{ "metadata": { "name": "", "signature": "sha256:ab6cb233ee6afa8e8253b650d9b15125740d73ba571b9d5b3c9431dc16631f9d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "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": {} } ] }