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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7 : radiation heat transfer"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.3 Page No : 215"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the fraction of radiation falls in visible range is 0.366 \n",
+ "the fraction of radiation on the left of visible range is 0.1229 \n",
+ "the fraction in right of visible range is 0.5111 \n",
+ "The maximum wavelength is 0.5014 micrometer is\n",
+ "The frequency is 5.98e+08 s**-1\n",
+ "the maximum spectral emissive power is 8.298e+13 W/m**2\n",
+ "the hemispherical total emissive power is 6.326e+07 W/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math \n",
+ "# Variables\n",
+ "Ts = 5780. \t\t\t#K, surface temp.\n",
+ "\n",
+ "# Calculations and Results\n",
+ "#(a)\n",
+ "lamda1 = 0.4 \t\t\t#micrometer, starting visible spectrum range \n",
+ "lamda2 = 0.7 \t\t\t#micrometer,ending visible spectrum range\n",
+ "E1 = lamda1*Ts \t\t\t#micrometer K, \n",
+ "E2 = lamda2*Ts \t\t\t#micrometer K, \n",
+ "#from table 7.2\n",
+ "#fraction of radiation lying between 0 and lamda1\n",
+ "F1 = 0.1229\n",
+ "#fraction of radiation lying between 0 and lamda2\n",
+ "F2 = 0.4889\n",
+ "#the fraction of radiation falls betweem lamda1 & lamda 2\n",
+ "F3 = F2-F1\n",
+ "print \"the fraction of radiation falls in visible range is %.3f \"%(F3)\n",
+ "#(b)\n",
+ "F4 = F1\n",
+ "print \"the fraction of radiation on the left of visible range is %.4f \"%(F4)\n",
+ "#(c)\n",
+ "F5 = 1-F2\n",
+ "print \"the fraction in right of visible range is %.4f \"%(F5)\n",
+ "#(d)\n",
+ "#from wein's print lacement law\n",
+ "lmax = 2898/Ts\n",
+ "print \"The maximum wavelength is %.4f micrometer is\"%(lmax)\n",
+ "c = 2.998*10**8 \t\t\t#m/s, speed of light\n",
+ "mu = c/lmax\n",
+ "print \"The frequency is %1.2e s**-1\"%(mu)\n",
+ "#(e)\n",
+ "#from eq. 7.4\n",
+ "h = 6.6256*10**-34 \t\t\t#Js planck's consmath.tant\n",
+ "k = 1.3805*10**-23 \t\t\t#J/K, boltzman consmath.tant\n",
+ "Eblmax = (2*math.pi*h*c**2*(lmax*10**-6)**-5)/((math.exp(h*c/(lmax*10**-6*k*Ts)))-1)\n",
+ "print \"the maximum spectral emissive power is %1.3e W/m**2\"%(Eblmax)\n",
+ "#(f)\n",
+ "s = 5.668*10**-8 \t\t\t#stephen math.cosmath.tant\n",
+ "Eb = s*Ts**4\n",
+ "print \"the hemispherical total emissive power is %1.3e W/m**2\"%(Eb)\n",
+ "\n",
+ "# note : rounding off error."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.4 Page No : 216"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Surface temp. is 515 C\n",
+ "wavength is 5.62 micrometer \n",
+ " from fig 7.1 it falls in the infrared region of spectrum.\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Variables\n",
+ "Eb = 4000. \t\t\t#W/m sq, Total emmisive power\n",
+ "s = 5.669*10**-8 \t\t\t#Stephen boltzman consmath.tant\n",
+ "\n",
+ "#Calculation\n",
+ "T = (Eb/s)**0.25 \t\t\t#k, surface temp. of black body\n",
+ "ym = 2898./T \t\t\t#micro meter,\n",
+ "#By weins law : Max. wavelength of emmision is inversaly proportional \n",
+ "#to temprature. and consmath.tant is 2898 micrometer.\n",
+ "\n",
+ "#Result\n",
+ "print \"Surface temp. is %.0f C\"%(T)\n",
+ "print \"wavength is %.2f micrometer \"%(ym)\n",
+ "print \" from fig 7.1 it falls in the infrared region of spectrum.\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.5 Page No : 219"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "total hemispherical) emissive power is 1.241e+05 W/m**2\n",
+ "total hemispherical) emissivity of the surface is 0.4326\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Variables\n",
+ "T = 1500. \t\t\t#K, surface temprature\n",
+ "#from fig 7.7\n",
+ "e1 = 0.2 \t\t\t#emissivity ,when wavelength(l1) is 0<l1<2 micrometer\n",
+ "e2 = 0.6 \t\t\t#emissivity ,when wavelength(l2) is 2<l2<6 micrometer\n",
+ "e3 = 0.1 \t\t\t#emissivity ,when wavelength(l3) is 6<l3<10 micrometer\n",
+ "e4 = 0 \t\t\t#emissivity ,when wavelength(l4) is l4>10 micrometer\n",
+ "#from table 7.2\n",
+ "F1 = 0.2733 \t\t\t#fraction of energy in wavelength (l1)\n",
+ "F2 = 0.89-F1 \t\t\t#fraction of energy in wavelength (l2)\n",
+ "F3 = 0.9689-0.89 \t\t\t#fraction of energy in wavelength (l3)\n",
+ "\n",
+ "#Calculation and Result\n",
+ "s = 5.669*10**-8 \t\t\t#stephen's consmath.tant\n",
+ "Eb = s*T**4 \t\t\t#emissive power \n",
+ "E = (e1*F1+e2*F2+e3*F3)*Eb\n",
+ "print \"total hemispherical) emissive power is %1.3e W/m**2\"%(E)\n",
+ "#(b)\n",
+ "e = E/(s*T**4)\n",
+ "print \"total hemispherical) emissivity of the surface is %.4f\"%(e)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.6 Page No : 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "fraction of radiation passes through hole 0.0588 \n",
+ "fraction of radiation intercepted by the ring 0.0791 \n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.integrate import quad \n",
+ "\n",
+ "# Variables\n",
+ "ri = 5. \t\t\t#cm ,inside radius of ring\n",
+ "w = 3. \t\t\t#cm, width\n",
+ "ro = ri+w \t\t\t#cm, outside radius \n",
+ "L = 20. \t\t\t#cm, surface dismath.tance\n",
+ "\n",
+ "# Calculations\n",
+ "def f4(r): \n",
+ " return 20.**2*r/(20.**2+r**2)**2\n",
+ "\n",
+ "F1 = 2* quad(f4,0,ri)[0]\n",
+ "\n",
+ "#view factor along surface dA1-A2\"\n",
+ "\n",
+ "def f5(r): \n",
+ " return 20**2*r/(20**2+r**2)**2\n",
+ "\n",
+ "F2 = 2* quad(f5,ri,ro)[0]\n",
+ "\n",
+ "# Results\n",
+ "print \"fraction of radiation passes through hole %.4f \"%(F1)\n",
+ "print \"fraction of radiation intercepted by the ring %.4f \"%(F2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.8 Page No : 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "view factor F11 = 0\n",
+ "view factor F22 = 1\n",
+ "view factor F21 = 0.5\n",
+ "view factor = 0.5\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variables\n",
+ "F11 = 0 \t\t\t#view factor\n",
+ "d = 1. \t\t\t#let it be\n",
+ "print \"view factor F11 = %.0f\" %(F11)\n",
+ "\n",
+ "#Calculation and Result\n",
+ "F12 = 1-F11 \t\t\t#view factor\n",
+ "print \"view factor F22 = %.0f\"%(F12)\n",
+ "\n",
+ "A1 = ((math.pi)*d**2)/4 \t\t\t#sq m, area\n",
+ "A2 = ((math.pi)*d**2)/2 \t\t\t#sq m, area\n",
+ "F21 = A1/A2 \t\t\t#from eq . 7.26\n",
+ "print \"view factor F21 = %.1f\"%( F21)\n",
+ "F22 = 1-F21 \n",
+ "#Results\n",
+ "print \"view factor = %.1f\"%(F22)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.9 Page No : 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "view factor F11 = 0\n",
+ "view factor F33 = 0.5\n",
+ "view factor F14 = 0.056\n",
+ "view factor F13 = 0.056\n",
+ "view factor F12 = 0.944\n",
+ "view factor F31 = 0.028\n",
+ "view factor F32 = 0.472\n",
+ "view factor F21 = 0.118\n",
+ "view factor F23 = 0.118\n",
+ "view factor F22 = 0.764\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable\n",
+ "s = 3. \t\t\t#no. of surface\n",
+ "tvf = s**2 \t\t\t#total view factor\n",
+ "\n",
+ "#using the result of example 7.8\n",
+ "F11 = 0 \n",
+ "F33 = 0.5\n",
+ "print \"view factor F11 = %.0f\"%(F11)\n",
+ "print \"view factor F33 = %.1f\"%(F33)\n",
+ "\n",
+ "#Calculation & Results\n",
+ "R1 = 0.25 \t\t\t#R = d/2*h &h = 2d\n",
+ "R2 = 0.25\n",
+ "X = 1+((1+R2**2)/(R1**2))\n",
+ "F14 = (0.5)*(X-math.sqrt((X**2)-4*(R2/R1)**2))\n",
+ "print \"view factor F14 = %.3f\"%(F14)\n",
+ "F13 = F14\n",
+ "print \"view factor F13 = %.3f\"%(F13)\n",
+ "F12 = 1-F11-F13 \t\t\t# from eq. 7.31 for surface 1\n",
+ "print \"view factor F12 = %.3f\"%(F12)\n",
+ "\n",
+ "d = 1. \t\t\t#say\n",
+ "A1 = (math.pi*(d**2))/4.\n",
+ "A3 = (math.pi*(d**2))/2.\n",
+ "F31 = A1*F13/(A3)\n",
+ "print \"view factor F31 = %.3f\"%(F31)\n",
+ "\n",
+ "# from eq. 7.31 for surface 3\n",
+ "F33 = 0.5\n",
+ "F32 = 1-F31-F33\n",
+ "print \"view factor F32 = %.3f\"%(F32)\n",
+ "\n",
+ "#for surface 2\n",
+ "A2 = 2*math.pi*d**2\n",
+ "F21 = A1*F12/A2\n",
+ "print \"view factor F21 = %.3f\"%(F21)\n",
+ "F23 = A3*F32/A2\n",
+ "print \"view factor F23 = %.3f\"%(F23)\n",
+ "F22 = 1-F21-F23\n",
+ "print \"view factor F22 = %.3f\"%(F22)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.10 Page No : 235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The view factor from surface 1 to 2 is 1\n",
+ "The view factor from surface 2 to 1 is 0.167\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "# Variables\n",
+ "ds = 0.3 \t\t\t#m, diameter of shell\n",
+ "r1 = 0.1 \t\t\t#m, dismath.tance from the centre\n",
+ "\n",
+ "#Calculation and Results\n",
+ "#by the defination of view factor\n",
+ "F12 = 1.\n",
+ "print \"The view factor from surface 1 to 2 is %.0f\"%(F12)\n",
+ "#F21\n",
+ "R = ds/2. \t\t\t#m, radius of sphere\n",
+ "r2 = math.sqrt(R**2-r1**2)\n",
+ "A1 = math.pi*r2**2 \t\t\t#m**2 area\n",
+ "A2 = 2*math.pi*R**2+2*math.pi*R*math.sqrt(R**2-r2**2)\n",
+ "#from reciprocity relation\n",
+ "F21 = (A1/A2)*F12\n",
+ "print \"The view factor from surface 2 to 1 is %.3f\"%(F21)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.12 Page No : 237"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The time required for the ball to cool is 10.3 h\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math \n",
+ "from scipy.integrate import quad \n",
+ "# Variables\n",
+ "d = 0.3 \t\t\t#m, diameter of steel sphere\n",
+ "Ti = 800. \t\t\t#K, initial temp. of sphere\n",
+ "T2 = 303. \t\t\t#C,ambient temp.\n",
+ "T1 = 343. \t\t\t#C, final tempreture\n",
+ "rho = 7801. \t\t\t#kg/m**3, density of steel\n",
+ "cp = 0.473 \t\t\t#kj/kg C, specific heat of steel\n",
+ "#calculation\n",
+ "R = d/2 \t\t\t#m, radius of sphere\n",
+ "A1 = 4*math.pi*R**2 \t\t\t#m**2, area of sphere\n",
+ "m = 4./3*math.pi*R**3*rho \t\t\t#m**3, mass of sphere\n",
+ "F12 = 1. \t\t\t#view factor\n",
+ "s = 5.669*10**-8 \t\t\t#stephen Boltzman's consmath.tant\n",
+ "#-dT1/dt = A1*F12*s*(T**4-T2**4)/(m*cp)\n",
+ "\n",
+ "def f1(T1): \n",
+ " return (1/(T1**4-T2**4))\n",
+ "\n",
+ "I = quad(f1,343,800)[0]\n",
+ "\n",
+ "t = I/(A1*F12*s/(m*cp*10**3))\n",
+ "\n",
+ "# Results\n",
+ "print \"The time required for the ball to cool is %.1f h\"%(t/3600)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.13 Page No : 247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a) Net rate of radiative heat loss Q12 = 596.6 W \n",
+ "b) Net rate of radiative heat loss Q12 = 441.5 W\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variables\n",
+ "d = 0.114 \t\t\t#m, dia.o f pipe\n",
+ "l = 1. \t\t\t#m, length of pipe\n",
+ "A = (math.pi)*d*l \t\t\t#m sq, area\n",
+ "e1 = 1. \t\t\t#emmisivity of black body\n",
+ "F12 = 1. \t\t\t#view factor, 1:pipe surface, 2:room walls\n",
+ "s = 5.67*10**-8 \t\t\t#stephen boltzman consmath.tant\n",
+ "T1 = 440. \t\t\t#K, steam temp.\n",
+ "T2 = 300. \t\t\t#K, wall temp.\n",
+ "#Caluclation\n",
+ "Q12 = A*e1*F12*s*(T1**4-T2**4) \t\t\t#net rate of radiative heat loss\n",
+ "\n",
+ "#Results\n",
+ "print \"a) Net rate of radiative heat loss Q12 = %.1f W \"%(Q12)\n",
+ "#Part-b\n",
+ "e2 = 0.74\n",
+ "Q12 = A*e2*F12*s*(T1**4-T2**4) \t\t\t#net rate of radiative heat loss\n",
+ "print \"b) Net rate of radiative heat loss Q12 = %.1f W\"%(Q12)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.14 Page No : 247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a-i) View factor F12 = 1\n",
+ "view factor F21 = 0.937\n",
+ "ii) The net rate of heat gain Q1net = 4.0 J/s\n",
+ "b) Rate of nitrogen loss = 72 g/h\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "#Variable declaration\n",
+ "F12 = 1. \t\t\t#view factor\n",
+ "r1 = 0.15 \t\t\t#m inner radius of phere\n",
+ "r2 = 0.155 \t\t\t#m , outer radius\n",
+ "\n",
+ "#Calculation\n",
+ "A1 = 4.*(math.pi)*r1**2 \t\t\t#sq m inner area\n",
+ "A2 = 4.*(math.pi)*r2**2 \t\t\t#sq m,outer area \n",
+ "F21 = A1/A2\n",
+ "h = 200. \t\t\t#J/g, heat of vaporization of nitrogen\n",
+ "s = 5.669*10**-8 \t\t\t# boltzman consmath.tant\n",
+ "T2 = 298. \t\t\t#K, temp. of outer wall\n",
+ "T1 = 77. \t\t\t#K, Temp. of inner wall\n",
+ "e1 = 0.06 \t\t\t#emmisivity\n",
+ "e2 = 0.06 \t\t\t#emmisivity\n",
+ "x = ((1-e1)/(e1*A1))+(1/(A1*F12))+((1-e2)/(e2*A2))\n",
+ "Q1net = (s*(T2**4-T1**4))/(x)\n",
+ "\n",
+ "#Result-a-i\n",
+ "print \"a-i) View factor F12 = %.0f\"%(F12)\n",
+ "print \"view factor F21 = %.3f\"%(F21)\n",
+ "#Result- b\n",
+ "print \"ii) The net rate of heat gain Q1net = %.1f J/s\"%(Q1net)\n",
+ "nl = Q1net/h\n",
+ "nl = nl*3600 \t\t\t#g/h\n",
+ "print \"b) Rate of nitrogen loss = %.0f g/h\"%(nl)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.15 Page No : 248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the net rate of radiant heat transfer to the wall is 2900 W\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "# Variables\n",
+ "x = 0.15 \t\t\t#m, length of opening on a furnace\n",
+ "y = 0.12 \t\t\t#m, width of opening on a furnace\n",
+ "x1 = 6. \t\t\t#m, width of wall\n",
+ "y1 = 5. \t\t\t#m, height of wall\n",
+ "e2 = 0.8 \t\t\t#emissivity of wall\n",
+ "T1 = 1400. \t\t\t#C, furnace temp.\n",
+ "T2 = 35. \t\t\t#C, wall temp.\n",
+ "T3 = 273. \t\t\t#C, smath.radians(numpy.arcmath.tan(ard temp.\n",
+ "s = 5.669*10**-8 \t\t\t#stephen boltzman's consmath.tant\n",
+ "#in fig. 7.29\n",
+ "l1 = 2. \t\t\t#m, l1 = AF\n",
+ "l2 = 1.5 \t\t\t#m, l2 = AH\n",
+ "h = 3. \t\t\t#m, E = dA1\n",
+ "\n",
+ "# Calculations\n",
+ "F1 = (1./(2*math.pi))*((l2/(math.sqrt(l2**2+h**2)))*math.tanh(l1/(math.sqrt(l2**2+h**2)))+(l1/(math.sqrt(l1**2+h**2)))*math.tan(l2/(math.sqrt(l1**2+h**2))))\n",
+ "#Similarly\n",
+ "#for the dA1-A3 pair the equation is\n",
+ "F2 = 0.1175\n",
+ "#for the dA1-A4 pair the equation is\n",
+ "F3 = 0.1641\n",
+ "#for the dA1-A5 pair the equation is\n",
+ "F4 = 0.0992\n",
+ "#view factor b/w the opening (dA1)and the wall (W) is \n",
+ "F5 = F1+F2+F3+F4\n",
+ "#Calculation of radient heat exchange\n",
+ "dA1 = x*y\n",
+ "Aw = x1*y1\n",
+ "Eb1 = s*(T1+T3)**4\n",
+ "Ebw = s*(T2+T3)**4\n",
+ "F6 = dA1*F5/Aw\n",
+ "Q = dA1*F5*e2*(Eb1*(1-(1-e2)*F6)-Ebw)\n",
+ "\n",
+ "# Results\n",
+ "print \"the net rate of radiant heat transfer to the wall is %.0f W\"%(round(Q,-2))\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.16 Page No : 250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the net rate of radiant heat loss = 17.1 kW \n",
+ "convective heat transfer coeff. = 90 W/sq m C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Variable declaration\n",
+ "l = 3. \t\t\t#m, length of wall\n",
+ "w = 2. \t\t\t#m, width of, wall\n",
+ "d = 3. \t\t\t#m\n",
+ "R1 = l/d\n",
+ "A1 = l*w \t\t\t#sq m,area 1: front part\n",
+ "A2 = A1 \t\t\t#sq m , area, 2\"back part\n",
+ "e1 = 0.7 \t\t\t#emmisivity\n",
+ "e2 = 0.7 \t\t\t#emmisivity\n",
+ "T1 = 673. \t\t\t#k\n",
+ "T2 = 523. \t\t\t#k\n",
+ "s = 5.669*10**-8 \t\t\t#stephen boltzman consmath.tant\n",
+ "\n",
+ "#Calculation\n",
+ "F12 = 0.148 \t\t\t#view factor ,from fig. 7.12\n",
+ "x = (A1+A2-2*A1*F12)/(A2-(A1*(F12**2)))+((1/e1)-1)+(A1/A2)*((1/e2)-1)\n",
+ "\n",
+ "#Results\n",
+ "Q1net = -1*A1*(s*(T2**4-T1**4))/(x)\n",
+ "print \"the net rate of radiant heat loss = %.1f kW \"%(Q1net/1000)\n",
+ "# (b)\n",
+ "F24 = 1. \t\t\t#from fig 7.12\n",
+ "T20 = 333. \t\t\t#K, outer surface temp. of surface 2\n",
+ "T4 = 303. \t\t\t#K, ambient temp\n",
+ "Q2rad = A2*e2*F24*s*(T20**4-T4**4)\n",
+ "q = Q1net-Q2rad\n",
+ "q1 = q/1000 \t\t\t# Kw\n",
+ "h = q/(A2*(T20-T4))\n",
+ "print \"convective heat transfer coeff. = %.0f W/sq m C\"%(h)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.17 Page No : 251"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "net rate of radiation exchange b/w disk 1 and 2 is 2286 W/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "from numpy import array, linalg\n",
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "r1i = 0.1 \t\t\t#m, inner radius of disk 1\n",
+ "r1o = 0.2 \t\t\t#m, outer radius of disk 1\n",
+ "r2i = 0.12 \t\t\t#m, inner radius of disk 2\n",
+ "r2o = 0.25 \t\t\t#m, outer radius of disk 2\n",
+ "h = 0.08 \t\t\t#m, dismath.tance between the disks\n",
+ "R2 = r2o/h\n",
+ "R1 = r1o/h\n",
+ "X = 1+(1+R1**2)/R2**2\n",
+ "F23_14 = 1./2*(X-math.sqrt(X**2-4*(R1/R2)**2))\n",
+ "\n",
+ "#calculation\n",
+ "R2_ = r2o/h\n",
+ "R1_ = r1i/h\n",
+ "X_ = 1+(1+R1_**2)/R2_**2\n",
+ "F23_4 = 1/2*(X_-math.sqrt(X_**2-4*(R1_/R2_)**2)) \t\t\t#view factor\n",
+ "#similarly\n",
+ "F3_14 = 0.815 \t\t\t#view factor\n",
+ "F34 = 0.4 \t\t\t#view factor\n",
+ "A23 = math.pi*r2o**2 \t\t\t#area\n",
+ "A3 = math.pi*r2i**2\n",
+ "A1 = math.pi*(r1o**2-r1i**2)\n",
+ "#from eq. 1\n",
+ "F12 = A23*(F23_14-F23_4)/A1-(A3*(F3_14-F34))/A1\n",
+ "\n",
+ "#calculation of the rate of radiative heat exchange\n",
+ "# Variables\n",
+ "T1 = 1000. \t\t\t#K, temprature of disk 1\n",
+ "T2 = 300. \t\t\t#K, temprature of disk 2\n",
+ "s = 5.669*10**-8 \t\t\t#stephen's Boltzman consmath.tant\n",
+ "e1 = 0.8 \t\t\t#emissivity\n",
+ "e2 = 0.7\n",
+ "A2 = math.pi*(r2o**2-r2i**2)\n",
+ "F1s = 1-F12\n",
+ "F2s = 1-(A1*F12/A2)\n",
+ "#calculation\n",
+ "#let some quantities equal to \n",
+ "a = (1-e1)/(e1*A1)\n",
+ "b = 1/(A1*F12)\n",
+ "c = (1-e2)/(e2*A2)\n",
+ "d = 1/(A1*F1s)\n",
+ "e = 1/(A2*F2s)\n",
+ "f = s*T1**4\n",
+ "g = s*T2**4\n",
+ "#from eq. 7.42(a)\n",
+ "#(f-J1)/a = (J1-J2)/b+J1/d\n",
+ "#(g-J2)/c = (J2-J1)/b+J1/e\n",
+ "#solving two eqns by matrix\n",
+ "A = array([[-0.0564,0.5036],[0.4712,-0.0564]])\n",
+ "B = array([[161.847],[21376.31]])\n",
+ "X = linalg.solve(A,B)\n",
+ "J1 = X[0]\n",
+ "J2 = X[1]\n",
+ "\n",
+ "#net rate of radiation exchange \n",
+ "Q12net = (J1-J2)/17.73\n",
+ "\n",
+ "# Results\n",
+ "print \"net rate of radiation exchange b/w disk 1 and 2 is %d W/m**2\"%(Q12net)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.18 Page No : 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The net rate of heat gain of tube is 0.30 W\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.optimize import fsolve \n",
+ "import math \n",
+ "\n",
+ "# Variables\n",
+ "di = 0.0254 \t\t\t#m, inner diameter of tube\n",
+ "Ti = 77. \t\t\t#K, liquid temprature\n",
+ "do = 52.5*10**-3 \t\t\t#m, pipe internal diameter\n",
+ "To = 270. \t\t\t#K, wall temprature\n",
+ "l = 1. \t\t\t#m, length of tube\n",
+ "e1 = 0.05 \t\t\t#emissivity of tube wall\n",
+ "e2 = 0.1 \t\t\t#emissivity of pipe wall\n",
+ "e3 = 0.02 \t\t\t#emissivity for inner surface of radiation field\n",
+ "e4 = 0.03 \t\t\t#emissivity for outer surface of radiation field\n",
+ "s = 5.669*10**-8 \t\t\t#stephen boltzman math.cosmath.tantl\n",
+ "\n",
+ "#Calculation\n",
+ "ds = (do+di)/2 \t\t\t#m, diameter of radiation shield\n",
+ "Ao = math.pi*do*l \t\t\t#m**2, outer pipe area\n",
+ "As = math.pi*ds*l \t\t\t#m**2, shield area\n",
+ "Ai = math.pi*di*l \t\t\t#m**2, inner pipe area\n",
+ "#View factors\n",
+ "#for the long cylindrical enclosure made up of the outer pipe and the shield\n",
+ "Fso = 1. \t\t\t#because outer surface of shield cant see itself\n",
+ "Fos = As/Ao \n",
+ "Fsi = Ai/As\n",
+ "#now assume \n",
+ "#(1-e2)/e2+ 1/Fos +Ao*(1-e4)/(As*e4) = x\n",
+ "#(1-e3)/e3 +1/Fsi +(1/Fsi)*(1-e1)/e1 = y\n",
+ "x = (1-e2)/e2+ 1/Fos +Ao*(1-e4)/(As*e4)\n",
+ "y = (1-e3)/e3 +1/Fsi +(1/Fsi)*(1-e1)/e1\n",
+ "#solving the equations for heat transfer from the outer pipe and inner pipe\n",
+ "def f(Ts): \n",
+ " return (Ao*(To**4-Ts**4)/x)-(Ai*(Ts**4-Ti**4)/x)\n",
+ "Ts = fsolve(f,1)\n",
+ "Qos = (Ao*s*(To**4-Ts**4))/x\n",
+ "\n",
+ "# Results\n",
+ "print \"The net rate of heat gain of tube is %.2f W\"%(Qos)\n",
+ "\n",
+ "# note : rounding off error."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.19 Page No : 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Rate of heat loss from the top surface : 403 W\n",
+ "Rate of heat loss from the side walls : 1271 W\n",
+ "Total rate of heat loss : 1674 W\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Variables\n",
+ "T1 = 300 + 273. #K\n",
+ "Ta = 30. + 273. # K\n",
+ "w = 0.075 # m\n",
+ "k = 0.08 # W/m c\n",
+ "l = 1.075 # m\n",
+ "delta = 5.669 * 10**-8 # W/m**2 K**4\n",
+ "A1 = 1 * 1.5 # M**2\n",
+ "A2 = A1\n",
+ "A2m = (1.5 + 1.9)/2 # m**2\n",
+ "A3m = (5. + 6.02)/2 # m**2 \n",
+ "\n",
+ "# Calculations\n",
+ "T2 = 545.1 # k\n",
+ "T2_ = 322.6\n",
+ "T3 = 544.7\n",
+ "T3_ = 328.4\n",
+ "rate_of_heatloss1 = int(A2m*k/w*(T2-T2_))\n",
+ "rate_of_heatloss2 = int(A3m*k/w*(T3-T3_))\n",
+ "total = rate_of_heatloss1 + rate_of_heatloss2\n",
+ "\n",
+ "# results\n",
+ "print \"Rate of heat loss from the top surface : %d W\"%rate_of_heatloss1\n",
+ "print \"Rate of heat loss from the side walls : %d W\"%rate_of_heatloss2\n",
+ "print \"Total rate of heat loss : %d W\"%total"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.20 Page No : 264"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "the spectral extinction coefficient is 24.08 m**-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "# Variables\n",
+ "T = 300. \t\t\t#K, temprature\n",
+ "per = 91. \t\t\t#percent, adsorbed radiation\n",
+ "lam = 4.2 \t\t\t#micrometer, wavelength radiation\n",
+ "L = 0.1 \t\t\t#m, path length\n",
+ "\n",
+ "#calculation\n",
+ "# I2/I1 = f\n",
+ "f = 1-per/100. \t\t\t#fraction of incident radiation transmitted\n",
+ "#from eq. 7.69\n",
+ "a = -math.log(f)/L\n",
+ "\n",
+ "# Results\n",
+ "print \"the spectral extinction coefficient is %.2f m**-1\"%(a)\n",
+ "\n",
+ "# note : rounding off error."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.21 Page No : 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The total rate of heat transfer from the gas to the wall is 22.5 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Variables\n",
+ "Ts = 800. \t\t\t#C, wall temp.\n",
+ "Tg = 1100. \t\t\t#C. burner temprature\n",
+ "CO2 = 8. \t\t\t#percent, composition of CO2 in flue gas\n",
+ "M = 15.2 \t\t\t#percent, composition of moisture in flue gas\n",
+ "a = 0.4 \t\t\t#m, length of duct\n",
+ "b = 0.4 \t\t\t#width of duct\n",
+ "h = 15. \t\t\t#W/m**2 C, heat transfer coefficient\n",
+ "P = 1. \t\t\t#atm pressure\n",
+ "#CAlCULATION of Eg(Tg)\n",
+ "pc = CO2/100.*P \t\t\t#atm, partial pressure of CO2\n",
+ "pw = M/100.*P \t\t\t#atm, partial pressure of moisture\n",
+ "l = 1. \t\t\t#m, length of duct\n",
+ "V = a*b*l \t\t\t#m**3, volume of duct\n",
+ "A = 1.6*l \t\t\t#m**2 area of duct\n",
+ "Le = 3.6*(V/A) \t\t\t#m, mean beam length\n",
+ "\n",
+ "pc*Le\n",
+ "pw*Le\n",
+ "Tg_ = Tg+273.\n",
+ "Ts_ = Ts+273.\n",
+ "#from fig 7.38\n",
+ "Ec = 0.06\n",
+ "Eg = 0.048 \t\t\t#from fig 7.39\n",
+ "#a correction dE need to be calculated\n",
+ "#pw/(pc+pw)\n",
+ "#pc*Le+pw*Le\n",
+ "#from fig. 7.39\n",
+ "dE = 0.003\n",
+ "Eg_Tg = Ec+Eg-dE \t\t\t#emissivity at temp. Tg\n",
+ "\n",
+ "#Calculation of alpha\n",
+ "#pc*Le*Ts/Tg\n",
+ "#from fig. 7.37\n",
+ "Ec1 = 0.068\n",
+ "#from fig. 7.38\n",
+ "Ew1 = 0.069\n",
+ "Cc = 1 \t\t\t#correction factor\n",
+ "Cw = 1 \t\t\t#correction factor\n",
+ "d_alpha = dE \t\t\t#AT 1 ATM TOTAL PRESSURE\n",
+ "alpha = Cc*Ec1*(Tg_/Ts_)**0.65+Cw*Ew1*(Tg_/Ts_)**0.45-dE\n",
+ "#radiant heat ransfer rate\n",
+ "s = 5.669*10**-8 \t\t\t#stephen's boltzman consmath.tant\n",
+ "Qrad = A*s*(Eg_Tg*Tg_**4-alpha*Ts_**4) \t\t\t#kW\n",
+ "Qconv = h*A*(Tg-Ts) \t\t\t#kW, convective heat transfer rate\n",
+ "Q = Qrad+Qconv\n",
+ "\n",
+ "# Results\n",
+ "print \"The total rate of heat transfer from the gas to the wall is %.1f kW\"%(Q/1000)\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-20 05:01:16 +0000