{
 "metadata": {
  "name": "CHAPTER 3"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 3:Steady-State Conduction in Multiple Dimensions"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.1 Page No.132"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "OD=0.02858              # outer diameter in m\n",
      "M=8.0                     # total number of heat-flow lanes\n",
      "N=6.0                     # number of squares per lane\n",
      "S_L=M/N                   # conduction shape factor\n",
      "k=0.128          # thermal conductivity in W/(m.K) for concrete from appendix table B3\n",
      "T1=85            # temperature of tube surface\n",
      "T2=0             # temperature of ground beneath the slab\n",
      "\n",
      "q_half=k*S_L*(T1-T2)\n",
      "q=2*q_half\n",
      "\n",
      "print\"The total heat flow per tube is\",round(q,0),\" W/m\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The total heat flow per tube is 29.0  W/m\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.2 Page No.134"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "OD=10.74/12 # diameter in ft\n",
      "R=OD/2\n",
      "T1=140.0\n",
      "T2=65.0\n",
      "k=0.072 # thermal conductivity in BTU/(hr-ft. degree R)\n",
      "d=18.0/12.0 # distance from centre-line\n",
      "S_L=(2*math.pi)/(math.acosh(d/R))\n",
      "q_L=k*S_L*(T1-T2)\n",
      "print\"The heat transferred from the buried pipe per unit length is \",round(q_L,2),\"BTU/(hr.ft)\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat transferred from the buried pipe per unit length is  18.05 BTU/(hr.ft)\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.3 Page No.135"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "k = 1.07           # thermal conductivity of silica brick from appendix table B3 in W/(m.K)\n",
      "S1_A=0.138*0.138/0.006\n",
      "nA=2\n",
      "\n",
      "St_A=nA*S1_A      # Total shape factor of component A\n",
      "\n",
      "S1_B=0.138*0.188/0.006\n",
      "nB=4\n",
      "St_B=nB*S1_B # Total shape factor of component B\n",
      "\n",
      "S3_C=0.15*0.006\n",
      "nC=8\n",
      "St_C=nC*S3_C # Total shape factor of component C\n",
      "\n",
      "S2_D=0.54*0.188\n",
      "nD=4\n",
      "St_D=nD*S2_D # Total shape factor of component D\n",
      "\n",
      "S2_E=0.138*0.54\n",
      "nE=8\n",
      "St_E=nE*S2_E # Total shape factor of component E\n",
      "\n",
      "S=St_A+St_B+St_C+St_D+St_E\n",
      "T1=550\n",
      "T2=30\n",
      "q=k*S*(T1-T2)\n",
      "S=St_A+St_B\n",
      "q_1=k*S*(T1-T2)\n",
      "Error=(q-q_1)/q\n",
      "\n",
      "print\"(a)The heat transferred through the walls of the furnace is \",round(q/1000,1),\"kw\"\n",
      "print\"(b The heat transferred is\",q_1/1000,1,\"kw\"\n",
      "print\"  The error introduced by neglecting heat flow through the edges and corners is \",round(Error*100,1),\" percent\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)The heat transferred through the walls of the furnace is  13.7 kw\n",
        "(b The heat transferred is 13.1555216 1 kw\n",
        "  The error introduced by neglecting heat flow through the edges and corners is  4.1  percent\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.4 Page No. 142"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "OD=4.5/12.0          # diameter in ft\n",
      "R=OD/2.0\n",
      "\n",
      "import math\n",
      "L_A=4.5           # length in ft\n",
      "S_A=(2*math.pi*L_A)/(math.log(2*(L_A)/R))\n",
      "L_B=18 # length in ft\n",
      "S_B=(2*math.pi*L_B)/(math.acosh(L_A/R))\n",
      "S=2*S_A+S_B\n",
      "\n",
      "print\"The total conduction shape factor for the system is\",round(S,1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The total conduction shape factor for the system is 43.8\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 3.5 Page No. 151"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "h=1.1           # convective coefficient in BTU/(hr.ft^2. degree R)\n",
      "Tw=200.0\n",
      "T_inf=68.0      # ambient temperature\n",
      "k=0.47          # thermal conductivity in BTU/(hr.ft.degree R) from table B3\n",
      "D=0.25/12       # diameter in ft\n",
      "\n",
      "A=math.pi*D**(2)/4.0     # cross sectional area in ft^2\n",
      "P=math.pi*D         # perimeter in ft\n",
      "L=6/12.0 # length in ft\n",
      "mL=L*((h*P)/(k*A))**(0.5)\n",
      "dz=1.0\n",
      "L=4.0\n",
      "de=dz/L\n",
      "K=2+(mL*de)**2\n",
      "\n",
      "T4=T_inf+(Tw-T_inf)*(2/(K**4-4*K**2+2))\n",
      "T3=T_inf+(Tw-T_inf)*(K/(K**4-4*K**2+2))\n",
      "T2=T_inf+(Tw-T_inf)*((K**2-1)/(K**4-4*K**2+2))\n",
      "T1=T_inf+(Tw-T_inf)*((K**3-3*K)/(K**4-4*K**2+2))\n",
      "\n",
      "print\"The temprature distribution is T4=\",round(T4,2),\"F\"\n",
      "print\"The temprature distribution is T3=\",round(T3,2),\"F\"\n",
      "print\"The temprature distribution is T2=\",round(T2,2),\"F\"\n",
      "print\"The temprature distribution is T1=\",round(T1,2),\"F\"\n",
      "\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "T=[200.0,77.33,68.66,68.05,68]\n",
      "z=[0,1.5,3,4.5,6]\n",
      "xlim(0,6)\n",
      "ylim(50,200)\n",
      "plt.ylabel('T (C)')\n",
      "plt.xlabel('z (in)')\n",
      "plt.annotate('Numeric approximation using 4 nodes', xy=(2,82), xytext=(0,30),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.05),\n",
      "            )\n",
      "a=plot(z,T)\n",
      "\n",
      "T1=[200.0,82.81,69.66,68.19,68.04]\n",
      "plt.ylabel('T1 (F)')\n",
      "plt.xlabel('z (in)')\n",
      "plt.annotate('exact solution', xy=(1.5,80), xytext=(0,60),\n",
      "            arrowprops=dict(facecolor='black', shrink=0.05),\n",
      "            )\n",
      "a=plot(z,T1)\n",
      "show(a)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The temprature distribution is T4= 68.04 F\n",
        "The temprature distribution is T3= 68.19 F\n",
        "The temprature distribution is T2= 69.68 F\n",
        "The temprature distribution is T1= 82.82 F\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nhs/kvd3vUVhcqG4wIUSVJQWhGps6FebPB0WBDm4daOnUkpijMWrHEkJUUVIQ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\nGjVqZNhneno6s2bNMqzj4ODA66+/TlB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       "text": [
        "<matplotlib.figure.Figure at 0x752b7f0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}