to the right\"%(Nax,Nax*3600);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mass transfer rate = 2.37e-06 mol/sec = 8.53e-03 mol/h \n", + "the plus sign indicates diffusion to the right\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.5 - Page No :105\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from sympy import *\n", + "\n", + "# Variables\n", + "# given\n", + "r = Symbol('r')\n", + "ro = 0.5; \t\t\t #[inch] - outside radius\n", + "ro = 0.0127; \t\t #[m] - outside radius in m\n", + "Tg = 2.*10**7; \t #[J/m**3*sec] - heat generated by electric current\n", + "Tw = 30.; \t\t\t #[degC] - outside surface temperature\n", + "km = 17.3; \t\t #[W/m*K] - mean conductivity\n", + "\n", + "# Calculations\n", + "# using the formula T = Tw+(Tg/4*km)*(ro**2-r**2)\n", + "T = Tw+(Tg/(4*km))*(ro**2-r**2);\n", + "\n", + "# Results\n", + "print \"T = \",T,\n", + "print \" where r is in meters and T is in degC\"\n", + "def t(r):\n", + " return Tw+(Tg/(4*km))*(ro**2-r**2);\n", + "\n", + "print \"At the centre line r = 0, the maximum temperature is %.1f degC. \\\n", + "\\nAt the outside the temperature reduces to the boundary condition value of %.2f degC.\\\n", + "\\nThe distribution is parabolic between these 2 limits\"%(t(0),t(0.0127));\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "T = -289017.341040462*r**2 + 76.6156069364162 where r is in meters and T is in degC\n", + "At the centre line r = 0, the maximum temperature is 76.6 degC. \n", + "At the outside the temperature reduces to the boundary condition value of 30.00 degC.\n", + "The distribution is parabolic between these 2 limits\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4.7 - Page No :119\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "# Variables\n", + "# given\n", + "r = 10.**-3; \t\t\t #[m] - radius\n", + "l = 1.; \t\t\t #[m] - length\n", + "Q = 10.**-7; \t\t\t #[m**3/s] - flow rate\n", + "pressure = 1.01325*10**5\n", + "sPage_No = 1.1;\n", + "pwater = 1000.; \t\t #[kg/m**3] - density of water at 4degC\n", + "\n", + "# Calculations\n", + "deltap = round((145 * pressure)/14.696,-4)\n", + "pfluid = sPage_No *pwater;\n", + "mu = abs(r*-(deltap)*(math.pi*r**3))/((4*Q)*(2*l));\n", + "mupoise = mu*10;\n", + "mucentipoise = mupoise*100;\n", + "\n", + "# Results\n", + "print \" mu = %.3f Ns-m**-2 = %.2f poise = %.0f cP\"%(mu,mupoise,mucentipoise);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " mu = 3.927 Ns-m**-2 = 39.27 poise = 3927 cP\n" + ] + } + ], + "prompt_number": 2 + } + ], + "metadata": {} + } + ] +}
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