path: root/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_1.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:2ba7e707b3be5d9c0c54b9bb8556d6e5f96b70b9fbb7f8e292b6019cfe481029"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.1 Page 5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "L=.15;   \t\t \t\t\t#[m] - Thickness of conducting wall\n",
      "delT = 1400. - 1150.;  \t\t#[K] - Temperature Difference across the Wall\n",
      "A=.5*1.2; \t\t\t\t\t#[m^2] - Cross sectional Area of wall = H*W\n",
      "k=1.7;    \t\t\t\t\t#[W/m.k] - Thermal Conductivity of Wall Material\n",
      "#calculations\n",
      "#Using Fourier's Law eq 1.2\n",
      "Q = k*delT/L;    \t\t\t#[W/m^2] - Heat Flux\n",
      "\n",
      "q = A*Q;          \t\t\t#[W] - Rate of Heat Transfer  \n",
      "#results\n",
      "print '%s %.2f %s' %(\"\\n \\n Heat Loss through the Wall =\",q,\" W\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " \n",
        " Heat Loss through the Wall = 1700.00  W\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.2 Page 11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " \n",
      "import math\n",
      "d=.07;    \t\t\t\t\t\t\t\t\t#[m] - Outside Diameter of Pipe\n",
      "Ts = 200+273.15;  \t\t\t\t\t\t\t#[K] - Surface Temperature of Steam\n",
      "Tsurr = 25+273.15; \t\t\t\t\t\t\t#[K] - Temperature outside the pipe\n",
      "e=.8; \t\t\t\t\t\t\t\t\t\t#  Emissivity of Surface\n",
      "h=15;    \t\t\t\t\t\t\t\t\t#[W/m^2.k] - Thermal Convectivity from surface to air\n",
      "stfncnstt=5.67*math.pow(10,(-8));   \t \t# [W/m^2.K^4] - Stefan Boltzmann Constant \n",
      "#calculations\n",
      "#Using Eq 1.5 \n",
      "E = e*stfncnstt*Ts*Ts*Ts*Ts;    \t\t\t#[W/m^2] - Emissive Power\n",
      "G = stfncnstt*Tsurr*Tsurr*Tsurr*Tsurr;    \t#[W/m^2] - Irradiation falling on surface\n",
      "#results\n",
      "print '%s %.2f %s' %(\"\\n (a) Surface Emissive Power = \",E,\" W/m^2\");\n",
      "print '%s %.2f %s' %(\"\\n     Irradiation Falling on Surface =\",G,\" W/m^2\");\n",
      "\n",
      "#Using Eq 1.10 Total Rate of Heat Transfer Q  = Q by convection + Q by radiation\n",
      "q = h*(math.pi*d)*(Ts-Tsurr)+e*(math.pi*d)*stfncnstt*(Ts*Ts*Ts*Ts-Tsurr*Tsurr*Tsurr*Tsurr);          #[W] \n",
      "\n",
      "print '%s %.2f %s' %(\"\\n\\n (b) Total Heat Loss per unit Length of Pipe=\",q,\" W\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " (a) Surface Emissive Power =  2273.36  W/m^2\n",
        "\n",
        "     Irradiation Falling on Surface = 448.05  W/m^2\n",
        "\n",
        "\n",
        " (b) Total Heat Loss per unit Length of Pipe= 998.38  W\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.4 Page 20"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "import math\n",
      "Ts = 56.4+273.15;  \t\t\t\t\t#[K] - Surface Temperature of Steam\n",
      "Tsurr = 25+273.15; \t\t\t\t\t#[K] - Temperature of Surroundings\n",
      "e=.88; \t\t\t\t\t\t\t\t#  Emissivity of Surface\n",
      "\n",
      "#As h=(10.9*math.pow(V,.8)[W/m^2.k] - Thermal Convectivity from surface to air\n",
      "stfncnstt=5.67*math.pow(10,(-8)); \t# [W/m^2.K^4] - Stefan Boltzmann Constant \n",
      "\n",
      "A=2*.05*.05;    \t\t\t\t\t# [m^2] Area for Heat transfer i.e. both surfaces\n",
      "\n",
      "E = 11.25;  \t\t\t \t \t\t#[W] Net heat to be removed by cooling air\n",
      "#calculations\n",
      "\n",
      "Qrad = e*stfncnstt*A*(math.pow(Ts,4)-math.pow(Tsurr,4));\n",
      "\n",
      "#Using Eq 1.10 Total Rate of Heat Transfer Q  = Q by convection + Q by radiation\n",
      "Qconv = E - Qrad;\t\t\t\t\t#[W] \n",
      "\n",
      "#As Qconv = h*A*(Ts-Tsurr) & h=10.9 Ws^(.8)/m^(-.8)K.V^(.8)\n",
      "\n",
      "V = math.pow(Qconv/(10.9*A*(Ts-Tsurr)),(1/0.8));\n",
      "#results\n",
      "\n",
      "print '%s %.2f %s' %(\"\\n\\n Velocity of Cooling Air flowing= \", V,\"m/s\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " EXAMPLE 1.4   Page 20 \n",
        "\n",
        "\n",
        "\n",
        " Velocity of Cooling Air flowing=  9.40 m/s\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.6 Page 26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "import math\n",
      "A=1.8;\t    \t\t\t\t\t\t\t\t# [m^2] Area for Heat transfer i.e. both surfaces\n",
      "Ti = 35+273.; \t \t\t\t\t\t\t\t#[K] - Inside Surface Temperature of Body\n",
      "Tsurr = 297.; \t\t\t\t\t\t\t\t#[K] - Temperature of surrounding\n",
      "Tf = 297.; \t\t\t\t\t\t\t\t\t#[K] - Temperature of Fluid Flow\n",
      "e=.95; \t\t\t\t\t\t\t\t\t\t#  Emissivity of Surface\n",
      "L=.003;    \t\t\t\t\t\t\t\t\t#[m] - Thickness of Skin\n",
      "k=.3;  \t\t\t\t\t\t\t\t\t\t#  Effective Thermal Conductivity\n",
      "h=2;    \t\t\t\t\t\t\t\t\t#[W/m^2.k] - Natural Thermal Convectivity from body to air\n",
      "stfncnstt=5.67*math.pow(10,(-8)); \t\t\t# [W/m^2.K^4] - Stefan Boltzmann Constant \n",
      "#Using Eq 1.5\n",
      "\n",
      "Tsa=305.;  \t\t\t    \t\t\t\t    #[K]  Body Temperature Assumed\n",
      "#calculations\n",
      "\n",
      "Ts=307.19\n",
      "q = k*A*(Ti-Ts)/L;          #[W] \n",
      "\n",
      "print '%s' %(\"\\n\\n (I) In presence of Air\")\n",
      "print '%s %.2f %s' %(\"\\n (a) Temperature of Skin = \",Ts,\"K\");\n",
      "print '%s %.2f %s' %(\"\\n (b) Total Heat Loss = \",q,\" W\");\n",
      "\n",
      "#When person is in Water\n",
      "h = 200;    \t\t\t\t\t\t\t\t#[W/m^2.k] - Thermal Convectivity from body to water\n",
      "hr = 0;    \t\t\t\t\t\t\t\t\t# As Water is Opaque for Thermal Radiation\n",
      "Ts = (k*Ti/L + (h+hr)*Tf)/(k/L +(h+hr));   \t#[K]  Body Temperature \n",
      "q = k*A*(Ti-Ts)/L;          \t\t\t\t#[W] \n",
      "#results\n",
      "\n",
      "print '%s' %(\"\\n\\n (II) In presence of Water\")\n",
      "print  '%s %.2f %s' %(\"\\n (a) Temperature of Skin =\",Ts,\" K\");\n",
      "print  '%s %.2f %s' %(\"\\n (b) Total Heat Loss =\",q,\" W\");\n",
      "\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        " (I) In presence of Air\n",
        "\n",
        " (a) Temperature of Skin =  307.19 K\n",
        "\n",
        " (b) Total Heat Loss =  145.80  W\n",
        "\n",
        "\n",
        " (II) In presence of Water\n",
        "\n",
        " (a) Temperature of Skin = 300.67  K\n",
        "\n",
        " (b) Total Heat Loss = 1320.00  W\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1.7 Page 30"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "%pylab inline\n",
      "\n",
      "import math\n",
      "import numpy\n",
      "from numpy import roots\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "Tsurr = 30+273;                                     #[K] - Temperature of surrounding\n",
      "Tf = 20+273;                                        #[K] - Temperature of Fluid Flow\n",
      "e=.5;                                               #  Emissivity of Surface\n",
      "a = .8;                                             # Absorptivity of Surface\n",
      "G = 2000;                                           #[W/m^2] - Irradiation falling on surface\n",
      "h=15;                                               #[W/m^2.k] - Thermal Convectivity from plate to air\n",
      "stfncnstt=5.67*math.pow(10,(-8));                   # [W/m^2.K^4] - Stefan Boltzmann Constant \n",
      "T=375;                                              #[K] Value initially assumed for trial-error approach\n",
      "#Using Eq 1.3a & 1.7 and trial-and error approach of Newton Raphson \n",
      "#calculations and results\n",
      "while(1>0):\n",
      "    f=((a*G)-(h*(T-Tf)+e*stfncnstt*(T*T*T*T - Tsurr*Tsurr*Tsurr*Tsurr)));\n",
      "    fd=(-h*T-4*e*stfncnstt*T*T*T);\n",
      "    Tn=T-f/fd;\n",
      "    if(((a*G)-(h*(Tn-Tf)+e*stfncnstt*(Tn*Tn*Tn*Tn - Tsurr*Tsurr*Tsurr*Tsurr)))<.01):\n",
      "        break;\n",
      "    T=Tn;\n",
      "\n",
      "print '%s %.2f %s' %(\"\\n (a) Cure Temperature of Plate =\",T-273.,\"degC\\n\");\n",
      "#solution (b)\n",
      "Treq=50+273;\n",
      "#def T(h):\n",
      "#    t=375;\n",
      "#    while(1>0):\n",
      "#        f=((a*G)-(h*(t-Tf)+e*stfncnstt*(t*t*t*t - Tsurr*Tsurr*Tsurr*Tsurr)));\n",
      "#        fd=(-h*t-4*e*stfncnstt*t*t*t);\n",
      "#        Tn=t-f/fd;\n",
      "#        if((a*G)-(h*(Tn-Tf)+e*stfncnstt*(Tn*Tn*Tn*Tn - Tsurr*Tsurr*Tsurr*Tsurr))<.01):\n",
      "#           break;\n",
      "#    tnew=Tn;\n",
      "#    return tnew;\n",
      "\n",
      "\n",
      "def T(h):\n",
      "    global rt\n",
      "    coeff = ([-e*stfncnstt, 0,0, -h, a*G+h*Tf+e*stfncnstt*Tsurr*Tsurr*Tsurr*Tsurr]);\n",
      "    rot=numpy.roots(coeff);\n",
      "    rt=rot[3];\n",
      "    #for i in range (0,3):\n",
      "    #    if 273<rot[i]<523:\n",
      "    #        rt=rot[i];\n",
      "    return rt\n",
      "\n",
      "h = range(0,100)\n",
      "tn=range(0,100)\n",
      "for i in range (0,100):\n",
      "    tn[i] = T(i) -273;\n",
      "\n",
      "Ti=50+273;\n",
      "hnew=((a*G)-(e*stfncnstt*(Ti**4 - Tsurr**4)))/(Ti-Tf);\n",
      "\n",
      "pyplot.plot(h,tn);\n",
      "pyplot.xlabel(\"h (W m^2/K)\");\n",
      "pyplot.ylabel(\"T (C)\");\n",
      "pyplot.show();\n",
      "print '%s %.2f %s' %(\"\\n (b) Air flow must provide a convection of =\",hnew,\" W/m^2.K\");\n",
      "print '%s' %(\"\\n The code for the graph requires more than 10 min to run. \")\n",
      "print '%s' %(\"\\n To run it, please remove comments. It is perfectly correct. The reason it takes such a long time\")\n",
      "print '%s' %(\"\\n  is that it needs to calculate using Newton raphson method at 100 points. Each point itself takes a minute.\")\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "\n",
        " (a) Cure Temperature of Plate = 104.30 degC\n",
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['f', 'e']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEPCAYAAABcA4N7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3886290>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " (b) Air flow must provide a convection of = 51.01  W/m^2.K\n",
        "\n",
        " The code for the graph requires more than 10 min to run. \n",
        "\n",
        " To run it, please remove comments. It is perfectly correct. The reason it takes such a long time\n",
        "\n",
        "  is that it needs to calculate using Newton raphson method at 100 points. Each point itself takes a minute.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}