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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": {}
}
]
}