path: root/TRANSPORT_PROCESSES_AND_UNIT_OPERATIONS/GeankoplisChapter04.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 4: Principles of Steady-State Heat Transfer"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.1-1, Page number 217"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Loss Through Insulating Wall\n",
      "\n",
      "#Variable declaration\n",
      "L = 0.0254        #Thickness of fibre insulating board\n",
      "T1 = 352.7        #Temperature of hot face, \u00b0C\n",
      "T2 = 297.1        #Temperature of cold face, \u00b0C\n",
      "A = 1.0           #Suface area, m2\n",
      "k = 0.048         #Thermal conductivity of fibre insulating board, W/(m.K)\n",
      "\n",
      "#Calculation\n",
      "q = k*(T1-T2)/L\n",
      "\n",
      "#Result\n",
      "print \"Heat loss per unit area:\", round(q,1), \"W/m2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat loss per unit area: 105.1 W/m2\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.2-1, Page number 222"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Length of tubing for Cooling Coil\n",
      "from math import log, pi\n",
      "\n",
      "#Variable declaration \n",
      "ri = 0.005       #Inside radius of tubing\n",
      "ro = 0.02        #Outside radius of tubing\n",
      "k = 0.151        #Thrmal conductivity of rubber tubing, W/mK\n",
      "Ti = 274.9       #Inside wall temaperature, K\n",
      "To = 297.1       #Outside wall temaperature, K\n",
      "Q = 14.65        #Total heat tranfer rate, W\n",
      "\n",
      "#Calculation\n",
      "Ai = 2*pi*ri*1.0\n",
      "Ao = 2*pi*ro*1.0\n",
      "Alm = (Ai-Ao)/(log(Ai/Ao))\n",
      "Q1 = k*Alm*(To-Ti)/(ro-ri)\n",
      "L = Q/Q1\n",
      "\n",
      "#Result\n",
      "print \"Length of tubing required \",round(L,3) , \"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Length of tubing required  0.964 m\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3-1, Page number 223"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Flow Through an Insulated Wall of a Cold Sorage\n",
      "\n",
      "#Variable declaration\n",
      "L1 = 0.0127      #Thickness of inner wall, m\n",
      "L2 = 0.1016      #Thickness of middle wall, m\n",
      "L3 = 0.0762      #Thickness of outer wall, m\n",
      "k1 = 0.151       #Thermal conductivity of inner wall, W/mK\n",
      "k2 = 0.0433      #Thermal conductivity of middle wall, W/mK\n",
      "k3 = 0.768       #Thermal conductivity of outer wall, W/mK\n",
      "A = 1.0          #Heat Area area, m2\n",
      "Ti = 255.4       #Inner wall surface temperature, K\n",
      "To = 297.1       #outer wall surface temperature, k\n",
      "\n",
      "#Calculation\n",
      "R1 = L1/(k1*A)   # Resistance of the inner wall, K/W\n",
      "R2 = L2/(k2*A)   # Resistance of the middle wall, K/W\n",
      "R3 = L3/(k3*A)   # Resistance of the outer wall, K/W\n",
      "Rt = R1 + R2 + R3 \n",
      "q = (Ti-To)/Rt\n",
      "T2 = Ti - q*R1\n",
      "\n",
      "#Result\n",
      "print 'Resistance offered by 1st wall %5.4f K/W'%(R1)\n",
      "print 'Resistance offered by 2nd wall %5.4f K/W'%(R2)\n",
      "print 'Resistance offered by 3rd wall %5.4f K/W'%(R3)\n",
      "print 'Total Resistance of composite wall %5.4f K/W'%(Rt)\n",
      "print \"Heat loss\",round(q,2),'W/m2'\n",
      "print \"Temperature at interface between pine wood and cork\",round(T2,2), \"K\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Resistance offered by 1st wall 0.0841 K/W\n",
        "Resistance offered by 2nd wall 2.3464 K/W\n",
        "Resistance offered by 3rd wall 0.0992 K/W\n",
        "Total Resistance of composite wall 2.5297 K/W\n",
        "Heat loss -16.48 W/m2\n",
        "Temperature at interface between pine wood and cork 256.79 K\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3-2, Page number 225"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Loss from an Insulated pipe\n",
      "from math import log, pi\n",
      "\n",
      "#Variable declaration\n",
      "ks = 21.63                 #Heat transfer coefficient of the pipe (W/K.m)\n",
      "ki = 0.2423                #Heat transfer coefficient of the insulation  (W/K.m)\n",
      "d1 = 0.0254                #Inner diameter of the pipe (m)\n",
      "d2 = 0.0508                #Inner diameter of the insulation (m)\n",
      "thks = 0.0254              \n",
      "T1 = 811                   #The wall temperature of the pipe (K)\n",
      "T3 = 310.8                 #The temperature of the outside wall of the insulation (k)\n",
      "L = .305                   #Length of the pipe (m)\n",
      "\n",
      "#Calculation\n",
      "r1 =d1/2.\n",
      "r2 = d2/2.\n",
      "r3 = r2 + thks\n",
      "A1 = 2*pi*r1*L\n",
      "A2 = 2*pi*r2*L\n",
      "A3 = 2*pi*r3*L\n",
      "A12lm = (A1-A2)/log(A1/A2)\n",
      "A23lm = (A2-A3)/log(A2/A3)\n",
      "R12 = (r2-r1)/(ks*A12lm)\n",
      "R23 = (r3-r2)/(ki*A23lm)\n",
      "Q = (T1-T3)/(R12+R23)\n",
      "T2 = T1 - Q*R12\n",
      "\n",
      "#Results\n",
      "print \"Temperature of Interface\", round(T2,1) ,\"K\"\n",
      "print \"Heat loss\", round(Q,1) ,\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temperature of Interface 805.5 K\n",
        "Heat loss 331.4 W\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3-3, Page number 228"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Loss by Convection and Conduction and Overall U\n",
      "from math import log, pi\n",
      "\n",
      "#Variable declaration\n",
      "di = 0.824                  #Inner diameter of the pipe (m)\n",
      "do = 1.05                   #Outer diameter of the pipe (m)\n",
      "thki = 1.5\n",
      "hi = 1000                   #Convective heat transfer coefficient (btu/h.ft2)\n",
      "ho = 2.                     #Convective heat transfer coefficient on the outside (btu/h.ft2) \n",
      "km = 26.                    #Mean thermal cunductivity of metal (btu/h.ft)\n",
      "ki = 0.037                  #Mean thermal cunductivity of insulation (btu/h.ft)\n",
      "Ts = 267                    #Surface temperature of the pipe (F)\n",
      "Ta = 80                     #Surrounding air temperature (F)\n",
      "L = 1.            \n",
      "\n",
      "#Calculation\n",
      "ri = di/(12.*2.)\n",
      "r1 = do/(12.*2.)\n",
      "ro = r1 + thki/12.\n",
      "Ai = 2*pi*ri*L\n",
      "A1 = 2*pi*r1*L\n",
      "Ao = 2*pi*ro*L\n",
      "Ai1lm = (Ai-A1)/log(Ai/A1)\n",
      "A1olm = (A1-Ao)/log(A1/Ao)\n",
      "Ri1 = (r1-ri)/(km*Ai1lm)\n",
      "R1o = (ro-r1)/(ki*A1olm)\n",
      "Ri = 1./(hi*Ai)\n",
      "Ro = 1./(ho*Ao)\n",
      "Rt = Ri+Ri1+R1o+Ro\n",
      "Q = (Ts-Ta)/(Rt)\n",
      "Ui = 1./(Ai*Rt)\n",
      "Q1 = Ui*Ai*(Ts-Ta)\n",
      "\n",
      "#Result\n",
      "print \"Heat lost to the surrounding using resistance\",round(Q,1), \"Btu/hr\"\n",
      "print \"Heat lost to the surrounding using Overall Heat TRansfer Coeff\",round(Q1,1), \"Btu/hr\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat lost to the surrounding using resistance 29.8 Btu/hr\n",
        "Heat lost to the surrounding using Overall Heat TRansfer Coeff 29.8 Btu/hr\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3-4, Page number 231"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Generation in a cylinder\n",
      "from math import pi\n",
      "#Variable declaration\n",
      "i = 200.           #Current through the wire, A\n",
      "r = 0.001268       #radius of the wire, m\n",
      "L = 0.91           #Length of wire, m\n",
      "R = 0.126          #Resistance of stainless steel, ohm\n",
      "Tw = 422.1         #Wall temperature of the wire, K\n",
      "k = 22.5           #Thermal conductivity of steel, W/mK \n",
      "\n",
      "#Calculation\n",
      "Q = i**2*R\n",
      "qdot = Q/(pi*r**2*L)\n",
      "To = Tw + qdot*r**2/(4*k)\n",
      "\n",
      "#Result\n",
      "print \"Temperature at the centre of the wire\",round(To,1),\"K\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temperature at the centre of the wire 441.7 K\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.3-5, Page number 232"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Insulating an Electrical Wire and Critical Radius\n",
      "from math import log, pi\n",
      "\n",
      "#Variable declaration\n",
      "d = 1.5         #Diameter of electrical wire, mm\n",
      "thki = 2.5      #Thickness of insulation, mm\n",
      "Ta = 300.       #Temrature of air, K\n",
      "ho = 20.        #Outside Heat transfer coefficient, W/m2.K\n",
      "ki = 0.4        #Thermal conductivity of insulation, W/mK\n",
      "Tw = 400.       #Surface temperature of the wire, K\n",
      "L = 1.          #Length of wire, m\n",
      "#Calculation\n",
      "r1 = d*1e-3/2.\n",
      "r2 = r1+thki*1e-3\n",
      "r2c = ki/ho\n",
      "A1 = 2*pi*r1*L\n",
      "Q = ho*A1*(Tw-Ta)\n",
      "\n",
      "Qi = 2*pi*L*(Tw-Ta)/(log(r2/r1)/ki + 1./(ho*r2))\n",
      "#Result\n",
      "print \"(a) Critical radius of insulation\",round(r2c*1e3,1),\"mm\"\n",
      "print \"(b) Heat Transfer rate without insulation\",round(Q,2),\"W/m\"\n",
      "print \"(c) Heat Transfer rate with insulation\",round(Qi,2),\"W/m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Critical radius of insulation 20.0 mm\n",
        "(b) Heat Transfer rate without insulation 9.42 W/m\n",
        "(c) Heat Transfer rate with insulation 32.98 W/m\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.4-1, Page number 235"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Two dimenssional conduction by Graphical Proceedure \n",
      "\n",
      "#Variable declaration\n",
      "T1 = 600.       #Inside temperature, K\n",
      "T2 = 400.       #Outside temperature, K\n",
      "k = 0.9         #Thermal conductivity, W/mK\n",
      "L = 5.          #Length of flue, m\n",
      "N = 4           #Number of temperature subdivisions\n",
      "M = 9.25        #\n",
      "#Calculation\n",
      "\n",
      "Q = 4*(M*k*L*(T1-T2)/4.)\n",
      "\n",
      "#Result\n",
      "print \"Heat Transfer Rate :\",round(Q), \"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat Transfer Rate : 8325.0 W\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5-1, Page number 240"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heating of Air in Turbulent Flow\n",
      "\n",
      "#Variable declaration\n",
      "Tc = 477.6       #Average temperature of air, K\n",
      "v = 7.62         #Velocity of air, m/s\n",
      "di = 0.0254      #inner diameter, m \n",
      "Ts = 488.7       #Steam temperature, K\n",
      "muab = 2.6e-5    #Viscosity of air, Pa.s\n",
      "ka = 0.03894     #Thermal conductivity of air, W/mK\n",
      "Npr = 0.686\n",
      "muw = 2.64e-5    #Viscosity of air at wall temperature, Pa.s\n",
      "P = 206.8        #Pressure, kPa  \n",
      "\n",
      "#Calculation\n",
      "\n",
      "rhoa =28.97*(1./22.414)*(P/101.325)*273.2/Tc\n",
      "Nre = di*v*rhoa/muab\n",
      "Nnu = 0.027*Nre**0.8*Npr**(1./3)*(muab/muw)**0.14\n",
      "hL = Nnu*ka/di\n",
      "q = hL*(Ts-Tc)\n",
      "\n",
      "#Result\n",
      "print \"Average Heat Transfer Coefficient for L/D > 60\", round(hL,2), \"W/m2.K\"\n",
      "print \"Heat Flux\", round(q,2), \"W/m2\"\n",
      "print 'The answers different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Average Heat Transfer Coefficient for L/D > 60 63.36 W/m2.K\n",
        "Heat Flux 703.33 W/m2\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5-2, Page number 241"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Water Heated by Steam, Trial and Error Solution\n",
      "from math import pi\n",
      "\n",
      "#Variable declaration\n",
      "di = 0.0266              #Inner diameter of the pipe (m)\n",
      "do = 0.0334              #Outer diameter of the pipe (m)\n",
      "L = 0.305                #Lenth of pipe, m\n",
      "T = 65.6                 #Average temperature of the steel pipe (deg C)\n",
      "v = 2.44                 #Velocity of the water flow (m/s)\n",
      "Ts = 107.8               #Temperature of the steam (deg C)\n",
      "ho = 10500.              #Heat transfer coefficient on the steam side (W/m2.K)\n",
      "# Properties of water at T=65.6\u00b0C\n",
      "Npr = 2.72               #Prandtl number\n",
      "rho = 980.               #Density of water (kg/m3)\n",
      "kw = 0.663               #Thermal conductivity of Water (W/m.K)\n",
      "mu = 4.32e-4             #Viscosity of water (Pa.s)\n",
      "k = 45.                  #Thermal conductivity of metal wall (W/m.K)\n",
      "# Properties of water at T=80\u00b0C\n",
      "muw = 3.56e-4\n",
      "\n",
      "#Calculation\n",
      "#Part A\n",
      "Nre = di*v*rho/mu\n",
      "Nnu = 0.027*(Nre**0.8)*(Npr**(1./3))*(mu/muw)**0.14\n",
      "hi = Nnu*kw/di\n",
      "\n",
      "#Part B\n",
      "Ai = pi*di*L\n",
      "Ao = pi*do*L\n",
      "Am = pi*L*(do+di)/2\n",
      "Ri = 1./(hi*Ai)\n",
      "Ro = 1./(ho*Ao)\n",
      "Rm = (do-di)/(2*k*Am)\n",
      "SR = Ri+Ro+Rm\n",
      "DelT = (Ts-T)\n",
      "DelTw = Ri*DelT/SR\n",
      "Tw = T + DelTw\n",
      "\n",
      "Ui = 1.0/(Ai*SR)\n",
      "Q = Ui*Ai*DelT\n",
      "#Result\n",
      "print \"Inside Heat Transfer Coefficient:\", round(hi), \"W/m2.K\"\n",
      "print \"The assumed temperature of water 80\u00b0C is comparable with Calculated\", round(Tw,2)\n",
      "print \"Heat Transfer Rate\", round(Q),\"W\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Inside Heat Transfer Coefficient: 13153.0 W/m2.K\n",
        "The assumed temperature of water 80\u00b0C is comparable with Calculated 80.26\n",
        "Heat Transfer Rate 4914.0 W\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5-3, Page number 243"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Liquid-Metal Heat Transfer Inside a Tube\n",
      "from math import pi\n",
      "\n",
      "#Variable declaration\n",
      "mdot = 4.                    #Flowrate of liquid metal (kg/s)\n",
      "di = 0.05                    #Inner diameter of pipe (m)\n",
      "Ti = 500.                    #Initial temperature of liquid entering (K)\n",
      "To = 505.                    #Final temperature of liquid leaving (K)\n",
      "mu = 7.1e-4                  #Viscosity of the liquid (Pa.s) \n",
      "rho = 7400.                  #Density of the liquid (kg/m3)\n",
      "cp = 120.                    #Specific heat (J/kg.K)\n",
      "k = 13.                      #Heat transfer coefficient (W/m.K)\n",
      "delT = 30.\n",
      "\n",
      "#Calculation\n",
      "Ac = pi*di**2/4.\n",
      "G = mdot/Ac\n",
      "Nre = di*G/mu\n",
      "Npr = cp*mu/k\n",
      "Npe = Nre*Npr\n",
      "Nnu = 0.625*Npe**0.4\n",
      "hL = Nnu*k/di\n",
      "Q = mdot*cp*(To-Ti)\n",
      "As = Q/(hL*delT) \n",
      "L = As/(pi*di)\n",
      "\n",
      "#Result\n",
      "print \"Heat Transfer coefficient\",round(hL,2),\"W/m2.K\"\n",
      "print \"The Length of the tube required\",round(L,3),\"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat Transfer coefficient 2512.75 W/m2.K\n",
        "The Length of the tube required 0.203 m\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5-4, Page number 245"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Transfer Area and Log Mean Temperature Difference\n",
      "from math import log\n",
      "#Variable declaration  \n",
      "cpm = 2300.                #Specific heat of the hydrocarbon oil (J/kg.K)\n",
      "Ti = 371.9                 #Initial temperature of the oil (K)\n",
      "To = 349.7                 #Final temperature of the oil (K)\n",
      "mdotoil = 3630.            #Flowrate of oil (kg/h)\n",
      "mdotw = 1450.              #Flowrate of water (kg/h)\n",
      "cpw = 4187.                #Specific heat of water (J/kg.K)\n",
      "Twi = 288.6                #Temperature of the inlet water (K)\n",
      "Ui = 340.                  #Overall heat tranfer coefficient (W/m2.K)\n",
      "\n",
      "#Calculations \n",
      "Q = mdotoil*cpm*(Ti-To)/3600\n",
      "Two = Twi + Q/((mdotw/3600)*cpw)\n",
      "    #Contercurrent\n",
      "delT1 = To - Twi\n",
      "delT2 = Ti - Two\n",
      "deltLM = (delT1-delT2)/log(delT1/delT2)\n",
      "Ai = Q/(Ui*deltLM)\n",
      "#Result\n",
      "print \"Heat lost by oil\",round(Q,1),\"W\"\n",
      "print \"Outlet Temperature of cooling water\",round(Two,1),\"K\"\n",
      "print \"Area required for cooling in Countercurrent flow:\",round(Ai,2),\"m2\"\n",
      "\n",
      "    #Co-current/Parallel flow\n",
      "delT1 = Ti - Twi\n",
      "delT2 = To - Two\n",
      "deltLM = (delT1-delT2)/log(delT1/delT2)\n",
      "Ai = Q/(Ui*deltLM)\n",
      "\n",
      "#Result\n",
      "print \"Area required for cooling in Co-current/Parallel flow:\",round(Ai,2),\"m2\"\n",
      "print 'The answers different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat lost by oil 51485.5 W\n",
        "Outlet Temperature of cooling water 319.1 K\n",
        "Area required for cooling in Countercurrent flow: 2.66 m2\n",
        "Area required for cooling in Co-current/Parallel flow: 2.88 m2\n",
        "The answers different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.5-5, Page number 246"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Laminar Heat Transfer and Trial and Error\n",
      "from scipy import interpolate\n",
      "from math import pi\n",
      "\n",
      "#Variable declaration SI Units \n",
      "Ti = 150.                     #Initial temperature of the hydrocarbon oil (F) \n",
      "di = 0.0303                   #Inside diameter of the pipe (ft)\n",
      "L = 15.                       #Length of the tube (ft)\n",
      "mdot = 80.                    #Flowrate of the oil (lbm/h)\n",
      "Tw = 350.                     #Inside wall temperature of the wall (F)\n",
      "Cp = 0.5                      #Specific heat of oil (btu/lbm)\n",
      "km = 0.083                    #Thermal conductivity, Btu/(h.ft.\u00b0F) \n",
      "T=[150,200,250,300,350]       #Temperature of hydrocarbon oil, \u00b0F\n",
      "mu=[6.5,5.05,3.8,2.82,1.95]   #Viscosity of hydrocarbon oil, \u00b0F\n",
      "cf = 2.4191                   #Specific Heat of hydrocarbon oil, \u00b0F\n",
      "\n",
      "#Calculations \n",
      "f = interpolate.interp1d(T,mu)\n",
      "muw = cf*f(Tw)\n",
      "Ac = pi*di**2/4.\n",
      "G = mdot/Ac\n",
      "Toass = 250.\n",
      "xx = 1.2\n",
      "#Calculation\n",
      "while(xx > 0.0001):\n",
      "    Tb = int((Ti+Toass)/2.)\n",
      "    mub = cf*f(Tb)\n",
      "    Nre = di*G/mub\n",
      "    Npr = Cp*mub/km\n",
      "    Nnu = 1.86*(Nre*Npr*di/L)**(1./3)*(mub/muw)**0.14\n",
      "    h = Nnu*km/di\n",
      "    tau = h*pi*di*L/(mdot*Cp)\n",
      "    tau2 = tau/(1+tau/2.)\n",
      "    To =  (tau*(Tw-Ti/2.)+Ti)/(1+tau/2.)\n",
      "    xx = abs((Toass - To)/Toass)\n",
      "    Toass = To\n",
      "\n",
      "#Result\n",
      "print \"The outlet temperature of the oil\",round(Toass,0),\"\u00b0F\"\n",
      "print \"The heat transfer coefficient calculated is\",round(h,2),\"Btu/(hr.ft2)\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The outlet temperature of the oil 255.0 \u00b0F\n",
        "The heat transfer coefficient calculated is 20.03 Btu/(hr.ft2)\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.6-1, Page number 248"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Cooling of Cooper Fin\n",
      "\n",
      "#Variable declaration\n",
      "l = 0.051       #length of square fin, m\n",
      "T = 82.2        #Temperature of fin, \u00b0C\n",
      "Ta = 15.6       #Temperature of air, \u00b0C\n",
      "P = 1.          #Absolute Pressure of air, atm\n",
      "v = 12.2        #Velocity of air, m/s\n",
      "k = 0.028       #Thermal conductivity of air at 48.9\u00b0C, W/(m.K)\n",
      "rho = 1.097     #Density of air at 48.9\u00b0C, kg/m3\n",
      "mu = 1.95e-5    #viscosity of air at 48.9\u00b0C, W/(m.K)\n",
      "Npr = 0.704     #Prandtl numbe for air at 48.9\u00b0C, W/(m.K)\n",
      "\n",
      "#Calculation\n",
      "Tf = (T+Ta)/2.\n",
      "Nre = l*v*rho/mu\n",
      "Nnu = 0.664*Nre**0.5*Npr**(1./3.)\n",
      "ha = Nnu*k/l\n",
      "\n",
      "Nnu = 0.0366*Nre**0.8*Npr**(1./3.)\n",
      "hb = Nnu*k/l\n",
      "#Result\n",
      "print \" A)  Heat Transfer Coeficient for Laminar Flow\", round(ha,1),\"W/(m2.K)\"\n",
      "print \" B)  Heat Transfer Coeficient for Turbulent Conditions\", round(hb,1),\"W/(m2.K)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " A)  Heat Transfer Coeficient for Laminar Flow 60.7 W/(m2.K)\n",
        " B)  Heat Transfer Coeficient for Turbulent Conditions 77.2 W/(m2.K)\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.6-2, Page number 249"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Cooling of Sphere\n",
      "\n",
      "#Variable declaration\n",
      "d = 0.051       #Diameter of sphere, m\n",
      "T = 82.2        #Temperature of fin, \u00b0C\n",
      "Ta = 15.6       #Temperature of air, \u00b0C\n",
      "P = 1.          #Absolute Pressure of air, atm\n",
      "v = 12.2        #Velocity of air, m/s\n",
      "k = 0.028       #Thermal conductivity of air at 48.9\u00b0C, W/(m.K)\n",
      "rho = 1.097     #Density of air at 48.9\u00b0C, kg/m3\n",
      "mu = 1.95e-5    #viscosity of air at 48.9\u00b0C, W/(m.K)\n",
      "Npr = 0.704     #Prandtl numbee for air at 48.9\u00b0C, W/(m.K)\n",
      "hflat = 77.2    #Film coeff for heat transfer from flat plate, W/(m2.K)\n",
      "\n",
      "#Calculation\n",
      "Tf = (T+Ta)/2.\n",
      "Nre = d*v*rho/mu\n",
      "Nnu = 2.+ 0.6*Nre**0.5*Npr**(1./3.)\n",
      "h = Nnu*k/d\n",
      "#Result\n",
      "print \"Reynolds number\", round(Nre)\n",
      "print \"Heat transfer coeffiecient\", round(h,1), \"W/(m2.K) is less than Heat Transfer coeff for flat plate in prevoius problem\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reynolds number 35003.0\n",
        "Heat transfer coeffiecient 55.9 W/(m2.K) is less than Heat Transfer coeff for flat plate in prevoius problem\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.6-3, Page number 250"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heating of air by a bank of tubes\n",
      "from math import pi\n",
      "\n",
      "#Variable declaration\n",
      "do = 0.0254     #Outside Diameter of tube,m\n",
      "L  = 0.305      #Length of tube bank,m \n",
      "Sn = 0.0381     #Normal Tube spacing, m\n",
      "Sp = 0.0381     #Parallel tube spacing,m\n",
      "Nt = 40         #Number of tubes in bank\n",
      "Tw = 57.2       #Surface temperature of tubes, \u00b0C\n",
      "Ti = 15.6       #Air inlet temperature, \u00b0C\n",
      "To = 21.1       #Assumed oultet temperature of air, \u00b0C\n",
      "P  = 1.         #Air Pressure, atm abs \n",
      "v  = 7.62       #Velocity of air, m/s\n",
      "rho = 1.137     #Density of air, kg/m3\n",
      "mu  = 1.9e-5    #Viscosity of air, Pa.s\n",
      "Cp = 1004.8     #Specific heat of air, kJ/(kg.K)\n",
      "Npr = 0.705     #Prandtl number of air\n",
      "k =  0.027      #Thermal conductivity of air,W/(m.K)\n",
      "rho156 = 1.2224 #Density of air at 15.6\u00b0C, kg/m3\n",
      "#Calculation\n",
      "snd = Sn/do\n",
      "spd = Sp/do\n",
      "#From table 4.6-2 \n",
      "C, m = 0.278, 0.620\n",
      "er = 1.0\n",
      "while er >= 0.2:\n",
      "    Tb = (Ti+To)/2.\n",
      "    Tf = (Tw+Tb)/2.\n",
      "    vmax = v*Sn/(Sn-do)\n",
      "    Nre = do*vmax*rho/mu\n",
      "    Nnu = C*Nre**m*Npr**(1./3.)\n",
      "    h = Nnu*k/do\n",
      "    #Correction factor for heat transfer coefficient from table4.3-3 for four transverse tubes\n",
      "    #is 0.9 \n",
      "    hc = 0.9*h\n",
      "    A =Nt*pi*do*L\n",
      "    Q = hc*A*(Tw-Tb)\n",
      "    Af = 10*Sn*L               #Frontal Area\n",
      "    m = Af*v*rho156\n",
      "    delT = Q/(m*Cp)\n",
      "    Tout = Ti + delT\n",
      "    er = abs(To-Tout)\n",
      "    To = (To+Tout)/2\n",
      "    \n",
      "#Result\n",
      "print \"Total Heat transfer Rate\", round(Q),\"W\"\n",
      "print 'The calculated outlet bulk gas temperature is %4.2f \u00b0C'%To\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total Heat transfer Rate 5852.0 W\n",
        "The calculated outlet bulk gas temperature is 21.04 \u00b0C\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.7-1 Page Number 254"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Natural Convection from Vertical Wall of an Oven\n",
      "\n",
      "#Variable Declaration\n",
      "H = 1.                        #Height of the wall (ft)\n",
      "Tw = 450                      #Temperature of the wall (deg F)\n",
      "Tb = 100.                     #Temperature of the wall in contact (F)\n",
      "L = 1.                        #Length of the wall (m)\n",
      "k = 0.0198                    #Heat transfer cofficient of the wall (btu/h.ft.F)\n",
      "rho = 0.0541                  #Density of air (lbm/ft3)\n",
      "Pr = 0.69                     #Prandtl number\n",
      "mu = 0.0562                   #Viscosity of air (cp)\n",
      "g = 32.174                    #Graitational accleration (ft/s2)\n",
      "\n",
      "#Calculations\n",
      "    #English Units\n",
      "Tf = (Tw+Tb)/2.\n",
      "beta = 1./(460.+Tf)\n",
      "delT = Tw - Tb\n",
      "Gr = L**3*rho**2*g*beta*3600**2*delT/(mu**2)\n",
      "a = 0.59\n",
      "m = 1./4.\n",
      "Nu = a*(Gr*Pr)**m\n",
      "h = k*Nu/L\n",
      "A = L*H\n",
      "Q = h*A*delT\n",
      "\n",
      "#Results\n",
      "print \"In English Units\"\n",
      "print \"The heat transfer cofficient is \",round(h,2),\"btu/h.ft2.F\"\n",
      "print \"The heat transfer rate across the wall is \",round(Q),\"btu/h\"\n",
      "\n",
      "    #SI Units\n",
      "H = 0.305                     #Height of the wall (m)\n",
      "Tw = 505.4                    #Temperature of the wall (K)\n",
      "Tb = 311.0                    #Temperature of the wall in contact (K)\n",
      "L = 0.305                     #Length of the wall (m)\n",
      "k = 0.0343                    #Thermal  conductivity of the wall (W/(m.K)\n",
      "rho = 0.867                   #Density of air (kg/m3)\n",
      "Pr = 0.69                     #Prandtl number\n",
      "mu = 2.32e-5                  #Viscosity of air (cp)\n",
      "g = 9.806                     #Graitational accleration (m/s2)\n",
      "\n",
      "#Calculations\n",
      "Tf = (Tw + Tb)/2\n",
      "beta = 1./Tf\n",
      "delT = Tw - Tb\n",
      "Gr = L**3*rho**2*g*beta*delT/(mu**2)\n",
      "a = 0.59\n",
      "m = 1./4.\n",
      "Nu = a*(Gr*Pr)**m\n",
      "h = k*Nu/L\n",
      "A = L*H\n",
      "Q = h*A*delT\n",
      "\n",
      "#Results\n",
      "print \"In SI Units\"\n",
      "print \"The heat transfer cofficient is \",round(h,2),\"W/(m2.K)\"\n",
      "print \"The heat transfer rate across the wall is \",round(Q,1),\"W\"\n",
      "\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In English Units\n",
        "The heat transfer cofficient is  1.24 btu/h.ft2.F\n",
        "The heat transfer rate across the wall is  434.0 btu/h\n",
        "In SI Units\n",
        "The heat transfer cofficient is  7.05 W/(m2.K)\n",
        "The heat transfer rate across the wall is  127.5 W\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.7-2 Page Number 257"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Natural Convection and Simplified Equation\n",
      "\n",
      "#Variable Declaration\n",
      "#From previous Example 4.7-1 Page Number 254\n",
      "L = 0.305                 #Length of the wall (m)\n",
      "delT = 194.4              #Temperature diffrence (K)\n",
      "\n",
      "\n",
      "#Calculation\n",
      "A = 0.305*0.305           #Area of the wall (m2)\n",
      "h = 1.37*(delT/L)**.25\n",
      "Q = h*A*delT\n",
      "\n",
      "#Results\n",
      "print \"The heat transfer coefficient calculated is \",round(h,2),\"W/m2/K\"\n",
      "print \"The heat transfer rate across the wall is \",round(Q,2),\"W\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The heat transfer coefficient calculated is  6.88 W/m2/K\n",
        "The heat transfer rate across the wall is  124.48 W\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.7-3 Page Number 258"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Natural Convection in Enclosed Vertical Space\n",
      "\n",
      "#Variable Declaration\n",
      "L = 0.6                 #Length of the plate (m) \n",
      "W = 0.4                 #Width of the plates (m)\n",
      "d = 0.03                #Distance between the plates (m)\n",
      "T1 = 394.3              #Temperature at one side of the plate (k)\n",
      "T2 = 366.5              #Temperature at the other side of the plate (k)\n",
      "rho = 0.9295            #Density of air (kg/m3)\n",
      "mu = 2.21e-5            #Viscosity of air (Pa.s)\n",
      "k = 0.03219             #Heat transfer coefficient of wall (W/m.K)\n",
      "Pr = 0.693              #Prandtl number\n",
      "g = 9.806               #Gravitational accleration (m/s)\n",
      "\n",
      "#Calculations\n",
      "Tf = (T1 + T2)/2.\n",
      "beta = 1/Tf\n",
      "Gr = d**3*rho**2*g*beta*(T1-T2)/(mu**2)\n",
      "h = k/d*0.2*(Gr*Pr)**(1./4.)/(L/d)**(1./9.)\n",
      "A = L*W\n",
      "Q = h*A*(T1-T2)\n",
      "\n",
      "#Results\n",
      "print \"Heat Transfer Coefficient\", round(h,3),\"W/m2.K\"\n",
      "print \"Heat Transfer Rate\", round(Q,2),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat Transfer Coefficient 1.909 W/m2.K\n",
        "Heat Transfer Rate 12.74 W\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.8-1 Page Number 261"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Rate of Heat Transfer in a Jacketed Kettle \n",
      "\n",
      "#Variable Declaration\n",
      "Tjs = 115.6                #Temperature of steam being condensed (deg C)\n",
      "dki = 0.656                #Inside diameter of the kettle (m)\n",
      "hk = 0.984                 #Height of the kettle (m)\n",
      "tw = 0.0032                #Thickness of the wall of the jacket (m)\n",
      "k = 16.27                  #Heat transfer coefficient of the wall (W/m.K)\n",
      "hi = 10200.                #Condensing steam cofficient (W/m2.K)\n",
      "Tsat = 100.                #Saturation temperature (deg C)\n",
      "A = 1.0\n",
      "\n",
      "#Calculations\n",
      "Twa = 110.\n",
      "Ri = 1./(hi*A)\n",
      "Rw = tw/(k*A)\n",
      "Riw = Ri + Rw\n",
      "\n",
      "xx = 1.2\n",
      "while(xx > 0.1):\n",
      "    delT = Twa - Tsat \n",
      "    ho = 5.56*delT**3\n",
      "    q = ho*delT\n",
      "    Ro = 1./(ho*A)\n",
      "    Rs = Riw + Ro\n",
      "    delTc = Ro*(Tjs-Tsat)/Rs\n",
      "    Tw = Tsat + delTc\n",
      "    xx = abs(Tw-Twa)\n",
      "    Twa = (Tw + Twa)/2.\n",
      "#Results vary because more iterations are done\n",
      "#Result\n",
      "print \"Ri:%5.2e\" %Ri\n",
      "print \"Rw:%5.2e\" %Rw\n",
      "print \"Ro:%5.2e\" %Ro\n",
      "print 'Wall Temperature: %4.1f'%Tw\n",
      "print \"Boiling Heat Transfer Coefficient\", round(ho,1),\"W/(m2.K)\"\n",
      "print \"Results vary because more iterations are done\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Ri:9.80e-05\n",
        "Rw:1.97e-04\n",
        "Ro:3.28e-04\n",
        "Wall Temperature: 108.2\n",
        "Boiling Heat Transfer Coefficient 3051.0 W/(m2.K)\n",
        "Results vary because more iterations are done\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.8-2 Page Number 265"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Condensation on Vertical Tubes\n",
      "from math import pi\n",
      "#Variable Declaration English Units\n",
      "Ps, Tsat = 10., 193        #Saturation Pressure ans temperature, psia and \u00b0F\n",
      "L , do = 1., 1./12         #Lenght and ouside diameter of the tube, m\n",
      "Tw = 187.                  #Wall temperature, \u00b0F\n",
      "hv, hl = 1143.3, 161.      #Latent heat of evaporation and enthalpy of liquid \n",
      "vl,vg = 0.01657, 40.95     #specific volume of liquid and vapor, ft3/lbm\n",
      "mul = 0.324                #Viscosity of liquid, lbm/(ft.hr)\n",
      "kl = 0.390                 #Thermal conductivity of liquid, Btu/(ft.hr.\u00b0F)\n",
      "g = 32.174                 #Gravitational acceleration, ft/s2\n",
      "\n",
      "#Calculation English Units\n",
      "g = g*3600**2\n",
      "mul = mul*2.4191\n",
      "rhol , rhov = 1./vl , 1./vg\n",
      "Tf = (Tw + Tsat)/2.\n",
      "hfg = hv-hl\n",
      "delT = Tsat - Tw\n",
      "Nu = 1.13*(rhol**2*g*hfg*L**3/(mul*kl*delT))**(1./4)\n",
      "h=Nu*kl/L\n",
      "A = pi*do*L\n",
      "Q = h*A*delT\n",
      "mdot = Q/hfg\n",
      "Re = 4*mdot/(pi*do*mul)\n",
      "print \"Average heat transfer coefficient\",round(h,2),\"Btu/(h.ft2.\u00b0F)\"\n",
      "print \"Reynolds number is,\", round(Re,1), \"hence flow is laminar\"\n",
      "\n",
      "#Variable Declaration SI Units\n",
      "Ps, Tsat = 68.9, 89.44\n",
      "L , do = 0.305, 0.0254\n",
      "Tw = 86.11\n",
      "hv, hl = 2657800, 374600\n",
      "vl,vg = 0.01657/16, 40.95/16\n",
      "mul = 3.24e-4\n",
      "kl = 0.675\n",
      "g = 9.806\n",
      "\n",
      "#Calculation SI Units\n",
      "\n",
      "rhol , rhov = 1./vl , 1./vg\n",
      "Tf = (Tw + Tsat)/2.\n",
      "hfg = hv-hl\n",
      "delT = Tsat - Tw\n",
      "Nu = 1.13*(rhol**2*g*hfg*L**3/(mul*kl*delT))**(1./4)\n",
      "h=Nu*kl/L\n",
      "A = pi*do*L\n",
      "Q = h*A*delT\n",
      "mdot = Q/hfg\n",
      "Re = 4*mdot/(pi*do*mul)\n",
      "\n",
      "#Results\n",
      "print \"Average heat transfer coefficient\",round(h,2),\"W/(m2.K)\"\n",
      "print \"Reynolds number is,\", round(Re,1), \"hence flow is laminar\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Average heat transfer coefficient 2353.51 Btu/(h.ft2.\u00b0F)\n",
        "Reynolds number is, 73.4 hence flow is laminar\n",
        "Average heat transfer coefficient 13354.93 W/(m2.K)\n",
        "Reynolds number is, 73.3 hence flow is laminar\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.9-1 Page Number 271"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Temperature Correction Factor for a Heat Exchanger\n",
      "\n",
      "#Variable Declration\n",
      "mdotc = 2.52              #Mass flow rate of water, kg/s \n",
      "Tci, Tco = 21.1, 54.4     #Inlet and outlet temperature of cold water, \u00b0C\n",
      "Thi, Tho = 115.6, 48.9    #Inlet and outlet temperature of hot water, \u00b0C\n",
      "Ao = 9.3                  #Outside surface area of exchanger, m2\n",
      "Cp = 4187.                #mean specific heat of water, J/(kg.K)\n",
      "\n",
      "#Calculations\n",
      "Qc= mdotc*Cp*(Tco-Tci)\n",
      "delT1 = Thi-Tco\n",
      "delT2 = Tho-Tci\n",
      "delTLM = (delT1-delT2)/log(delT1/delT2)\n",
      "Z = (Thi-Tho)/(Tco-Tci)\n",
      "Y = (Tco-Tci)/(Thi-Tci)\n",
      "                #PART \"A\" 1-2 pass \n",
      "Fta = 0.74          # correction factor for Z and Y values in part a from chart\n",
      "delTMa = Fta*delTLM\n",
      "Uoa = Qc/(Ao*delTMa)\n",
      "                #PArt \"B\" 2-4\n",
      "Ftb = 0.94         # correction factor for Z and Y values in part b from chart\n",
      "delTMb = Ftb*delTLM\n",
      "Uob = Qc/(Ao*delTMb)\n",
      "#Result\n",
      "print \"PART A\"\n",
      "print \"Mean Temperature Difference for 1-2 pass Heat Exchanger\", round(delTMa,1),\"\u00b0C or K\"\n",
      "print \"Required Overall outside Heat Transfer coefficient for 1-2 pass\", round(Uoa,1),\"W/(m.K)\"\n",
      "\n",
      "print \"PART B\"\n",
      "print \"Mean Temeperature Difference for 2-4 pass Heat Exchanger\", round(delTMb,1),\"\u00b0C or K\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "PART A\n",
        "Mean Temperature Difference for 1-2 pass Heat Exchanger 31.3 \u00b0C or K\n",
        "Required Overall outside Heat Transfer coefficient for 1-2 pass 1206.2 W/(m.K)\n",
        "PART B\n",
        "Mean Temeperature Difference for 2-4 pass Heat Exchanger 39.8 \u00b0C or K\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.9-2 Page Number 275"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Effectiveness of Heat Exchanger\n",
      "from math import exp\n",
      "#Variable Declaration\n",
      "mc, mh  = 0.667, 2.85        #mass flow rate of cold water and hot oil,kg/s\n",
      "cpc, cph = 4192., 1890.      #Specific heat of cold water and hot oil,kJ/(kg.K)\n",
      "Tci,Thi = 308., 383.         #Inlet temperatures of cold water and hot oil, \u00b0C\n",
      "U,A = 300., 15.              #Overall heat transfer coefficient W/(m2.K) and Surface area, m2\n",
      "\n",
      "#Calcualtions\n",
      "Cc = mc*cpc       #(m*cp)C\n",
      "Ch = mh*cph       #(m*cp)H\n",
      "if Cc > Ch:\n",
      "    Cmin = Ch\n",
      "    Cmax = Cc\n",
      "else:\n",
      "    Cmin = Cc\n",
      "    Cmax = Ch\n",
      "\n",
      "NTU = U*A/Cmin\n",
      "Cminbymax = Cmin/Cmax\n",
      "\n",
      "#Using figure \"a\" on page 274\n",
      "Enum = 1. - exp(-NTU*(1-Cminbymax))\n",
      "Eden = 1. - Cminbymax*exp(-NTU*(1-Cminbymax))\n",
      "Tco= 350.\n",
      "epsilon = Enum/Eden\n",
      "\n",
      "Q = epsilon*Cmin*(Thi-Tci)\n",
      "Tco = Q/Cmin + Tci\n",
      "\n",
      "#Results     \n",
      "print \"Heat Tranfer Rate\", round(Q,2),\"W\" \n",
      "print \"Outlet Temperature of cold fluid\", round(Tco,1),\"K\"\n",
      "print 'The answers are different than book because book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.708413929951\n",
        "Heat Tranfer Rate 148557.8 W\n",
        "Outlet Temperature of cold fluid 361.1 K\n",
        "The answers are different than book because book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.10-1 Page Number 279"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Radiation to Metal Tube\n",
      "import scipy.constants as sc\n",
      "from math import pi\n",
      "\n",
      "#Variable Declaration\n",
      "do, L = 0.0254, 0.61      #Outside diameter of tube, and length, m \n",
      "Ts = 588.                 #Surface temperature of the tube, K\n",
      "ep = 0.6                  #emmisivity of metal tube at 1088 K\n",
      "Te = 1088.                #Temperature of surrounding air, K\n",
      "\n",
      "#Calculations \n",
      "        #SI Units\n",
      "A = pi*do*L\n",
      "Q = ep*A*5.676e-8*(Ts**4-Te**4)\n",
      "\n",
      "print \"Heat Transferred to tube from the surrounding in SI units\", round(Q,1), \"W\"\n",
      "\n",
      "#Variable Declaration\n",
      "do, L = 1./12, 2.0       #Outside diameter of tube, and length, ft \n",
      "Ts = 600                 #Surface temperature of the tube, \u00b0F\n",
      "ep = 0.6                 #emmisivity of metal tube at 1500 \u00b0F\n",
      "Te = 1500.               #Temperature of surrounding air, \u00b0F\n",
      "\n",
      "#Calculations \n",
      "        #English Units\n",
      "A = pi*do*L\n",
      "Q = ep*A*0.1714e-8*((Ts+460)**4-(Te+460)**4)\n",
      "print \"Heat Transferred to tube from the surrounding in English units\", round(Q,1), \"Btu/hr\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat Transferred to tube from the surrounding in SI units -2124.7 W\n",
        "Heat Transferred to tube from the surrounding in English units -7266.9 Btu/hr\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.10-2 Page Number 280"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Combined Covection Plus Radiation from a Tube\n",
      "import scipy.constants as sc\n",
      "from math import pi\n",
      "\n",
      "#Variable declaration\n",
      "do, L = 0.0254, 0.61     #Outside diameter of tube, and length, m \n",
      "Ts = 588.                #Surface temperature of the tube, K\n",
      "ep = 0.6                 #emmisivity of metal tube at 1088 K\n",
      "Te = 1088.               #Temperature of surrounding air, K\n",
      "\n",
      "#Calculations\n",
      "A = pi*do*L\n",
      "hc = 1.32*((Te-Ts)/do)**0.25\n",
      "hr = ep*5.676e-8*(Te**4-Ts**4)/(Te-Ts)\n",
      "Q = A*(hc + hr)*(Ts-Te)\n",
      "#Results\n",
      "print \"Convective Heat Transfer Coefficient\",round(hc,2)\n",
      "print \"Radiation Heat Transfer Coefficient\",round(hr,2)\n",
      "print \"Heat Transferred to the tube from the surrounding\", round(Q,2), \"W\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Convective Heat Transfer Coefficient 15.64\n",
        "Radiation Heat Transfer Coefficient 87.3\n",
        "Heat Transferred to the tube from the surrounding -2505.23 W\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.11-1 Page Number 285"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Radiation between Parallel Plated\n",
      "import scipy.constants as sc\n",
      "\n",
      "#Variable declaration \n",
      "ep1, ep2 = 0.8, 0.7       #emmissivities of plate 1 and 2\n",
      "T1, T2 = 866.5, 588.8     #Temperatures of surface 1 and 2, K\n",
      "\n",
      "#Calculations PART \"SI\"\n",
      "q12 = 5.676e-8*(T1**4-T2**4)/(1./ep1+1./ep2-1.)\n",
      "q12b = 5.676e-8*(T1**4-T2**4)\n",
      "#Results\n",
      "print \"SI Units\"\n",
      "print \"a)  Heat Flux from Plate 1 to Plate 2\", round(q12,2),\"W/m2\"\n",
      "print \"b)  Heat Flux from Plate 1 to Plate 2 when both surfaces are balck body\", round(q12b,2),\"W/m2\"\n",
      "#Variable declaration \n",
      "\n",
      "\n",
      "#Calculations PART \"British\"\n",
      "ep1, ep2 = 0.8, 0.7     #emmissivities of plate 1 and 2\n",
      "T1, T2 = 1100, 600      #Temperatures of surface 1 and 2, \u00b0F\n",
      "\n",
      "q12 = 0.1714e-8*((T1+460)**4-(T2+460)**4)/(1./ep1+1./ep2 -1.)\n",
      "q12b = 0.1714e-8*((T1+460)**4-(T2+460)**4)\n",
      "\n",
      "#Results\n",
      "print \"English Units\"\n",
      "print \"a)  Heat Flux from Plate 1 to Plate 2\", round(q12,2),\"Btu/ft2.h\"\n",
      "print \"b)  Heat Flux from Plate 1 to Plate 2 when both surfaces are balck body\", round(q12b,2),\"Btu/ft2.h\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SI Units\n",
        "a)  Heat Flux from Plate 1 to Plate 2 14998.18 W/m2\n",
        "b)  Heat Flux from Plate 1 to Plate 2 when both surfaces are balck body 25175.52 W/m2\n",
        "English Units\n",
        "a)  Heat Flux from Plate 1 to Plate 2 4758.29 Btu/ft2.h\n",
        "b)  Heat Flux from Plate 1 to Plate 2 when both surfaces are balck body 7987.12 Btu/ft2.h\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.11-7 Page Number 296"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Gas Radiation to a Furnace Enclosure\n",
      "import scipy.constants as sc\n",
      "\n",
      "#Variable Declaration\n",
      "L = 0.3             #Inside length of cubical furnace, m    \n",
      "P = 1.              #Pressure of gas inside furnace, atm\n",
      "Tg = 1100.          #Temperature of gas, K\n",
      "Tw = 600.           #Temperature of furnace wall, K \n",
      "xco2 = 0.1          #mole fraction of CO2  \n",
      "\n",
      "#Calculations\n",
      "Lbm = .60*L\n",
      "pco2 = P*xco2\n",
      "pgL = pco2*Lbm\n",
      "        #from figure 4.11-10\n",
      "epg = 0.064\n",
      "alphag600 = pgL*(Tw/Tg)\n",
      "alphaguc = 0.048\n",
      "alphagc = alphaguc*(Tg/Tw)**0.65\n",
      "q = sc.sigma*(epg*Tg**4-alphagc*Tw**4)\n",
      "A = L*L*6\n",
      "Q = q*A\n",
      "\n",
      "#Results\n",
      "print \"Heat Transfer rate in Gas radiation\", round(Q/1000,3), \"kW\"\n",
      "print 'The answer is different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heat Transfer rate in Gas radiation 2.587 kW\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4.12-1 Page Number 298"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heating a Non-Newtonian Fluid in Laminar Flow\n",
      "from scipy.optimize import root\n",
      "\n",
      "#Variable Declaration\n",
      "mdot = 7.56e-2     #Mass flow rate of non-Newtonian fluid, kg/s\n",
      "di = 0.0254        #Inside Diameter of the tube, m\n",
      "L = 1.524          #Length of the tube, m\n",
      "Ti =  37.8         #Inlet temperature of the fluid, \u00b0C \n",
      "Tw = 93.3          #Inside wall temperature, \u00b0C\n",
      "rho = 1041.        #density of fluid, kg/m3\n",
      "cpm = 2.093e3      #specific heat of fluid, J/(kg.K)\n",
      "k =  1.212         #Thermal conductivity of fluid, W/(m.K)        \n",
      "n = 0.4            #Rheological constants for fluid\n",
      "K378 = 139.9       \n",
      "K933 = 62.5\n",
      "\n",
      "#Calculations\n",
      "Tbo = 54.4\n",
      "Tb = (Ti + Tbo)/2.0\n",
      "slope = (log(K378)-log(K933))/(Ti-Tw)\n",
      "c = log(139.9)-slope*Ti\n",
      "Kb = exp(slope*Tb+c)\n",
      "Kw = exp(slope*Tw+c)\n",
      "delta = (3.*n+1)/(4*n)\n",
      "NGz = mdot*cpm/(k*L)\n",
      "gamabw = Kb/Kw\n",
      "Nu = 1.75*delta**(1./3)*NGz**(1./3)*gamabw**0.14\n",
      "\n",
      "ha = k*Nu/di\n",
      "Tk = (2.*Tw-Ti)/2.\n",
      "mT = 1./2\n",
      "\n",
      "f = lambda T: mdot*cpm*(T-Ti)-ha*pi*di*L*(Tk-mT*T)\n",
      "sol = root(f,25)\n",
      "Tbo = sol.x[0]\n",
      "\n",
      "#Results\n",
      "print \"Gratez Number\", round(NGz,1)\n",
      "print \"Heat Transfer Coefficient\", round(ha,1),\"W/m2.K\"\n",
      "print \"Oultlet bulk temperature of the fluid\",round(Tbo,1),\"\u00b0C\"  \n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Gratez Number 85.7\n",
        "Heat Transfer Coefficient 450.5 W/m2.K\n",
        "Oultlet bulk temperature of the fluid 54.2 \u00b0C\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Example 4.13-1 Page Number 301"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Heat Transfer Coefficient in Agitated Vessel\n",
      "\n",
      "#Variable Declaration\n",
      "Dt = 1.83       #Diameter of agitated vessel,m\n",
      "Tl = 300.       #Temperature of liquid to be heated, K\n",
      "Da = 0.61       #Diameter of agitator vessel,m\n",
      "N = 100.        #RPM of agitator\n",
      "Tw = 355.4      #Wall temperature of Jaket, K\n",
      "rho = 961.      #Density of liquid, kg/m3\n",
      "cp = 2500.      #Density of liquid, K/(kg.K)\n",
      "k = 0.173       #Thermal conductivity of liquid, W/(m.K)\n",
      "mu = 1.0        #Viscosity of liquid at 300K, Pa.s\n",
      "muw = 0.084     #Viscosity of liquid at Wall temperature 355.5K, Pa.s\n",
      "\n",
      "#Calculations\n",
      "Nre = Da**2*(N/60)*rho/mu\n",
      "Npr = cp*mu/k\n",
      "#for equation 4.13-1 a = 0.74, b=2/3\n",
      "a = 0.74\n",
      "b = 2./3\n",
      "Nu = a*Nre**b*Npr**(1./3)*(mu/muw)**0.14\n",
      "h = Nu*k/Dt\n",
      "\n",
      "#Results\n",
      "print 'Reynolds number is %3.0f'%Nre\n",
      "print 'Prandtl number is %5.0f'%Npr\n",
      "print \"Heat transfer coefficient to the wall of jacket\",round(h,1),\"W/(m2.K)\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reynolds number is 596\n",
        "Prandtl number is 14451\n",
        "Heat transfer coefficient to the wall of jacket 170.7 W/(m2.K)\n",
        "The answers are different than book, because of book uses rounded numbers\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Example 4.13-2 Page Number 306"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Fin efficiency and Heat Loss from Fin\n",
      "\n",
      "#Variable Declaration\n",
      "k = 222.        #W/(m.K)\n",
      "r1 = 0.04       #Outer radius of tube, m\n",
      "L = 0.04        #Fin length, m \n",
      "To = 523.2      #Fin base temperature, K\n",
      "Ta = 343.2      #Surrounding Temperature, K\n",
      "t = 2./1000     #Thickness of fin, m\n",
      "h = 30.         #Surrounding convective coefficient, W/(m2.K)\n",
      "\n",
      "#Calculation\n",
      "Lc = L + t/2\n",
      "asbc = Lc*(h/k*t)**0.5\n",
      "param = (Lc+r1)/r1\n",
      "#From fig4.13-5 b for parameter and abscisa value eff = 0.89\n",
      "eff = 0.89\n",
      "Afc = 2*pi*((Lc+r1)**2-r1**2)\n",
      "qf = eff*h*Afc*(To-Ta)\n",
      "\n",
      "#Result\n",
      "print \"Efficiency of the fin is\", round(eff,4)\n",
      "print \"Rate of Heat Loss\", round(qf,1),\"W\"\n",
      "print 'The answers are different than book, because of book uses rounded numbers'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Efficiency of the fin is 0.89\n",
        "Rate of Heat Loss 149.8 W\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Example 4.15-1 Page Number 313"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Steady State Heat Conduction in Two Directions\n",
      "import numpy as np\n",
      "\n",
      "#Variable Declaration\n",
      "D = 8.0            #Ouside dimention of square, m\n",
      "Hi = 4.0           #Inside Height of chamber, m\n",
      "Wi = 2.0           #Inside width of chamber, m\n",
      "Ti = 600.0         #Inside Temperature of chamber, K\n",
      "To = 300.0         #Outside Temperature of chamber, K\n",
      "k = 1.5            #Thermal conductivity of material, W/(m.K)\n",
      "Gl = Gw = 1.0      #Grid size in Height and width Directions, m\n",
      "L = 1.0            #Length of Chamber, m\n",
      "\n",
      "#Calculations\n",
      "np.set_printoptions(precision=1)\n",
      "#Column indices used are one less than used in book\n",
      "T0 = np.zeros(3)\n",
      "T1 = np.zeros(3)\n",
      "T2 = np.zeros(6)\n",
      "T3 = np.zeros(6)\n",
      "T4 = np.zeros(6)\n",
      "T5 = np.zeros(6)\n",
      "    \n",
      "def printT():\n",
      "    print 'Temperature at various nodes are as follows'\n",
      "    print 'T   2      3      4      5'\n",
      "    print 1,T1[1:2]\n",
      "    print 2,T2[1:2]\n",
      "    print 3,T3[1:5]\n",
      "    print 4,T4[1:5]\n",
      "\n",
      "\n",
      "#Initialize\n",
      "T0[2]=T1[2]=T2[2]=T2[3]=T2[4]=T2[5]=600.                                #INNER NODES \n",
      "T0[0]=T1[0]=T2[0]=T3[0]=T4[0]=T5[0]=T5[1]=T5[2]=T5[3]=T5[4]=T5[5]=300   #outer nodes\n",
      "T1[1]=T3[3]=450.\n",
      "T2[1]=T3[1]=T3[2]=T4[4]=400.\n",
      "T3[4]=500.\n",
      "T4[1]=325.\n",
      "T4[2]=350.\n",
      "T4[3]=375.\n",
      "T0[1]=T2[1]\n",
      "T3[5]=T3[3]\n",
      "T4[5]=T4[3]\n",
      "\n",
      "r = 1.2           #Initial value of residue\n",
      "\n",
      "#Calculations\n",
      "while abs(r)>0.001:\n",
      "    r11 = T1[0]+T1[2]+T0[1]+T2[1]-4*T1[1]\n",
      "    T1[1]=(T1[0]+T1[2]+T0[1]+T2[1])/4\n",
      "    r21 = (T2[0]+T2[2]+T1[1]+T3[1]-4*T2[1])\n",
      "    T2[1]=T0[1]=(T2[0]+T2[2]+T1[1]+T3[1])/4\n",
      "    r31=(T3[0]+T3[2]+T2[1]+T4[1]-4*T3[1])\n",
      "    T3[1]=(T3[0]+T3[2]+T2[1]+T4[1])/4\n",
      "    r32 = T2[2]+T4[2]+T3[1]+T3[3]-4*T3[2]\n",
      "    T3[2] =(T2[2]+T4[2]+T3[1]+T3[3])/4\n",
      "    r33 = T3[2]+T3[4]+T2[3]+T4[3]-4*T3[3]\n",
      "    T3[3]=T3[5]=(T3[2]+T3[4]+T2[3]+T4[3])/4\n",
      "    r34 = T3[3]+T3[5]+T2[4]+T4[4]-4*T3[4]\n",
      "    T3[4]=(T3[3]+T3[5]+T2[4]+T4[4])/4\n",
      "    r41 = T4[0]+T4[2]+T3[1]+T5[1]-4*T4[1]\n",
      "    T4[1]=(T4[0]+T4[2]+T3[1]+T5[1])/4\n",
      "    r42 = T4[1]+T4[3]+T3[2]+T5[2]-4*T4[2]\n",
      "    T4[2]=(T4[1]+T4[3]+T3[2]+T5[2])/4\n",
      "    r43 = T4[2]+T4[4]+T3[3]+T5[3]-4*T4[3]\n",
      "    T4[3]=T4[5]=(T4[2]+T4[4]+T3[3]+T5[3])/4\n",
      "    r44 = T4[3]+T4[5]+T3[4]+T5[4]-4*T4[4]\n",
      "    T4[4] = (T4[3]+T4[5]+T3[4]+T5[4])/4\n",
      "    r = r11+r21+r31+r32+r33+r34+r41+r42+r43+r44\n",
      "    \n",
      "#Results\n",
      "print 'Recidue at convergence %10.8f'%r\n",
      "printT()\n",
      "Q1 = 4*k*(0.5*(T1[2]-T1[1]) + (T2[2]-T2[1]) + (T2[2]-T3[2]) + (T2[3]-T3[3]) + 0.5*(T2[4]-T3[4]))\n",
      "Q2 = 4*k*(0.5*(T1[1]-T1[0]) + (T2[1]-T2[0]) + (T3[1]-T3[0]) + (T4[1]-T4[0]) + (T4[1]-T5[1])+(T4[2]-T5[2])+(T4[3]-T5[3])+0.5*(T4[4]-T5[4]))\n",
      "print 'Heat transfer from inner surface %5.1f into the solid'%Q1\n",
      "print 'Heat transfer from outer surface %5.1f out from solid'%Q2\n",
      "Qavg = (Q1+Q2)*0.5\n",
      "print \"Average Heat loss per unit chamber length\",round(Qavg,1),\"W/m\"\n",
      "print 'Book is using rounded values of temperature throughout the iterations hence answers are different'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Recidue at convergence 0.00090090\n",
        "Temperature at various nodes are as follows\n",
        "T   2      3      4      5\n",
        "1 [ 440.3]\n",
        "2 [ 430.6]\n",
        "3 [ 382.   459.2  483.7  489.5]\n",
        "4 [ 338.2  370.9  386.3  390.5]\n",
        "Heat transfer from inner surface 3369.8 into the solid\n",
        "Heat transfer from outer surface 3369.8 out from solid\n",
        "Average Heat loss per unit chamber length 3369.8 W/m\n",
        "Book is using rounded values of temperature throughout the iterations hence answers are different\n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}