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diff --git a/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb new file mode 100644 index 00000000..ff0dc69f --- /dev/null +++ b/Heat_Transfer_Principles_And_Applications_by_Dutta/ch8.ipynb @@ -0,0 +1,494 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8 : Heat Exchanger" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1 Page No : 303" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the heat duty of the exchanger is 47000 kj/h\n", + "the water flow rate is 1122 kg/h\n", + "heat transfer coefficient based on inside area is 3560 W/m**2 C \n", + "heat transfer coefficient based on outside area is 880.3 W/m**2 C \n", + "overall heat transfer coefficient outside area basis is 663.1 W/m**2 C \n", + "overall heat transfer coefficient inside area basis is 802.0 W/m**2 C \n", + "The fouling factor is 0.000949 m**2 C/W\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Variables\n", + "#for Benzene\n", + "Mb = 1000. \t\t\t#Kg, mass of benzene\n", + "T1 = 75. \t\t\t#C initial temp. of benzene\n", + "T2 = 50. \t\t\t#C final temp. of benzene\n", + "Cp1 = 1.88 \t\t\t#Kj/Kg C. specific heat of benzene\n", + "mu1 = 0.37 \t\t\t#cP. vismath.cosity of benzene\n", + "rho1 = 860. \t\t\t#kg/m**3, density\n", + "k1 = 0.154 \t\t\t#W/m K. thermal conductivity\n", + "\n", + "#for water\n", + "Tav = 35. \t\t\t#C av, temp.\n", + "Cp2 = 4.187 \t\t\t#specific heat\n", + "mu2 = 0.8 \t\t\t#cP. vismath.cosity\n", + "k2 = 0.623 \t\t\t#W/m K. thermal conductivity\n", + "T3 = 30. \t\t\t#C. initial temp.\n", + "T4 = 40. \t\t\t#C final temp.\n", + "\n", + "#Calculation and Results\n", + "#(a)\n", + "HD = Mb*Cp1*(T1-T2) \t\t\t#Kj/h, heat duty\n", + "WR = HD/(Cp2*(T4-T3)) \t\t\t#kg/h Water rate\n", + "print \"the heat duty of the exchanger is %.0f kj/h\"%(HD)\n", + "print \"the water flow rate is %d kg/h\"%(WR)\n", + "\n", + "#(b)\n", + "#tube side (water) calculations\n", + "# Variables\n", + "di1 = 21. \t\t\t#mm, inner diameter of inner tube \n", + "do1 = 25.4 \t\t\t#mm, outer dia. of inner tube\n", + "t = 2.2 \t\t\t#mm/ wall thickness\n", + "kw = 74.5 \t\t\t#W/m K. thermal conductivity of the wall\n", + "di2 = 41. \t\t\t#mm, inner diameter of outer pipe\n", + "do2 = 48. \t\t\t#mm, outer diameter of outer pipe\n", + "\n", + "FA1 = (math.pi/4)*(di1*10**-3)**2 \t\t\t#m**2, flow area\n", + "FR1 = WR/1000.\n", + "v1 = FR1/(FA1*3600) \t\t\t#m/s, velocity\n", + "Re1 = (di1*10**-3)*v1*1000/(mu2*10**-3) \t\t\t#Reynold no.\n", + "Pr1 = Cp2*1000*(mu2*10**-3)/k2 \t\t\t#Prandtl no.\n", + "#umath.sing dittus boelter eq.\n", + "Nu1 = 0.023*(Re1)**(0.8)*(Pr1)**(0.3) \t\t\t#nusslet no.\n", + "h1 = round(Nu1*k2/(di1*10**-3),-1) \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "#Outer side (benzene) calculation\n", + "FA2 = (math.pi/4)*(di2*10**-3)**2-(math.pi/4)*(do1*10**-3)**2 \t\t\t#flow area\n", + "wp = math.pi*(di2*10**-3+do1*10**-3) \t\t\t#wettwd perimeter\n", + "dh = 4*FA2/wp \t\t\t#hydrolic diameter\n", + "bfr = Mb/rho1 \t\t\t#m**3/h benzene flow rate\n", + "v2 = bfr/(FA2*3600) \t\t\t#m/s, velocity\n", + "Re2 = dh*v2*rho1/(mu1*10**-3) \t\t\t#Reynold no\n", + "Pr2 = Cp1*10**3*(mu1*10**-3)/k1 \t\t\t#Prandtl no.\n", + "Nu2 = 0.023*(Re2)**(0.8)*(Pr2)**(0.4) \t\t\t#nusslet no.\n", + "h2 = Nu2*k1/(dh) \t\t\t#W/m**2 C, heat transfer coefficient\n", + "\n", + "print \"heat transfer coefficient based on inside area is %.0f W/m**2 C \"%(h1)\n", + "print \"heat transfer coefficient based on outside area is %.1f W/m**2 C \"%(h2)\n", + "\n", + "#Calculation of clean overall heat transfer coefficient, outside area basis\n", + "#from eq. 8.28\n", + "# Variables\n", + "l = 1. \t\t\t#assume , length\n", + "Ao = math.pi*do1*10**-3*l\n", + "Ai = math.pi*di1*10**-3*l\n", + "Am = (do1*10**-3-di1*10**-3)*math.pi*l/(math.log(do1*10**-3/(di1*10**-3)))\n", + "\n", + "#overall heat transfer coefficient\n", + "Uo = 1/((1/h2)+(Ao/Am)*((do1*10**-3-di1*10**-3)/(2*kw))+(Ao/Ai)*(1/h1))\n", + "Ui = Uo*Ao/Ai\n", + "\n", + "#Calculation of LMTD\n", + "dt1 = T1-T4\n", + "dt2 = T2-T3\n", + "LMTD = (dt1-dt2)/math.log(dt1/dt2) \t\t\t#math.log mean temp. difference correction factor\n", + "Q = HD*1000/3600 \t\t\t#W, heat required\n", + "Ao_ = Q/(Uo*LMTD) \t\t\t#m**@, required area\n", + "len = Ao_/(math.pi*do1*10**(-3)) \t\t\t#m, tube length necessary\n", + "\n", + "#(c)\n", + "la = 15. \t\t\t#m ,actual length\n", + "Aht = (math.pi*do1*10**(-3)*la)\n", + "Udo = Q/(Aht*LMTD) \t\t\t#W/m**2 C, overall heat transfer coefficient with dirt factor\n", + "#from eq. 8.2\n", + "Rdo = (1/Udo)-(1/Uo) \t\t\t#m**2 C/W\n", + "print \"overall heat transfer coefficient outside area basis is %.1f W/m**2 C \"%(Uo)\n", + "print \"overall heat transfer coefficient inside area basis is %.1f W/m**2 C \"%(Ui)\n", + "print \"The fouling factor is %f m**2 C/W\"%(Rdo)\n", + "\n", + "# note : rounding off error. please check." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2 Page No : 309" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tube side Pressure drop is 1.118e+04 N/m**2 \n", + "Shell side Pressure drop is 120 N/m**2 \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "Cp = 50. \t\t\t#tpd, plant capacity\n", + "T1 = 135. \t\t\t#C, Temp.\n", + "T2 = 40. \t\t\t#C temp.\n", + "T3 = 30. \t\t\t#C temp.\n", + "dt1 = (T1-T2) \t\t\t#C hot end temp. \n", + "dt2 = (T2-T3) \t\t\t#C cold end temp.\n", + "#Properties of ethylbenzene\n", + "rho1 = 840. \t\t\t#kg/m**3, density\n", + "cp1 = 2.093 \t\t\t#kj/kg K , specific heat\n", + "T = 87.5 \t\t\t#C\n", + "mu1 = math.exp(-6.106+1353/(T+273)+5.112*10**-3*(T+273)-4.552*10**-6*((T+273)**2))\n", + "k1 = 0.2142-(3.44*10**-4)*(T+273)+(1.947*10**-7)*(T+273)**2\n", + "k1_ = k1*0.86 \t\t\t#kcal/h m K\n", + "#properties of water\n", + "rho2 = 993. \t\t\t#kg/m**3, density\n", + "mu2 = 8*10.**-4 \t\t\t#kg/m s , vismath.cosity \n", + "cp2 = 4.175 \t\t\t#kj/kg K , specific heat\n", + "k2 = 0.623 \t\t\t#W/m K, thermal conductivity\n", + "k2_ = k2*0.8603 \t\t\t#kcal/h m**2 K\n", + "#Calculation\n", + "#(i) Energy balance\n", + "Cp = Cp*1000./24 \t\t\t#kg/h, plant capacity\n", + "Cp = 2083. \t\t\t#approx.\n", + "HD = Cp*cp1*dt1 \t\t\t#kj/h, Heat duty \n", + "HD_ = HD*0.238837 \t\t\t#kcal/h\n", + "wfr = HD/(cp2*dt2)\n", + "\n", + "#(ii)\n", + "mu1 = mu1 \t\t\t#cP, vismath.cosity of ethylbenzene\n", + "k1 = k1 \t\t\t#W/m K, thermal conductivity of ethylbenzene\n", + "\n", + "#(iii)\n", + "#LMTD calculation\n", + "LMTD = (dt1-dt2)/math.log(dt1/dt2)\n", + "#assume\n", + "Udo = 350. \t\t\t#kcal/h m**2 C, overall coefficient\n", + "A = HD_/(Udo*LMTD) \t\t\t#m**2, area required\n", + "\n", + "#(iv)\n", + "id_ = 15.7 \t\t\t#mm, internal diameter of tube\n", + "od = 19. \t\t\t#mm, outer diameter of tube\n", + "l = 3000. \t\t\t#mm, length\n", + "OSA = math.pi*(od*10**-3)*(l*10**-3) \t\t\t#m**2. outer surface area\n", + "n = A/OSA \t\t\t#no. of tubes required\n", + "fa = n*(math.pi/4)*(id_*10**-3)**2 \t\t\t#m**2, flow arae\n", + "lv = (wfr/1000)/(3600*fa) \t\t\t#m/s, linear velocity\n", + "\n", + "#(v)\n", + "n1 = 44. \t\t\t#total no. of tubes that can be accomodated in a 10 inch shell\n", + "np = 11. \t\t\t#no. of tubes in each pass\n", + "#(vi)\n", + "bf = 0.15 \t\t\t#m, baffel spacing\n", + "#(vii)\n", + "#estimation of heat transfer coefficient\n", + "#Tube side (water)\n", + "fa1 = (math.pi/4)*(id_*10**-3)**2*np \t\t\t#m**2, flow area\n", + "v1 = (wfr/1000.)/(3600*fa1) \t\t\t#m/s, velocity\n", + "Re = (id_*10**-3)*v1*rho2/mu2 \t\t\t#Reynold no.\n", + "#from fig . 8.11(a)\n", + "jh = 85. \t\t\t#colburn factor\n", + "#jh = (hi*di)/k*(cp*mu/k)**-1/3 \n", + "#assume, (cp*mu/k) = x\n", + "hi = jh*(k2_/(id_*10**-3))*(cp2*1000*mu2/k2)**(1/3) \t\t\t#kcal/h m**2 C\n", + "\n", + "#shell side(organic)\n", + "B = bf \t\t\t#m, baffel spacing\n", + "p = 0.0254 \t\t\t#m,radius of 1 tube\n", + "Ds = 0.254 \t\t\t#m, inside diameter of shell\n", + "c = 0.0064 \n", + "#from eq. 8.32\n", + "As = c*B*Ds/p \t\t\t#m**2, flow area\n", + "Gs = Cp/As \t\t\t#kg/m**2 h, mass flow rate of shell fluid\n", + "do = od/10 \t\t\t#cm, outside diameter of shell\n", + "#from eq. 8.31\n", + "Dh = 4*((0.5*p*100)*(0.86*p*100)-((math.pi*(do)**2)/8))/((math.pi*do)/2)\n", + "Dh_ = Dh*10**-2 \t\t\t#m, hydrolic diameter\n", + "Re1 = (Dh_*Gs)/(3600*(mu1*10**-3)) \t\t\t#Reynold no.\n", + "#from fig 8.11(b)\n", + "jh1 = 32 \t\t\t#colburn factor\n", + "ho = jh1*(k1_/Dh_)*((6)**(1./3))\n", + "#from eq. 8.28\n", + "ratio = od/id_ \t\t\t#ratio = Ao/Ai\n", + "Rdo = 0.21*10**-3 \t\t\t#outside dirt factor\n", + "Rdi = 0.35*10**-3 \t\t\t#inside dirt factor\n", + "Udo = 1/((1/ho)+Rdo+(ratio)*Rdi+(ratio)*(1/hi))\n", + "\n", + "#SECOND TRIAL\n", + "#estimation of heat transfer coefficient\n", + "#Tube side (water)\n", + "np1 = 12 \t\t\t#\n", + "fa2 = (math.pi/4)*(id_*10**-3)**2*np1 \t\t\t#m**2, flow area\n", + "v2 = (wfr/1000)/(3600*fa2) \t\t\t#m/s, velocity\n", + "Re2 = (id_*10**-3)*v2*rho2/mu2 \t\t\t#Reynold no.\n", + "#from fig . 8.11(a)\n", + "jht = 83. \t\t\t#colburn factor\n", + "#jh = (hi*di)/k*(cp*mu/k)**-1/3 \n", + "#assume, (cp*mu/k) = x\n", + "hit = jht*(k2_/(id_*10**-3))*(cp2*1000*mu2/k2)**(1./3) \t\t\t#kcal/h m**2 C\n", + "\n", + "#shell side\n", + "B2 = 0.1 \t\t\t#m, baffel spacing\n", + "p2 = 0.0254 \t\t\t#m,radius of 1 tube\n", + "Ds2 = 0.254 \t\t\t#m, inside diameter of shell\n", + "c2 = .0064\n", + "#from eq. 8.32\n", + "As2 = c2*B2*Ds2/p2 \t\t\t#m**2, flow area\n", + "Gs2 = Cp/As2 \t\t\t#kg/m**2 h, mass flow rate of shell fluid\n", + "do2 = od/10 \t\t\t#cm, outside diameter of shell\n", + "#from eq. 8.30\n", + "Dh2 = 4*((p2*100)**2-((math.pi*(do2)**2)/4))/((math.pi*do2))\n", + "Dh2_ = Dh2*10**-2 \t\t\t#m, hydrolic diameter\n", + "Re2 = (Dh2_*Gs2)/(3600*(mu1*10**-3))\n", + "#from fig 8.11(b)\n", + "jh2 = 48 \t\t\t#colburn factor\n", + "ho2 = jh2*(k1_/Dh2_)*((6)**(1./3))\n", + "#from eq. 8.28\n", + "ratio = od/id_ \t\t\t#ratio = Ao/Ai\n", + "Rdo2 = 0.21*10**-3 \t\t\t#outside dirt factor\n", + "Rdi2 = 0.35*10**-3 \t\t\t#inside dirt factor\n", + "Udo2 = 1/((1/ho2)+Rdo+(ratio)*Rdi+(ratio)*(1/hit))\n", + "\n", + "#from eq. 8.10(a)\n", + "tauc = (T2-T3)/(T1-T3) \t\t\t#Temprature ratio\n", + "R = (T1-T2)/(T2-T3) \t\t\t#Temprature ratio\n", + "Ft = 0.8 \t\t\t#LMTD correction ftor\n", + "Areq = HD_/(Udo2*Ft*LMTD) \t\t\t#area required\n", + "tubes = 48. \t\t\t#no. of tubes\n", + "lnt = 4.5 \t\t\t#length of 1 tube\n", + "Aavl = (math.pi*od*10**-3)*tubes*lnt \t\t\t#available area\n", + "excA = ((Aavl-Areq)/Areq)*100 \t\t\t#% excess area\n", + "\n", + "#Pressure drop calculation\n", + "#Tube side\n", + "#from eq. 8.33\n", + "Gt = wfr/(3600*fa2) \t\t\t#kg/m**2 s, mass flow rate of tube fluid\n", + "n2 = 4. \t\t\t#tube passes\n", + "fit = 1. \t\t\t#dimensionless vismath.cosity ratio\n", + "g = 9.8 \t\t\t#gravitational consmath.tant\n", + "f = 0.0037 \t\t\t#friction factor\n", + "dpt = f*Gt**2*lnt*n2/(2*g*rho2*id_*10**-3*fit) \t\t\t#kg/m**2, tube side pressure drop\n", + "\n", + "#eq.8.35\n", + "dpr = 4*n2*v2**2*rho2/(2*g) \t\t\t#kg/m**2, return tube pressure loss\n", + "dpr_ = dpr*9.801 \t\t\t#N/m**2\n", + "tpr = dpt+dpr \t\t\t#kg/m**2, total pressure drop\n", + "#shell side\n", + "fs = 0.052 \t\t\t#friction factor for shell\n", + "bf1 = 0.1 \t\t\t#m, baffel spacing\n", + "Nb = lnt/bf1-1 \t\t\t#no. of baffles\n", + "dps = fs*(Gs2/3600)**2*Ds*(Nb+1)/(2*g*rho1*Dh2_*fit) \t\t\t#kg/m**2, shell side pressure drop\n", + "dps_ = dps*9.81 \t\t\t#N/m**2, shell side pressure drop\n", + "print \"Tube side Pressure drop is %1.3e N/m**2 \"%(dpr_)\n", + "print \"Shell side Pressure drop is %.0f N/m**2 \"%(round(dps_,-1))\n", + "\n", + "# note : rounding off error." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3 Page No : 320" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Th2 = 49.5 C\n", + "The new rate of heat transfer : 161003 kcal/h\n", + "the heat teansfer rate will be affected by 1.3 percent \n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "#for hot stream\n", + "Wh = 10000. \t\t\t#kg/h, Rate of leaving a hydrolic system by the oil\n", + "Cph = 0.454 \t\t\t#Kcal/Kg C, specific heat of oil\n", + "Th1 = 85. \t\t\t#C initial temp. of oil\n", + "Th2 = 50. \t\t\t#C final temp. of oil \n", + "\n", + "#For cold stream\n", + "Cpc = 1. \t\t\t#Kcal/Kg C, specific heat of water\n", + "Tc2 = 30. \t\t\t#C final temp. of water\n", + "Tc1 = 38. \t\t\t#C initial temp. of water\n", + "\n", + "# Calculations\n", + "#from heat balance eq.\n", + "#kg/h, Rate of leaving a hydrolic system by the water\n", + "Wc = Wh*Cph*(Th1-Th2)/(Cpc*(Tc1-Tc2))\n", + "#For the hot stream\n", + "Cmin = Wh*Cph \t\t\t#Kcal/h C.Taking hot stream as min. stream\n", + "#For cold stream\n", + "Cmax = Wc*Cpc \t\t\t#Kcal/h C.Taking cold stream as max. stream\n", + "Cr = Cmin/Cmax \t\t\t#Capacity ratio\n", + "n = (Th1-Th2)/(Th1-Tc2) \t\t\t#effectiveness factor\n", + "#From eq. 8.57\n", + "#No. of transfer units\n", + "NTU = -(1+(Cr)**2)**-(1./2)*math.log(((2/n)-(1+Cr)-(1+(Cr)**2)**(1./2))/((2./n)-(1+Cr)+(1+(Cr)**2)**(1./2)))\n", + "Ud = 400. \t\t\t#kcal/h m**2C , overall dirty heat transfer coefficient\n", + "#from eq. 8.53\n", + "A = (NTU*Cmin)/Ud \t\t\t#Area required\n", + "#if the water rate is increased by 20 %,\n", + "a = 20.\n", + "Wc_ = Wc+(Wc*(a/100))\n", + "Cmax_ = Wc_*Cpc\n", + "Cr_ = Cmin/Cmax_\n", + "#From eq. 8.56\n", + "n_ = 2*((1+Cr_)+(1+(Cr_)**2)**(1./2)*(1+math.exp(-(1+(Cr_)**2)**(1./2)*NTU))/(1-math.exp(-(1+(Cr_)**2)**(1./2)*NTU)))**(-1)\n", + "Th2_ = Th1-(n_*(Th1-Tc2))\n", + "q1 = Wh*Cph*(Th1-Th2) \t\t\t#kcal/h previous rate of heat transfer\n", + "q2 = Wh*Cph*(Th1-Th2_) \t\t\t#kcal/h new rate of heat transfer\n", + "#increase in rate of heat transfer\n", + "dq = (q2-q1)/q1 \n", + "\n", + "# Results\n", + "print \"Th2 = %.1f C\"%Th2_\n", + "print \"The new rate of heat transfer : %d kcal/h\"%q2\n", + "print \"the heat teansfer rate will be affected by %.1f percent \"%(dq*100 )\n", + "\n", + "# note : rounding off error would be there." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4 Page No : 337" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the time required to heat the charge 22 min\n" + ] + } + ], + "source": [ + "import math\n", + "# Variables\n", + "p = 0.0795 \t\t\t#m. pitch of the coil\n", + "d1 = 0.0525 \t\t\t#m,coil diameter\n", + "h = 1.464 \t\t\t#m,height of the limpetted section\n", + "d2 = 1.5 \t\t\t#m,diameter of batch polymerization reactor\n", + "d3 = 0.5 \t\t\t#m,diameter of agitator\n", + "rpm = 150. \t\t\t#speed of agitator\n", + "rho = 850. \t\t\t#kg/m3,density of monomer\n", + "rho1 = 900. \t\t\t#kg/m3,density of fluid\n", + "mu = 0.7*10**-3 \t\t\t#poise, vismath.cosity of monomer\n", + "mu1 = 4*10.**-3 \t\t\t#poise, vismath.cosity of fluid\n", + "cp = 0.45 \t\t\t#kcal/kg C, specific heat of monomer\n", + "cp1 = 0.5 \t\t\t#kcal/kg C, specific heat of fluid\n", + "k = 0.15 \t\t\t#kcal/h mC, thermal conductivity of monomer\n", + "k1 = 0.28 \t\t\t#kcal/h mC, thermal conductivity of fluid\n", + "Rdi = 0.0002 \t\t\t#h m2 C/kcal, fouling factor for vessel\n", + "Rdc = 0.0002 \t\t\t#h m2 C/kcal, fouling factor for coil\n", + "Tci = 120. \t\t\t#C, initial temp. of coil liquid\n", + "Tvi = 25. \t\t\t#C, initial temp. of vessel liquid\n", + "Tvf = 80. \t\t\t#C, final temp. of vessel liquid\n", + "\n", + "#calculation\n", + "a = math.pi*d2*h \t\t\t#outside area of the vessel\n", + "x = 60. \t\t\t#%. added of the unwetted area to the wetted area\n", + "ao = ((d1+(x/100)*(p-d1))/p)*a \t\t\t#m**2,effective outside heat transfer area of vessel\n", + "ai = 6.9 \t\t\t#m**2,inside heat transfer area of vessel\n", + "#same as outside area , if thickness is very small\n", + "#vessel side heat transfer coefficient\n", + "Re = (d3**2*(rpm/60)*rho)/mu \t\t\t#reynold no.\n", + "Pr = ((cp*3600)*(mu))/k\n", + "#from eq. 8.66\n", + "y = 1 \t\t\t#x = mu/muw = 1\n", + "Nu = 0.74*(Re**(0.67))*(Pr**(0.33))*(y**(0.14)) \t\t\t#Nusslet no\n", + "hi = Nu*(k/d2) \t\t\t#heat transfer coefficient\n", + "\n", + "#coil side heat transfer coefficient\n", + "v = 1.5 \t\t\t#m/s, linear velocity of fluid\n", + "fa = ((math.pi/4)*d1**2) \t\t\t#m2, flow area of coil\n", + "fr = v*fa*3600 \t\t\t#m3/h , flow rate of the fluid\n", + "Wc = fr*rho \t\t\t#kg/h , flow rate\n", + "dh = (4*(math.pi/8)*d1**2)/(d1+(math.pi/2)*d1) \t\t\t#m,hydrolic diameter of limpet coil\n", + "Re1 = v*rho1*dh/mu1 \t\t\t#coil reynold no.\n", + "Pr1 = cp1*mu1*3600/k1 \t\t\t#prandtl no. of the coil fluid\n", + "#from eq. 8.68\n", + "d4 = 0.0321 \t\t\t#m, inside diameter of the tube\n", + "Nu1 = 0.021*(Re1**(0.85)*Pr1**(0.4)*(d4/d2)**(0.1)*y**0.14) \n", + "hc = Nu1*(k1/dh) \t\t\t#coil side coefficient\n", + "\n", + "U = 1/((1/hi)+(ai/(hc*ao))+Rdi+Rdc) \t\t\t#overall heat transfer corfficient\n", + "#from eq. 8.63\n", + "beeta = math.exp(U*ai/(Wc*cp1))\n", + "Wv = 2200. \t\t\t#kg, mass of fluid vessel\n", + "t = (beeta/(beeta-1))*((Wv*cp)/(Wc*cp1))*math.log((Tci-Tvi)/(Tci-Tvf)) \n", + "\n", + "# Results\n", + "print \"the time required to heat the charge %.0f min\"%(t*60)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + 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