path: root/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_1.ipynb

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  {
   "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",
      "%matplotlib 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": 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xxx83UlNTDcMw/HZfjB071lixYoVhGIZx5coV4+zZs365L3Jzc42uXbsaly5d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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": {}
  }
 ]
}