path: root/Engineering_Heat_Transfer/CHAPTER12.ipynb

{
 "metadata": {
  "name": "CHAPTER12"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 12: Radient Heat Transfer between Surfaces"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.3 Page No 598"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Determination of the heat transferred by radiation from dA1 to A. \n",
      "\n",
      "#Given\n",
      "# The view factor Fd1_2 can be calculated as Fd1_2=Fd1_3+Fd1_4+Fd1_5\n",
      "# For Fd1_3\n",
      "a_13=100.0\n",
      "b_13=250.0\n",
      "c_13=100.0\n",
      "X_13=a_13/c_13\n",
      "Y_13=b_13/c_13\n",
      "Fd1_3=0.17      # value for Fd1_3 corresponding to above calculated values of a/c and b/c\n",
      "# For Fd1_4\n",
      "a_14=300\n",
      "b_14=50\n",
      "c_14=100\n",
      "\n",
      "#Calculation\n",
      "X_14=a_14/c_14\n",
      "Y_14=b_14/c_14\n",
      "Fd1_4=0.11       #value for Fd1_4 corresponding to above calculated values of a/c and b/c\n",
      "# For Fd1_5\n",
      "a_15=100\n",
      "b_15=50\n",
      "c_15=100\n",
      "X_15=a_15/c_15\n",
      "Y_15=b_15/c_15\n",
      "Fd1_5=0.09       #value for Fd1_3 corresponding to above calculated values of a/c and b/c\n",
      "Fd1_2=Fd1_3+Fd1_4-Fd1_5\n",
      "sigma=0.1714e-8  # Stefan-Boltzmann constant\n",
      "T1=660\n",
      "T2=560\n",
      "q12_A1=sigma*Fd1_2*(T1**4-T2**4)\n",
      "\n",
      "#result\n",
      "print\"The net heat transferred is \",round(q12_A1,1),\"BTU/(hr.sq.ft)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The net heat transferred is  29.8 BTU/(hr.sq.ft)\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.4 Page No 601"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Determination of the heat transferred to the conveyed parts for the conditions given\n",
      "\n",
      "#Given\n",
      "import math\n",
      "L1=1\n",
      "angle=math.pi*45/180.0\n",
      "L2=L1*math.sin(angle)\n",
      "L3=L2\n",
      "T1=303\n",
      "T2=473\n",
      "\n",
      "#Calculation\n",
      "sigma=5.67e-8      # Stefan-Boltzmann constant\n",
      "q21_A2=sigma*(T2**4-T1**4)*((L1/L2)+1-(L3/L2))/2.0\n",
      "q31_A3=sigma*(T2**4-T1**4)*((L1/L2)-1+(L3/L2))/2.0\n",
      "\n",
      "#result\n",
      "print\"The heat transferred from A3 to A1 is \",round(q31_A3,0),\" W/sq.m\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat transferred from A3 to A1 is  1669.0  W/sq.m\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.5 Page No 605"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Determination of the heat exchanged between the two plates\n",
      "\n",
      "#Given\n",
      "# The view factor can be found with the crossed-string method\n",
      "# from figure 12.13(b)\n",
      "ac=1\n",
      "bd=1\n",
      "ad=(9+1)**0.5\n",
      "bc=ad\n",
      "\n",
      "#calculation\n",
      "crossed_strings=ad+bc\n",
      "uncrossed_strings=ac+bd\n",
      "L1_F12=(1/2.0)*(crossed_strings-uncrossed_strings)\n",
      "L1=3\n",
      "F12=L1_F12/L1\n",
      "sigma=5.67e-8 # Stefan-Boltzmann constant\n",
      "T1=560\n",
      "T2=460\n",
      "q12_A1=sigma*(T1**4-T2**4)*F12\n",
      "\n",
      "#Result\n",
      "print\"The heat transfer rate is \",round(q12_A1,0),\"W/sq m\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat transfer rate is  2189.0 W/sq m\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.6 Page No 608"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  Determination of the heat that must be supplied to each of the isothermal surfaces, and also the temperature of the insulated surface. \n",
      "\n",
      "#Given\n",
      "# we can apply the equations as follows\n",
      "# q1=sigma*A1*[(T1**4-T2**4)F12+(T1**4-T3**4)F13]..... (1)\n",
      "# q2=sigma*A2*[(T2**4-T1**4)F21+(T2**4-T3**4)F23]..... (2)\n",
      "# q3=sigma*A3*[(T3**4-T1**4)F31+(T3**4-T2**4)F32]..... (3)\n",
      "# given data:\n",
      "T1=1000.0\n",
      "T3=500.0\n",
      "q2=0\n",
      "F12=1/2.0\n",
      "F13=1/2.0\n",
      "F21=1/2.0\n",
      "F23=1/2.0\n",
      "F31=1/2.0\n",
      "F32=1/2.0\n",
      "\n",
      "#Calculation\n",
      "T2=((T1**4+T3**4)/2.0)**(1/4.0) # using equation (2)\n",
      "sigma=0.1714e-8                 # Stefan-Boltzmann constant\n",
      "q1_A1=sigma*((T1**4-T2**4)*F12+(T1**4-T3**4)*F13) # using equation (1)\n",
      "q3_A3=sigma*((T3**4-T1**4)*F31+(T3**4-T2**4)*F32) # using equation (3)\n",
      "\n",
      "#result\n",
      "print\"The temperature is \",round(T2,1),\"R\"\n",
      "print\"The heat flux through area A1 is\",round(q1_A1,0),\"BTU/(hr.sq.ft)\"\n",
      "print\"The heat flux through area A3 is\",round(q3_A3,0),\"BTU/(hr.sq.ft)\"\n",
      "print\"In the book there is calculation mistake\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The temperature is  853.7 R\n",
        "The heat flux through area A1 is 1205.0 BTU/(hr.sq.ft)\n",
        "The heat flux through area A3 is -1205.0 BTU/(hr.sq.ft)\n",
        "In the book there is calculation mistake\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.7 Page No 613"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Determination of the heat lost by the oven through its top surface. \n",
      "\n",
      "#Given\n",
      "# all energy leaving A1 is intercepted by A2 and vice versa\n",
      "F12=1\n",
      "F21=1\n",
      "F11=0             # the surfaces are flat\n",
      "F22=0\n",
      "emissivity1=0.94  # for oxidized steel from appendix table E1\n",
      "emissivity2=0.94\n",
      "T1=533\n",
      "T2=323\n",
      "sigma=5.67e-8      # Stefan-Boltzmann constant\n",
      "\n",
      "#Calculation\n",
      "q1=(sigma*(T1**4-T2**4))/((1/emissivity1)+(1/emissivity2)-1)\n",
      "q2=-q1\n",
      "\n",
      "#Result\n",
      "print\"The heat lost through bottom surface is \",round(q1,1),\"W/sq m\"\n",
      "print\"The heat lost through top surface is \",round(q2,1),\"W/sq m\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat lost through bottom surface is  3510.7 W/sq m\n",
        "The heat lost through top surface is  -3510.7 W/sq m\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 12.8 Page No 616"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Determination of the net heat exchanged between the dish and the surroundings by radiation at the instant the dish is removed from the oven. Perform the calculations (a) if the dish and surroundings behave like black bodies, and again (b) if the dish has an emissivity of 0.82 and the surroundings have an emissivity of 0.93.\n",
      "\n",
      "#Given\n",
      "D=1.0           # diameter in ft\n",
      "L=6/12.0        # length in ft\n",
      "\n",
      "#Calculation\n",
      "A=2*math.pi*D**2/4+math.pi*D*L\n",
      "F12=1           # the view factor between the dish and the surroundings is unity\n",
      "T1=810\n",
      "T2=530\n",
      "sigma=0.1714e-8 # Stefan-Boltzmann constant\n",
      "q1=sigma*A*(T1**4-T2**4)*F12\n",
      "\n",
      "# For gray-surface behavior, we can apply the following Equation\n",
      "# q1/(A1e1)-[F11*(q1/A1)*(1-e1)/e1+F12*(q2/A2)*(1-e2)/e2]=sigma*T1**4-(F11*sigma*T1**4+F12*sigma*T2**4)... equation (1)\n",
      "F11=0\n",
      "e1=0.82\n",
      "e2=0.93\n",
      "# putting q2/A2=0 in equation (1) as A2 tends to infinity\n",
      "q1_=A*e1*(sigma*T1**4-F12*sigma*T2**4)\n",
      "\n",
      "#Result\n",
      "print\"(a)The heat exchanged between the dish and the surroundings is\",round(q1,0),\"BTU/hr\"\n",
      "print\"(b)The heat exchanged between the dish and the surroundings for the second case is \",round(q1_,0),\"BTU/hr\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)The heat exchanged between the dish and the surroundings is 1893.0 BTU/hr\n",
        "(b)The heat exchanged between the dish and the surroundings for the second case is  1552.0 BTU/hr\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}