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diff --git a/Transport_Phenomena:_A_Unified_Approach/ch3.ipynb b/Transport_Phenomena:_A_Unified_Approach/ch3.ipynb new file mode 100755 index 00000000..d6bb6acf --- /dev/null +++ b/Transport_Phenomena:_A_Unified_Approach/ch3.ipynb @@ -0,0 +1,227 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3 : The general property balance" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3.1 - Page No :65\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "# Variables\n", + "a = 0.0006; \t\t #[m**2] - area\n", + "l = 0.1; \t\t\t #[m] - length\n", + "\n", + "# (a) using the fourier law\n", + "deltax = 0.1; \t\t #[m] - thickness of copper block\n", + "T2 = 100.; \t\t #[degC] - temp on one side of copper block\n", + "T1 = 0.; \t\t\t #[degC] - temp on other side of the copper block\n", + "k = 380.; \t\t\t #[W/mK] - thermal conductivity\n", + "\n", + "# Calculations\n", + "# using the formula (q/A)*deltax = -k*(T2-T1)\n", + "g = -k*(T2-T1)/deltax;\n", + "print \" a) The steady state heat flux across the copper block is q/A = %5.1e J*m**-2*sec**-1 \"%(g);\n", + "\n", + "# (b)\n", + "V = a*l; \t\t\t #[m**3] - volume\n", + "# using the overall balance equation with the accumulation and generation term\n", + "Qgen = 1.5*10**6; \t\t\t #[j*m**-3*sec**-1]\n", + "SIx = (g*a-Qgen*V)/a;\n", + "\n", + "# Results\n", + "print \" b) the flux at face 1 is %5.1e j*m**-2*sec**-1;the negative sign indicates that the \\\n", + "\\nheat flux is from right to left negative x direction\"%(SIx);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " a) The steady state heat flux across the copper block is q/A = -3.8e+05 J*m**-2*sec**-1 \n", + " b) the flux at face 1 is -5.3e+05 j*m**-2*sec**-1;the negative sign indicates that the \n", + "heat flux is from right to left negative x direction\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3.2 - Page No :68\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from sympy import *\n", + "\n", + "# Variables\n", + "x = Symbol('x')\n", + "SIx2 = -3.8*10**5; \t\t #[j*m**-2*sec**-1] - flux at x = 0.1,i.e through face2\n", + "Qgen = 1.5*10**6; \t\t\t #[j*m**-3*sec**-1] - uniform generation in the volume\n", + "T2 = 100+273.15; \t\t\t #[K] temperature at face 2\n", + "x2 = 0.1; \t\t\t #[m]\n", + "k = 380.; \t\t\t #[W/mK] - thermal conductivity\n", + "\n", + "# Calculations\n", + "# using the equation der(SIx)*x = SIx+c1;where c1 is tyhe constant of integration\n", + "c1 = (Qgen*x2)-SIx2;\n", + "SIx = Qgen*x-c1;\n", + "\n", + "# Results\n", + "print \"SIx = \",SIx\n", + "print \" where SIx is in units of J m**-2 sec**-1 and x is in units of m\"\n", + "\n", + "# using the equation -k*T = der(SIx)*x**2-c1*x+c2;where c2 is the constant of integration\n", + "c2 = -k*T2-(Qgen*(x2)**2)/2+c1*x2;\n", + "T = -(Qgen/k)*x**2+(c1/k)*x-(c2/k);\n", + "print \"T = \",T\n", + "print \" where T is in units of kelvin K\"\n", + "\n", + "\n", + "# Answer may vary because of rouding error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "SIx = 1500000.0*x - 530000.0\n", + " where SIx is in units of J m**-2 sec**-1 and x is in units of m\n", + "T = -3947.36842105263*x**2 + 1394.73684210526*x + 253.413157894737\n", + " where T is in units of kelvin K\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3.3 - Page No :69\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "import math \n", + "from sympy import *\n", + "\n", + "\n", + "# Variables\n", + "# given\n", + "x = Symbol('x')\n", + "t = Symbol('t')\n", + "hf1 = -270.; \t\t\t #[J/sec] - heat flow at face 1\n", + "hf2 = -228.; \t\t\t #[J/sec] - heat flow at face2\n", + "Qgen = 1.5*10**6; \t\t #[J*m**-3*sec**-1] generation per unit volume per unit time\n", + "v = 6*10**-5; \t\t\t #[m**3] volume\n", + "Cp = 0.093; \t\t\t #[cal*g**-1*K**-1] heat capacity of copper\n", + "sp = 8.91; \t\t\t #specific gravity of copper\n", + "a = 0.0006; \t\t\t #[m**2] - area\n", + "\n", + "# Calculation and Results\n", + "# (a) using the overall balance\n", + "acc = hf1-hf2+Qgen*v;\n", + "print \"a) the rate of accumulation is %d J/sec \"%(acc);\n", + "\n", + "# (b) \n", + "SIx1 = hf1/a;\n", + "SIx2 = hf2/a;\n", + "x1 = 0.;\n", + "\n", + "# solving for the constant of integration c1 in the equation [del(p*cp*T)/delt-der(SIx)]*x = -SIx+c1;\n", + "c1 = 0+SIx1;\n", + "x2 = 0.1;\n", + "g = (-(SIx2)+c1)/x2+Qgen;\n", + "SIx = c1-(g-Qgen)*x;\n", + "print \"SI(x) = \",\"(b)\",SIx\n", + "\n", + "# solving for constant of integration c3 in the equation p*cp*T = g*t+c3\n", + "T2 = 100+273.15;\n", + "t2 = 0;\n", + "p = sp*10**3; \t\t\t #[kg/m**3] - density\n", + "cp = Cp*4.1840; \t\t\t #[J*kg**-1*K**-1]\n", + "c3 = p*cp*T2-g*t2;\n", + "T = (g*(10**-3)/(p*cp))*t+c3/(p*cp);\n", + "print \"Relationship between T and t at x=0.1m is T = \",T\n", + "\n", + "# solving for constant of integration c2 in the equation -k*T = der(SIx)*x**2-c1*x+c2\n", + "k = 380.; \t\t\t #[w/m**1*K**1]\n", + "x2 = 0.1;\n", + "c2 = k*T+(3.5*10**5)*x2**2-(4.5*10**5)*x2;\n", + "\n", + "def T(t,x):\n", + " return (-(3.5*10**5)*x**2+(4.5*10**5)*x+87.7*t+1.00297*10**5)/k;\n", + "\n", + "# at face 1;\n", + "x1 = 0.;\n", + "t1 = 60.; \t\t\t #[sec]\n", + "T1 = T(t1,x1);\n", + "print \"Temperature profile as a function of x and t is T = %.2f K, at face 1\"%T1\n", + "\n", + "# at face 2\n", + "x2 = 0.1;\n", + "t2 = 60.; \t\t\t # [sec]\n", + "T2 = T(t2,x2);\n", + "print \"Temperature at face 2 = %.0f K ,at face 2\"%T2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a) the rate of accumulation is 48 J/sec \n", + "SI(x) = (b) 700000.0*x - 450000.0\n", + "Relationship between T and t at x=0.1m is T = 0.230747847543697*t + 373.15\n", + "Temperature profile as a function of x and t is T = 277.79 K, at face 1\n", + "Temperature at face 2 = 387 K ,at face 2\n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +}
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