path: root/Fundamentals_of_Heat_and_Mass_Transfer/Chapter_11.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Heat Exchangers"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.1 Page 680 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "#Operating Conditions\n",
      "Tho = 60+273    \t\t\t\t\t\t\t;#[K] Hot Fluid outlet Temperature\n",
      "Thi = 100+273   \t\t\t\t\t\t\t; #[K] Hot Fluid intlet Temperature\n",
      "Tci = 30+273    \t\t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "mh = .1          \t\t\t\t\t\t\t;#[kg/s] Hot Fluid flow rate\n",
      "mc = .2          \t\t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "Do = .045        \t\t\t\t\t\t\t;#[m] Outer annulus\n",
      "Di = .025        \t\t\t\t\t\t\t;#[m] Inner tube\n",
      "\n",
      "#Table A.5 Engine Oil Properties T = 353 K\n",
      "cph = 2131              \t\t\t\t\t;#[J/kg.K] Specific Heat\n",
      "kh = .138               \t\t\t\t\t; #[W/m.K] Conductivity\n",
      "uh = 3.25/100.           \t\t\t\t\t; #[N.s/m^2] Viscosity\n",
      "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n",
      "cpc = 4178              \t\t\t\t\t;#[J/kg.K] Specific Heat\n",
      "kc = 0.625               \t\t\t\t\t; #[W/m.K] Conductivity\n",
      "uc = 725*math.pow(10,-6)           \t\t\t; #[N.s/m^2] Viscosity\n",
      "Pr = 4.85                \t\t\t\t\t;#Prandtl Number\n",
      "#calculations and results\n",
      "\n",
      "\n",
      "q = mh*cph*(Thi-Tho); \t\t\t\t\t\t#Heat transferred\n",
      "\n",
      "Tco = q/(mc*cpc)+Tci;\n",
      "\n",
      "T1 = Thi-Tco;\n",
      "T2 = Tho-Tci;\n",
      "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));\t\t#logarithmic mean temp. difference\n",
      "\n",
      "#Through Tube\n",
      "Ret = 4*mc/(math.pi*Di*uc);\n",
      "print '%s %.2f %s' %(\"\\n Flow through Tube has Reynolds Number as\", Ret,\" .Thus the flow is Turbulent\");\n",
      "#Equation 8.60\n",
      "Nut = .023*math.pow(Ret,.8)*math.pow(Pr,.4);#Nusselt number\n",
      "hi = Nut*kc/Di;\n",
      "\n",
      "#Through Shell\n",
      "Reo = 4*mh*(Do-Di)/(math.pi*uh*(Do*Do-Di*Di));\n",
      "print '%s %.2f %s' %(\"\\n Flow through Tube has Reynolds Number as\",Reo,\". Thus the flow is Laminar\");\n",
      "#Table 8.2\n",
      "Nuo = 5.63;\n",
      "ho = Nuo*kh/(Do-Di);\n",
      "\n",
      "U = 1./(1./hi+1./ho); \t\t\t\t\t\t#overall heat transfer coefficient\n",
      "L = q/(U*math.pi*Di*Tlm); \t\t\t\t\t#Length\n",
      "\n",
      "print '%s %.2f' %(\"\\n Tube Length to achieve a desired hot fluid temperature is (m) = \",L);\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " Flow through Tube has Reynolds Number as 14049.54  .Thus the flow is Turbulent\n",
        "\n",
        " Flow through Tube has Reynolds Number as 55.97 . Thus the flow is Laminar\n",
        "\n",
        " Tube Length to achieve a desired hot fluid temperature is (m) =  65.71\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.2 Page 683"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "import numpy\n",
      "from numpy import linspace\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "#Operating Conditions\n",
      "Tho = 60.+273    \t\t\t;#[K] Hot Fluid outlet Temperature\n",
      "Thi = 100.+273    \t\t\t;#[K] Hot Fluid intlet Temperature\n",
      "Tci = 30.+273   \t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "mh = .1          \t\t\t;#[kg/s] Hot Fluid flow rate\n",
      "mc = .2          \t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "Do = .045        \t\t\t;#[m] Outer annulus\n",
      "Di = .025        \t\t\t;#[m] Inner tube\n",
      "\n",
      "#Table A.5 Engine Oil Properties T = 353 K\n",
      "cph = 2131              \t;#[J/kg.K] Specific Heat\n",
      "kh = .138                \t;#[W/m.K] Conductivity\n",
      "uh = 3.25/100.           \t;#[N.s/m^2] Viscosity\n",
      "rhoh = 852.1            \t;#[kg/m^3] Density\n",
      "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n",
      "cpc = 4178              \t;#[J/kg.K] Specific Heat\n",
      "kc = 0.625                \t;#[W/m.K] Conductivity\n",
      "uc = 725*math.pow(10,-6)    ;#[N.s/m^2] Viscosity\n",
      "Pr = 4.85                \t;#Prandtl Number\n",
      "rhoc = 994              \t;#[kg/m^3] Density\n",
      "#calculations\n",
      "\n",
      "q = mh*cph*(Thi-Tho); \t\t#Heat required\n",
      "\n",
      "Tco = q/(mc*cpc)+Tci;\n",
      "\n",
      "T1 = Thi-Tco;\n",
      "T2 = Tho-Tci;\n",
      "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));\n",
      "N=numpy.zeros(61)\n",
      "for i in range (0,60):\n",
      "\tN[i]=i+20;\n",
      "\n",
      "L = numpy.zeros(61)\n",
      "for i in range (0,60):\n",
      "\ta=float(N[i]);\n",
      "\tL[i] = q/Tlm*(1./(7.54*kc/2.)+1/(7.54*kh/2.))/(a*a-a);\n",
      "\n",
      "pyplot.plot(N,L);\n",
      "pyplot.xlabel(\"L (m)\");\n",
      "pyplot.ylabel('Number of Gaps(N)')\n",
      "pyplot.show()\n",
      "#Close the graph to complete the execution\n",
      "N2 = 60;\n",
      "L = q/((N2-1)*N2*Tlm)*(1./(7.54*kc/2.)+1/(7.54*kh/2.));\n",
      "a = L/N2;\n",
      "Dh = 2*a        \t\t\t;#Hydraulic Diameter [m]\n",
      "#For water filled gaps\n",
      "umc = mc/(rhoc*L*L/2.);\n",
      "Rec = rhoc*umc*Dh/uc;\n",
      "#For oil filled gaps\n",
      "umh = mh/(rhoh*L*L/2.);\n",
      "Reh = rhoh*umh*Dh/uh;\n",
      "print '%s %.2f %s %.2f %s' %(\"\\n Flow of the fluids has Reynolds Number as\",Reh,\" & \",Rec,\" Thus the flow is Laminar for both\");\n",
      "\n",
      "#Equations 8.19 and 8.22a\n",
      "delpc = 64/Rec*rhoc/2*umc*umc/Dh*L        ;#For water\n",
      "delph = 64/Reh*rhoh/2*umh*umh/Dh*L        ;#For oil\n",
      "\n",
      "#For example 11.1\n",
      "L1 = 65.9;\n",
      "Dh1c = .025;\n",
      "Dh1h = .02;\n",
      "Ret = 4*mc/(math.pi*Di*uc);\n",
      "f = math.pow((.790*2.30*math.log10(Ret)-1.64),-2)       ;#friction factor through tube Eqn 8.21\n",
      "umc1 = 4*mc/(rhoc*math.pi*Di*Di);\n",
      "delpc1 = f*rhoc/2*umc1*umc1/Dh1c*L1;\n",
      "Reo = 4*mh*(Do-Di)/(math.pi*uh*(Do*Do-Di*Di));\t\t  \t#Reynolds number\n",
      "umh1 = 4*mh/(rhoh*math.pi*(Do*Do-Di*Di));\n",
      "delph1 = 64/Reo*rhoh/2*umh1*umh1/Dh1h*L1;\n",
      "#results\n",
      "\n",
      "print '%s %.3f %s' %(\"\\n Exterior Dimensions of heat Exchanger L =\",L,\"m\");\n",
      "print '%s %.3f %s' %(\"\\n Pressure drops within the plate-type Heat exchanger with N=60 gaps\\n For water = \",  delpc,\" N/m^2\")   \n",
      "print '%s %.3f %s' %(\" For oil = \",delph,\" N/m^2\\n \")\n",
      "print '%s %.3f %s' %(\"Pressure drops tube Heat exchanger of example 11.1\\n For water = \",delpc1 ,\"N/m^2\")   \n",
      "print '%s %.3f %s' %(\"\\n For oil =\",delph1,\" N/m^2\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " Flow of the fluids has Reynolds Number as 1.57  &  140.77  Thus the flow is Laminar for both\n",
        "\n",
        " Exterior Dimensions of heat Exchanger L = 0.131 m\n",
        "\n",
        " Pressure drops within the plate-type Heat exchanger with N=60 gaps\n",
        " For water =  3.768  N/m^2\n",
        " For oil =  98.523  N/m^2\n",
        " \n",
        "Pressure drops tube Heat exchanger of example 11.1\n",
        " For water =  6331.255 N/m^2\n",
        "\n",
        " For oil = 18287.329  N/m^2\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.3 Page 692"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Operating Conditions\n",
      "Tho = 100+273.    \t\t\t\t;#[K] Hot Fluid outlet Temperature\n",
      "Thi = 300+273.    \t\t\t\t;#[K] Hot Fluid intlet Temperature\n",
      "Tci = 35+273.    \t\t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "Tco = 125+273.   \t\t\t\t; #[K] Cold Fluid outlet Temperature\n",
      "mc = 1          \t\t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "Uh = 100        \t\t\t\t;#[W/m^2.K] Coefficient of heat transfer\n",
      "#Table A.5 Water Properties T = 353 K\n",
      "cph = 1000       \t\t\t\t;#[J/kg.K] Specific Heat\n",
      "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n",
      "cpc = 4197        \t\t\t\t;#[J/kg.K] Specific Heat\n",
      "#calculations\n",
      "\n",
      "Cc = mc*cpc;\n",
      "#Equation 11.6b and 11.7b\n",
      "Ch  = Cc*(Tco-Tci)/(Thi-Tho);\n",
      "# Equation 11.18\n",
      "qmax = Ch*(Thi-Tci); \t\t\t#Max. heat\n",
      "#Equation 11.7b \n",
      "q = mc*cpc*(Tco-Tci); \t\t\t#Heat available\n",
      "\n",
      "e = q/qmax; \n",
      "ratio = Ch/Cc; \n",
      "#results\n",
      "\n",
      "print '%s %.2f %s %.2f' %(\"\\n As effectiveness is\", e,\" with Ratio Cmin/Cmax =\", ratio);\n",
      "print '%s' %(\", It follows from figure 11.14 that NTU = 2.1\");\n",
      "NTU = 2.1; \t\t\t\t\t\t#No. of transfer units\n",
      "A = 2.1*Ch/Uh;\n",
      "\n",
      "print '%s %.2f' %(\"\\n Required gas side surface area  (m^2) = \",A);\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " As effectiveness is 0.75  with Ratio Cmin/Cmax = 0.45\n",
        ", It follows from figure 11.14 that NTU = 2.1\n",
        "\n",
        " Required gas side surface area  (m^2) =  39.66\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.4  Page 695"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "#Operating Conditions\n",
      "Thi = 250+273.    \t\t\t;#[K] Hot Fluid intlet Temperature\n",
      "Tci = 35+273.    \t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "mc = 1          \t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "mh = 1.5        \t\t\t;  #[kg/s] Hot Fluid flow rate\n",
      "Uh = 100       \t\t \t\t;#[W/m^2.K] Coefficient of heat transfer\n",
      "Ah = 40         \t\t\t; #[m^2] Area\n",
      "#Table A.5 Water Properties T = 353 K\n",
      "cph = 1000.       \t\t\t;#[J/kg.K] Specific Heat\n",
      "#Table A.6 Saturated water Liquid Properties Tc = 308 K\n",
      "cpc = 4197.        \t\t\t;#[J/kg.K] Specific Heat\n",
      "#calculations\n",
      "\n",
      "Cc = mc*cpc;\n",
      "Ch  = mh*cph;\n",
      "Cmin = Ch;\n",
      "Cmax = Cc;\n",
      "\n",
      "NTU = Uh*Ah/Cmin;\t\t\t#No.of transfer units\n",
      "ratio = Cmin/Cmax;\n",
      "#results\n",
      "\n",
      "print '%s %.2f' %(\"\\n As Ratio Cmin/Cmax =\", ratio)\n",
      "print '%s %.2f' %(\"and Number of transfer units NTU =\", NTU)\n",
      "print '%s' %(\", It follows from figure 11.14 that e = .82\");\n",
      "e = 0.82;\n",
      "qmax = Cmin*(Thi-Tci);\t\t#Max. heat transferred\n",
      "q = e*qmax; \t\t\t\t#Actual heat transferred\n",
      "\n",
      "#Equation 11.6b\n",
      "Tco = q/(mc*cpc) + Tci;\n",
      "#Equation 11.7b\n",
      "Tho = -q/(mh*cph) + Thi;\n",
      "print '%s %.2e %s' %(\"\\n Heat Transfer Rate  =\",q,\" W \")\n",
      "print '%s %.1f %s' %(\"\\n Fluid Outlet Temperatures Hot Fluid (Tho) =\" ,Tho-273,\"degC\") \n",
      "print '%s %.2f %s'\t%(\"Cold Fluid (Tco) =\", Tco-273,\"degC\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " As Ratio Cmin/Cmax = 0.36\n",
        "and Number of transfer units NTU = 2.67\n",
        ", It follows from figure 11.14 that e = .82\n",
        "\n",
        " Heat Transfer Rate  = 2.64e+05  W \n",
        "\n",
        " Fluid Outlet Temperatures Hot Fluid (Tho) = 73.7 degC\n",
        "Cold Fluid (Tco) = 98.01 degC\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.5 Page 696"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "#Operating Conditions\n",
      "q = 2*math.pow(10,9)       \t \t\t\t;#[W] Heat transfer Rate\n",
      "ho = 11000.        \t\t\t\t\t\t;#[W/m^2.K] Coefficient of heat transfer for outer surface\n",
      "Thi = 50+273.    \t\t\t\t\t\t;#[K] Hot Fluid Condensing Temperature\n",
      "Tho = Thi    \t\t\t\t\t\t\t;#[K] Hot Fluid Condensing Temperature\n",
      "Tci = 20+273.    \t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "mc = 3*math.pow(10,4)     \t\t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "m =  1          \t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate per tube\n",
      "D = .025        \t\t\t\t\t\t;#[m] diameter of tube\n",
      "#Table A.6 Saturated water Liquid Properties Tf = 300 K\n",
      "rho = 997        \t\t\t\t\t\t;#[kg/m^3] Density\n",
      "cp = 4179        \t\t\t\t\t\t;#[J/kg.K] Specific Heat\n",
      "k = 0.613        \t\t\t\t\t\t;#[W/m.K] Conductivity\n",
      "u = 855*math.pow(10,-6)    \t\t\t\t;#[N.s/m^2] Viscosity\n",
      "Pr = 5.83        \t\t\t\t\t\t;# Prandtl number\n",
      "#calculations and results\n",
      "\n",
      "#Equation 11.6b\n",
      "Tco = q/(mc*cp) + Tci;\n",
      "\n",
      "Re = 4*m/(math.pi*D*u);\n",
      "print '%s %.2f' %(\"\\n As the Reynolds number of tube fluid is\", Re)\n",
      "print '%s' %(\". Hence the flow is turbulent. Hence using Diettus-Boetllor Equation 8.60\");\n",
      "Nu = .023*math.pow(Re,.8)*math.pow(Pr,.4);\n",
      "hi = Nu*k/D;\t\t\t\t\t\t\t#Heat transfer coefficient\n",
      "U = 1/(1/ho + 1/hi); \t\t\t\t\t#Overall heat transfer coefficient\n",
      "N = 30000.            \t\t\t\t\t;#No of tubes\n",
      "T1 = Thi-Tco;\n",
      "T2 = Tho-Tci;\n",
      "Tlm = (T1-T2)/(2.30*math.log10(T1/T2));#Logarithmic mean temp. difference\n",
      "L2 = q/(U*N*2*math.pi*D*Tlm);\n",
      "\n",
      "\n",
      "print '%s %.1f %s' %(\"\\n Outlet Temperature of cooling Water = \",Tco-273,\" degC\")\n",
      "print  '%s %.2f %s' %(\"\\n Tube length per pass to achieve required heat transfer =\",L2,\" m\");\n",
      "#END"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " As the Reynolds number of tube fluid is 59566.76\n",
        ". Hence the flow is turbulent. Hence using Diettus-Boetllor Equation 8.60\n",
        "\n",
        " Outlet Temperature of cooling Water =  36.0  degC\n",
        "\n",
        " Tube length per pass to achieve required heat transfer = 4.51  m\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11.6 Page 702"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "#Operating Conditions\n",
      "hc = 1500.        \t\t\t\t\t\t\t\t;#[W/m^2.K] Coefficient of heat transfer for outer surface\n",
      "hi = hc;\n",
      "Th = 825.    \t\t\t\t\t\t\t\t\t;#[K] Hot Fluid Temperature\n",
      "Tci = 290.    \t\t\t\t\t\t\t\t\t;#[K] Cold Fluid intlet Temperature\n",
      "Tco = 370.    \t\t\t\t\t\t\t\t\t;#[K] Cold Fluid outlet Temperature\n",
      "mc = 1          \t\t\t\t\t\t\t\t;#[kg/s] Cold Fluid flow rate\n",
      "mh =  1.25         \t\t\t\t\t \t\t\t;#[kg/s] Hot Fluid flow rate\n",
      "Ah = .20            \t\t\t\t\t\t\t;#[m^2] Area of tubes\n",
      "Di = .0138        \t\t\t\t\t\t\t\t;#[m] diameter of tube\n",
      "Do = .0164        \t\t\t\t\t\t\t\t;#[m] Diameter\n",
      "#Table A.6 Saturated water Liquid Properties Tf = 330 K\n",
      "cpw = 4184.         \t\t\t\t\t\t\t;#[J/kg.K] Specific Heat\n",
      "#Table A.1 Aluminium Properties T = 300 K\n",
      "k = 237             \t\t\t\t\t\t\t;#[W/m.K] Conductivity\n",
      "#Table A.4 Air Properties Tf = 700 K\n",
      "cpa = 1075         \t\t\t\t\t\t\t\t;#[J/kg.K] Specific Heat\n",
      "u = 33.88*math.pow(10,-6)    \t\t\t\t\t;#[N.s/m^2] Viscosity\n",
      "Pr = .695          \t\t\t\t\t\t\t\t;# Prandtl number\n",
      "#calculations\n",
      "\n",
      "#Geometric Considerations\n",
      "si = .449;\n",
      "Dh = 6.68*math.pow(10,-3)        \t\t\t\t;#[m] hydraulic diameter\n",
      "G = mh/si/Ah;\n",
      "Re = G*Dh/u; \t\t\t\t\t\t\t\t\t#Reynolds number\n",
      "#From Figure 11.16\n",
      "jh = .01;\n",
      "hh = jh*G*cpa/math.pow(Pr,.66667); \t\t\t\t#Heat transfer coefficient\n",
      "\n",
      "AR = Di*2.303*math.log10(Do/Di)/(2*k*(.143));\t#Area of cross section\n",
      "#Figure 11.16\n",
      "AcAh = Di/Do*(1-.830);\n",
      "#From figure 3.19\n",
      "nf = .89;\n",
      "noh = 1-(1-.89)*.83;\n",
      "\n",
      "U = 1/(1/(hc*AcAh) + AR + 1/(noh*hh));\t\t\t#Overall heat transfer coefficient\n",
      "\n",
      "Cc = mc*cpw;\n",
      "q = Cc*(Tco-Tci); \t\t\t\t\t\t\t\t#Heat released\n",
      "Ch = mh*cpa;\n",
      "qmax = Ch*(Th-Tci); \t\t\t\t\t\t\t#MAx. heat transferred\n",
      "e = q/qmax;\n",
      "ratio = Ch/Cc;\n",
      "#results\n",
      "\n",
      "print '%s %.2f %s %.2f' %(\"\\n As effectiveness is\",e,\" with Ratio Cmin/Cmax = \",ratio)\n",
      "print '%s' %(\", It follows from figure 11.14 that NTU = .65\");\n",
      "NTU = .65;\n",
      "A = NTU*Ch/U; \t\t\t\t\t\t\t\t\t#Area of cross section\n",
      "#From Fig 11.16\n",
      "al = 269.;            \t\t\t\t\t\t\t#[m^-1] gas side area per unit heat wxchanger volume\n",
      "V = A/al;\n",
      "#Answers may vary a bit due to rounding off errors.!\n",
      "print '%s %.2f %s' %(\"\\n Gas-side overall heat transfer coefficient.r =\", U , \"W/m^2.K\")\n",
      "print '%s %.3f %s' %(\" \\n Heat exchanger Volume = \",V,\" m^3\");\n",
      "#END;"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " As effectiveness is 0.47  with Ratio Cmin/Cmax =  0.32\n",
        ", It follows from figure 11.14 that NTU = .65\n",
        "\n",
        " Gas-side overall heat transfer coefficient.r = 95.55 W/m^2.K\n",
        " \n",
        " Heat exchanger Volume =  0.034  m^3\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}