{ "metadata": { "name": "", "signature": "sha256:0879cd22772a64b93e3052735e29d09cf3e246362da6a06c0b0212fbf34b9367" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 8: Condensation and boiling" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.1 , Page no:318" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "Ts = 80 ; #C\n", "Tw = 70 ; #C\n", "L = 1 ; #m\n", "g = 9.8 ; #m/s^2\n", "#From table A.1\n", "rho = 978.8 ; #kg/m^3\n", "k = 0.672 ; #W/m K\n", "hfg = 2309 ; #At 80 C,kJ/kg\n", "\n", "#calculations\n", "Tm = (Ts + Tw)/2 ; #Assuming condensate film is laminar and Re < 30\n", "u = 381 *10**-6 ; #kg/m s\n", "v = u/rho ;\n", "#Substituting in eqn 8.3.9, we get\n", "h = 0.943*(( hfg *1000*( rho**2)*g*(k**3)) /(( Ts -Tw)*u*L) )**(1/4) ; #W/m^2 K\n", "rate = h*L*(Ts -Tw)/( hfg *1000) ; #kg/m s\n", "Re = 4* rate /u;\n", "#Substituting h = Re*(lambda*1000)*u/(4*L*(Ts-Tw)), in eqn 8.3.12\n", "Re_1 = (((4* L*(Ts -Tw)*k/( hfg *1000* u)*(g/(v**2) )**(1/3) )+5.2)/1.08)**(1/1.22) ; #Substituting h = Re*(hfg*1000)*u/(4*L*(Ts-Tw))\n", "#From eqn 8.3.12\n", "h_1 = ((Re /(1.08*( Re**1.22) -5.2) )*k *(( g/v**2)**(1/3) )); #W/m^2 K\n", "m = h_1*L *10/( hfg *1000) ; #rate of condensation,kg/m s\n", "\n", "#result\n", "print\"Assuming condensate film is laminar and Re < 30\";\n", "print\"h =\",round(h,4),\"W/m^2 K\";\n", "print\"ReL =\",round(Re,4);\n", "print\"Initial assumption was wrong, Now considering the effect of ripples, we get\";\n", "print\"Re =\",round(Re_1,4);\n", "print\"Heat Transfer Cofficient =\",round(h_1,4),\"W/m^2 K\";\n", "print\"Rate of condensation =\",round(m,6),\"kg/m s\";" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Assuming condensate film is laminar and Re < 30\n", "h = 6078.7864 W/m^2 K\n", "ReL = 276.3936\n", "Initial assumption was wrong, Now considering the effect of ripples, we get\n", "Re = 320.4829\n", "Heat Transfer Cofficient = 7287.8478 W/m^2 K\n", "Rate of condensation = 0.031563 kg/m s\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.2 , Page no:321" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "Ts = 262 ; #K\n", "D = 0.022 ; #m\n", "Tw = 258 ; #K\n", "#Properties at Tm\n", "rho = 1324 ; #kg/m^3\n", "k = 0.1008 ; #W/m K\n", "g = 9.81 ; #m/s^2\n", "\n", "#calculations\n", "Tm = (Ts+Tw) /2;\n", "v = 1.90*10**-7 ; #m^2/s\n", "hfg = 215.1*10**3 ; #J/kg\n", "u = v*rho ; #Viscosity\n", "#From eqn 8.4.1\n", "h = 0.725*( hfg *( rho**2) *g*(k**3) /(( Ts -Tw)*u*D))**(1/4) ;\n", "rate = h*3.14*D*(Ts -Tw) / hfg ; #kg/s m\n", "Re = 4* rate /u ;\n", "\n", "#result\n", "print\"Heat transfer coefficient =\",round(h,4),\"W/m^2 K\";\n", "print\"Condensation rate per unit length =\",round(rate,6),\"kg/s m\";\n", "print\"Film Reynolds number =\",round(Re,4);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heat transfer coefficient = 2622.2475 W/m^2 K\n", "Condensation rate per unit length = 0.003369 kg/s m\n", "Film Reynolds number = 53.5629\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.3 , Page no:322" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "m = 25/60 ; #kg/sec\n", "ID = 0.025 ; #m\n", "OD = 0.029 ; #m\n", "Tci = 30 ; #C\n", "Tce = 70 ; #C\n", "g = 9.8 ; #m/s^2\n", "Ts = 100 ; #C\n", "#Assuming 5.3.2 is valid, properties at 50 C\n", "#Properties at Tm\n", "rho = 988.1 ; #kg/m^3\n", "k = 0.648 ; #W/m K\n", "Pr = 3.54 ;\n", "#From eqn 4.6.4a\n", "f = 0.005635;\n", "#From eqn 5.3.2\n", "Nu = 198.39 ;\n", "Tw = 90 ; #Assuming average wall temperature = 90 C\n", "#Properties at Tm\n", "#Properties at Tm\n", "rho = 961.9 ; #kg/m^3\n", "k = 0.682 ; #W/m K\n", "l = 0; #initial guess, assumed value for fsolve function\n", "\n", "#calculations\n", "v = 0.556*10**-6; #m^2/s\n", "Re = 4*m/(3.14*ID*rho *v);\n", "h = Nu*k/ID ;\n", "u = 298.6*10**-6 ; #kg/m s\n", "hfg = 2257*10**3 ; #J/kg\n", "#Equating the heat flow from the condensing steam to the tube wall, to the heat flow from the tube wall to the flowing water.\n", "#Solving the simplified equation\n", "h = 0.725*(hfg *( rho**2) *g*(k**3) /(( Ts -Tw)*u*OD))**(1/4) ;\n", "#By solving trial and error method, the temperature value we get\n", "T=86.964984;# in oC\n", "#Therefore\n", "hc = 21338.77/(100 - T)**(1/4) ; #W/m^2 K\n", "#Now, equating the heat flowing from the condensing steam to the tube wall to the heat gained by the water, we have\n", "#Solving by trial and error method, we get\n", "L=5.216152; #in meter\n", "\n", "#result\n", "print\"Temperature obtained from trial and error =\",round(T,4),\"oC\";\n", "print\"hc =\",round(hc,4),\"W/m^2 K\";\n", "print\"Length of the tube =\",round(L,4),\"m\";" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature obtained from trial and error = 86.965 oC\n", "hc = 11230.3034 W/m^2 K\n", "Length of the tube = 5.2162 m\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.4 , Page no:322" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "#Properties at (Tw+Ts)/2 = 100.5 degree celsius\n", "deltaT1 = 1; #in degree celsius\n", "p1 = 7.55*10**-4; #[K^(-1) p1 is coefficient of cubical expansion\n", "v1 = 0.294*10**-6; #[m^2/sec] viscosity at 100.5 degree celsius\n", "k1 = 0.683; #[W/m-k]thermal conductivity\n", "Pr1 = 1.74; #Prandtl number\n", "g = 9.81; #acceleration due to gravity\n", "L = 0.14*10**-2; #diameter in meters\n", "#Properties at (Tw+Ts)/2 =102.5\n", "deltaT2 = 5; #in degree celsius\n", "p2 = 7.66*10**-4; #[K^(-1) p1 is coefficient of cubical expansion\n", "v2 = 0.289*10**-6; #[m^2/sec] viscosity at 102.5 degree celsius \n", "k2 = 0.684; #[W/m-k]thermal conductivity\n", "Pr2 = 1.71; #Prandtl number \n", "#Properties at (Tw+Ts)/2 =105\n", "deltaT3 = 10; #in degree celsius\n", "p3 = 7.80*10**-4; #[K^(-1) p1 is coefficient of cubical expansion\n", "v3 = 0.284*10**-6; #[m^2/sec] viscosity at 105 degree celsius \n", "k3 = 0.684; #[W/m-k]thermal conductivity\n", "Pr3 = 1.68; #Prandtl number\n", "\n", "\n", "#Calculations\n", "\n", "Ra1 = ((p1*g*deltaT1*L**3)/(v1**2))*Pr1;\n", "q1=(k1/L)*(deltaT1)*(0.36+(0.518*Ra1**(1/4))/(1+(0.559/Pr1)**(9/16))**(4/9))\n", "\n", "Ra2 = ((p2*g*deltaT2*L**3)/(v2**2))*Pr2;\n", "q2=(k2/L)*(deltaT2)*(0.36+(0.518*Ra2**(1/4))/(1+(0.559/Pr2)**(9/16))**(4/9))\n", "\n", "Ra3 = ((p3*g*deltaT3*L**3)/(v3**2))*Pr3;\n", "q3=(k3/L)*(deltaT3)*(0.36+(0.518*Ra3**(1/4))/(1+(0.559/Pr3)**(9/16))**(4/9))\n", "\n", "#At 100 degree celsius\n", "Cpl = 4.220; #[kJ/kg]\n", "lamda = 2257; #[kJ/kg]\n", "ul = 282.4*10**-6; #viscosity is in kg/m-sec\n", "sigma = 589*10**-4; #Surface tension is in N/m\n", "pl = 958.4; #density in kg/m^3\n", "pv =0.598; #density of vapour in kg/m^3\n", "deltap = pl-pv;\n", "Prl = 1.75; #Prandtl no. of liquid\n", "Ksf = 0.013;\n", "deltaT11=5;\n", "deltaT12=10;\n", "deltaT13=20;\n", "q11=141.32*deltaT11**3\n", "q12=141.32*deltaT12**3\n", "q13=141.32*deltaT13**3\n", "\n", "\n", "L1 = (L/2)*(g*(pl-pv)/sigma)**(1/2);\n", "f_L = 0.89+2.27*math.exp(-3.44*L1**(0.5));\n", "q2 = f_L*((3.14/24)*lamda*10**(3)*pv**(0.5)*(sigma*g*(pl-pv))**(0.25));\n", "\n", "Tn=pow(q2/141.32,1/3)\n", "q3 = 0.09*lamda*10**3*pv*(sigma*g*(pl-pv)/(pl+pv)**(2))**(0.25);\n", "Ts1 = 140; #surface temperature in degree celsius\n", "Ts2 = 200; #surface temperature in degree celsius\n", "Ts3 = 600; #surface temperature in degree celsius\n", "Twm1 = (140+100)/2; #Mean film temperature\n", "#properties of steam at 120 degree celsius and 1.013 bar\n", "kv = 0.02558; #thermal conductivity in W/mK\n", "pv1 = 0.5654; #vapor density in kg/m**3\n", "uv=13.185*10**(-6); #viscosity of vapour in kg/m sec\n", "lamda1 = (2716.1-419.1)*10**(3);#Latent heat of fusion in J/kg\n", "hc = 0.62*((kv**3)*pv*(pl-pv)*g*lamda1/(L*uv*(140-100)))**(0.25);\n", "qrad = 5.67*10**(-8)*(413**4 - 373**4)/((1/0.9)+1-1);\n", "hr = qrad/(413-373);\n", "h = hc + 0.75*hr;\n", "\n", "hc_200 = 0.62*((kv**3)*pv*(pl-pv)*g*lamda1/(L*uv*(200-100)))**(0.25);\n", "qrad1 = 5.67*10**(-8)*(473**4 - 373**4)/((1/0.9)+1-1);\n", "hr_200 = qrad1/(200-100);\n", "h_200 = hc_200 +0.75*hr_200;\n", "hc_600 = 0.62*((kv**3)*pv*(pl-pv)*g*lamda1/(L*uv*(600-100)))**(0.25);\n", "qrad2 = 5.67*10**(-8)*(873**4 - 373**4)/((1/0.9)+1-1);\n", "hr_600 = qrad1/(600-100)\n", "\n", "#Results\n", "\n", "print \"\\n q/A = \",round(q1,2),\" W/m^2 at (Tw-Ts)=1\";\n", "print \"\\n q/A = \",round(q2,2),\" W/m^2 at (Tw-Ts)=5\";\n", "print \"\\n q/A = \",round(q3,2),\" W/m^2 at (Tw-Ts)=10\";\n", "print \"\\n q/A at deltaT = 5 degree celsius = \",q11,\" W/m^2\";\n", "print \"\\nq/A at deltaT = 10 degree celsius = \",q12,\" W/m^2\";\n", "print \"\\n q/A at deltaT =20 degree celsius = \",q13,\" W/m^2\";\n", "print \"\\n Peak heat flux L = \",round(L1,2); \n", "print \"\\n f(l) = \",round(f_L,2);\n", "print \"\\n q/A = \",q2,\" W/m^2\";\n", "print \"Tw-Ts = \",Tn,\" degree celsius\"\n", "print \"\\n\\n Minimum heat flux\";\n", "print \"\\n q/A \",q3, \"W/m^2\"\n", "print \"\\n\\n Stable film boiling\"\n", "print \"\\n hc = \",hc,\" W/m^2\"\n", "print \"\\n q/A due to radiation = \",qrad,\" W/m^2\";\n", "print \"\\n hr = \",hr,\" W/m^2 K \";\n", "print \"\\n Since hr" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.5 , Page no:337" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "D = 0.02 ; #m\n", "l = 0.15 ; #m\n", "T = 500+273 ; #K\n", "Tc = -196+273 ; #K\n", "e = 0.4;\n", "#Properties\n", "k = 0.0349 ; #W/m K\n", "rho = 0.80 ; #kg/m^3\n", "Cpavg = 1.048 ; #kJ/kg J\n", "rholiq = 800 ; #kg/m^3\n", "\n", "#calculations\n", "s = 5.670*10**-8;\n", "#Film boiling will occur, hence eqn 8.7.9 is applicable\n", "Tm = (T+Tc) /2; #Film boiling will occur\n", "u = 23*10**-6 ; #kg/m s\n", "latent = 201*10**3 ; #J/kg\n", "hfg = (latent + Cpavg *(Tm -Tc) *1000); #Jk/g\n", "hc = 0.62*((( k**3) *rho *799.2*9.81* hfg )/(D*u*(T-Tc)) )**(1/4) ; #W/m^2 K\n", "#Taking the emissivity of liquid surface to be unity and using equation 3.9.1, the exchange of radiant heat flux\n", "flux = s*(T**4- Tc**4) /(1/ e +1/1 -1) ; #W/m^2\n", "hr = flux /(T-Tc);\n", "#Since h_r < h_c, total heat transfer coefficient is determined from eqn 8.7.11\n", "h = hc +3/4* hr ; #W/m^2 K\n", "fluxi = h*(T-Tc);\n", "Rate = fluxi *3.14*D*l; #W\n", "\n", "#result\n", "print\"Initial heat flux =\",round(fluxi,4),\"W/m^2\";\n", "print\"Initial heat transfer rate =\",round(Rate,4),\"W\";" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Initial heat flux = 69646.6128 W/m^2\n", "Initial heat transfer rate = 656.0711 W\n" ] } ], "prompt_number": 5 } ], "metadata": {} } ] }