{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 6 : Boiling and condensation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.1 Page No : 177" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "So a bubble nucleus that has been detached from a cavity will not collapse in the liquid if it is larger than 1.89 micrometer \n", "The superheat of the liquid is 9 C\n" ] } ], "source": [ "from scipy.optimize import fsolve \n", "import math \n", "import warnings\n", "warnings.filterwarnings('ignore', 'The iteration is not making good progress')\n", "# Variables\n", "#(a)\n", "Tsat = 350 \t\t\t#K, saturated temp.\n", "Tl = Tsat+5 \t\t\t#K, liquid temp.\n", "#By antoine eqn.\n", "T = Tl-273 \t\t\t#C, \n", "\n", "# Calculations and Results\n", "pl = math.exp(4.22658-(1244.95/(T+217.88)))\n", "ST = 26.29-0.1161*T \t\t\t#dyne/cm, Surface tension of liquid\n", "ST_ = ST*10**-3 \t\t\t#N/m Surface tension of liquid\n", "Lv = 33605 \t\t\t#kj/kgmol, molar heat of vaporization\n", "R = 0.08314 \t\t\t#m**3 bar/kgmol K, gas math.cosmath.tant\n", "r = (2*ST_*R*Tsat**2)/((Tl-Tsat)*pl*(Lv*10**3))\n", "print \"So a bubble nucleus that has been detached from a cavity will not collapse in \\\n", "the liquid if it is larger than %.2f micrometer \"%(r*10**6)\n", "\n", "#(b)\n", "r1 = 10**-6 \t\t\t#m\n", "#pl1 = exp(4.22658-(1244.95/(Tl_-273+217.88))) \t\t\t#vapour pressure\n", "#ST1 = 0.02629-1.161*10**-4(Tl_-273) \t\t\t#surface tension\n", "\n", "def f(Tl): \n", " return (Tl-Tsat)-2*(0.02629-1.161*10**-4*(Tl-273))*R*Tsat**2/(r1*Lv*10**3)\n", "Tl = fsolve(f,0.1)\n", "T_ = (Tl-273.5)-(Tsat-273)\n", "print \"The superheat of the liquid is %d C\"%(T_)\n", "\n", "# note : answers are slightly different because of rounding off error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.2 Page No : 180" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "total rate of boiling of water is 69 kg/h \n", "Qs2 compares reasonably well with the Qs1\n" ] } ], "source": [ "import math\n", "\n", "# Variables\n", "d = 0.35 \t\t\t#m, diameter of pan\n", "p = 1.013 \t\t\t#bar, pressure\n", "T1 = 115. \t\t\t#C, bottom temp.\n", "T2 = 100. \t\t\t#C, boiling temp.\n", "Te = T1-T2 \t\t\t#C, excess temp.\n", "#For Water\n", "mu1 = 2.70*10**-4 \t\t\t#Ns/m**2, vismath.cosity\n", "cp1 = 4.22 \t\t\t#kj/kg C, specific heat\n", "rho1 = 958. \t\t\t#kg/m63. density\n", "Lv1 = 2257. \t\t\t#kj/kg, enthalpy of vaporization \n", "s1 = 0.059 \t\t\t#N/m , surface tension\n", "Pr1 = 1.76 \t\t\t#Prandtl no.\n", "#For saturated steam\n", "rho2 = 0.5955\n", "#For the pan\n", "Csf = 0.013 \t\t\t#consmath.tant\n", "n = 1. \t\t\t#exponent\n", "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", "\n", "# Calculations and Results\n", "#from eq. 6.6 \t\t\t#heat flux\n", "Qs1 = mu1*Lv1*(g*(rho1-rho2)/s1)**(1./2)*(cp1*Te/(Csf*Lv1*(Pr1)**n))**3\n", "Rate = Qs1/Lv1 \t\t\t#kg/m**2 s. rate of boiling\n", "Ap = math.pi/4*d**2 \t\t\t#m**2, pan area\n", "Trate = Rate*Ap \t\t\t#kg/s, Total rate of boiling\n", "Trate_ = Trate*3600.5 \t\t\t#kg/h. Total rate of boiling\n", "print \"total rate of boiling of water is %.0f kg/h \"%(Trate_)\n", "\n", "#umath.sing Lienhard's eq., \t\t\t#critical heat flux\n", "Qmax = 0.149*Lv1*rho2*(s1*g*(rho1-rho2)/(rho2)**2)**(1/4)\n", "#by Mostinski eq.\n", "Pc = 221.2 \t\t\t#critical pressure\n", "Pr = p/Pc \t\t\t#reduced pressure\n", "hb = 0.00341*(Pc)**(2.3)*Te**(2.33)*Pr**(0.566) \t\t\t#boiling heat transfer coefficient\n", "hb_ = hb/1000 \t\t\t#kW/m**2 C boiling heat transfer coefficient\n", "Qs2 = hb_*(Te)\n", "print \"Qs2 compares reasonably well with the Qs1\"\n", "\n", "# note: rounding off error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.3 Page No : 181" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The boilins rate is 63 kg/m**2 h\n" ] } ], "source": [ "import math\n", "\n", "# Variables\n", "A = 12.5673\n", "B = 4234.6\n", "pv = 1.813\n", "T1 = 200. \t\t\t#C, tube wall temp.\n", "#For methanol\n", "Tc = 512.6 \t\t\t#K, critical temp.\n", "w = 0.556 \t\t\t#acentric factor\n", "Zra = 0.29056-0.08775*w\n", "R = 0.08314 \t\t\t#m**3bar/gmol K, universal gas consmath.tant\n", "Pc = 80.9 \t\t\t#bar, critical temp.\n", "Mw = 32. \t\t\t#g, molecular wt\n", "\n", "#Calculation\n", "#Estimation of liquid and vapour properties \n", "#from antoine eq.\n", "T = B/(A-math.log(pv)) \t\t\t#K, boiling point\n", "Te = (T1+273)-T \t\t\t#K, excess temp.\n", "Tm = ((T1+273)+T)/2 \t\t\t#K, mean temp.\n", "#Liquid properties\n", "#(a)\n", "Tr = T/Tc \t\t\t#K, reduced temp.\n", "#from Rackett technique\n", "Vm = R*Tc*(Zra)**(1+(1-Tr)**(2/7))/Pc \t\t\t#m**3/kg mol, molar volume\n", "rhol = Mw/Vm \t\t\t#kg/m**3, density of satorated liquid density\n", "#(b)\n", "#from Missenard technique\n", "T2 = 348. \t\t\t#K,given data temp.\n", "T3 = 373. \t\t\t#K,given data temp.\n", "Cp2 = 107.5 \t\t\t#j/g mol K specific heat at T2\n", "Cp3 = 119.4 \t\t\t#j/g mol K specific heat at T3\n", "#By linear interpolation at T = 353.7 K\n", "Cp = Cp2+(Cp3-Cp2)*((T-T2)/(T3-T2)) \t\t\t#kj/kg mol C, specific heat at T = 353.7 K\n", "Cp_ = Cp*0.03125 \t\t\t#kj/kg C\n", "#(c)Surface tension at given temp.(K)\n", "T4 = 313.\n", "St4 = 20.96\n", "T5 = 333.\n", "St5 = 19.4\n", "#By linear interpolation at T = 353.7 K\n", "S = 17.8 \t\t\t#dyne/cm, surface temp.\n", "#(d) liquid vismath.cosity\n", "T6 = 298. \n", "MUt6 = 0.55 \t\t\t#cP, liquid vismath.cosity at temp = 298\n", "MU = ((MUt6)**-0.2661+((T-T6)/233))**(-1/0.2661) \t\t\t#cP\n", "#(e)Prandtl no. a,b,c are consmath.tant\n", "a = 0.3225\n", "b = -4.785*10**-4\n", "c = 1.168*10**-7\n", "kl = a+b*T+c*T**2 \t\t\t#W/m C, thermal conductivity\n", "Prl = Cp_*1000*MU*10**-3/kl \t\t\t#Prandtl no.\n", "#(f)heat of vaporization at 337.5 K\n", "Lv = 1100. \t\t\t#kj/kg, enthalpy of vaporization\n", "\n", "#Properties of methanol vapour at Tm\n", "#(a)\n", "Vm1 = R*Tm/pv \t\t\t#m**3/kg mol, molar volume\n", "rhov = Mw/Vm1 \t\t\t#kg/m**3, density of vapour\n", "#(b) a1,b1,c1,d1 are math.cosmath.tants\n", "a1 = -7.797*10**-3\n", "b1 = 4.167*10**-5\n", "c1 = 1.214*10**-7\n", "d1 = -5.184*10**-11\n", "#thermal conductivity of vapour\n", "kv = a1+b1*Tm+c1*Tm**2+d1*Tm**3 \t\t\t#W/m C\n", "#(c)heat capacity of vapour, a2,b2,c2,d2 are math.cosmath.tants\n", "a2 = 21.15\n", "b2 = 7.092*10**-2\n", "c2 = 2.589*10**-5\n", "d2 = -2.852*10**-8\n", "#heat capacity of vapour, in kj/kh mol K\n", "Cpv = a2+b2*Tm+c2*Tm**2+d2*Tm**3\n", "\n", "#(d)vismath.cosity of vapour\n", "T7 = 67.\n", "MUt7 = 112.\n", "T8 = 127.\n", "MUt8 = 132.\n", "#from linear inter polation at Tm\n", "MUv = 1.364*10**-5 \t\t\t#kg/m s\n", "\n", "#from Rohsenow's eq.\n", "Csf = 0.027 \t\t\t#consmath.tant\n", "n = 1.7 \t\t\t#exponent value\n", "#from eq. 6.6\n", "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", "#heat flux \t\t\t#kW/m**2\n", "Q = MU*10**-3*Lv*(g*(rhol-rhov)/S*10**-3)**(1./2)*(Cp_*Te/(Csf*Lv*(Prl)**n))**3\n", "#from eq. 6.11\n", "#from eq 6.11, critical heat flux\n", "Qmax = 0.131*Lv*(rhov)**(1./2)*(S*10**-3*g*(rhol-rhov))**(1./4)\n", "#dimensionless radius r_\n", "r = 0.016\n", "r_ = r*(g*(rhol-rhov)/(S*10**-3))**(1./2)\n", "#peak heat flux\n", "Qmax1 = Qmax*(0.89+2.27*math.exp(-3.44*math.sqrt(r_)))\n", "#from eq. 6.12\n", "#heat transfer coefficient hb\n", "d = 0.032 \t\t\t#m, tube diameter\n", "hb = 0.62*((kv**3)*rhov*(694-rhov)*g*(Lv*10**3+0.4*Cpv*Te)/(d*MUv*Te))**(1./4)\n", "Qb = hb*Te \t\t\t#kw/m**2, heat flux\n", "BR = Qb*10**-3/Lv \t\t\t#kg/m**2s, boilng rate \n", "\n", "# Results\n", "print \"The boilins rate is %.0f kg/m**2 h\"%(BR*3600)\n", "\n", "# note : rounding off error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.4 Page No : 188" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The total tube length is 0.393 m\n" ] } ], "source": [ "import math \n", "\n", "# Variables\n", "W1 = 200. \t\t\t#kg/h, rate of entering toluene\n", "muv = 10.**-5 \t\t\t#kg/m s, vismath.cosity of toluene vapour\n", "mul = 2.31*10**-4 \t\t\t#kg/m s, vismath.cosity of benzene\n", "rhol = 753. \t\t\t#kg/m**3, density of benzene\n", "rhov = 3.7 \t\t\t#kg/m**3, density of toluene vapour\n", "Cpl = 1968. \t\t\t#j/kg C, specific heat of benzene\n", "kl = 0.112 \t\t\t#W/m C, thermal conductivity of benzene\n", "T1 = 160. \t\t\t#C tube wall temp.\n", "T2 = 120. \t\t\t#C , saturated temp.\n", "Te = T1-T2 \t\t\t#C, excess temp.\n", "Lv = 3.63*10**5 \t\t\t#j/kg, enthalpy of vaporization\n", "s = 1.66*10**-2 \t\t\t#N/m, surface tension\n", "\n", "#Calculation of hc & hb\n", "w = 0.125 \t\t\t#m, mean step size\n", "d = 0.0211 \t\t\t#, internal diameter of tube\n", "G = W1/(3600*math.pi/4*(d**2)) \t\t\t#kg/m**2 s, mass flow rate\n", "Re1 = G*(1-w)*d/mul \t\t\t#Reynold no. \n", "Prl = Cpl*mul/kl \t\t\t#Prandtl no.\n", "#from eq. 6.23\n", "x = (w/(1-w))**(0.9)*(rhol/rhov)**(0.5)*(muv/mul)**0.1 \t\t\t#let x = 1/succepsibility\n", "#from eq. 6.22 \n", "F = 2.35*(x+0.231)**0.736 \t\t\t#factor signifies 'liquid only reynold no.' to a two phase reynold no.\n", "#from eq. 7.21\n", "Re2 = 10**-4*Re1*F**1.25 \t\t\t#Reynold no.\n", "#from eq. 6.18\n", "S = (1+0.12*Re2**1.14)**-1 \t\t\t#boiling supression factor\n", "#from eq. 6.15\n", "hc = 0.023*Re1**(0.8)*Prl**(0.4)*(kl/d)*F \t\t\t#W/m**2 C, forced convection boiling part\n", "#from eq. 6.16\n", "mulv = (1/rhov)-(1/rhol) \t\t\t#m**3/kg, kinetic vismath.cosity of liquid vpaour\n", "dpsat = Te*Lv/((T2+273)*mulv) \t\t\t#N/m**2, change in saturated presssure \n", "#nucleate boiling part hb\n", "hb = 1.218*10**-3*(kl**0.79*Cpl**0.45*rhol**0.49*Te**0.24*dpsat**0.75*S/(s**0.5*mul**0.29*Lv**0.24*rhov**0.24))\n", "h = hc+hb \t\t\t#W/m**2 C, total heat transfer coefficient\n", "\n", "#calculation of required heat transfer area\n", "a = 5. \t\t\t#%, persentage change in rate of vaporization\n", "W2 = W1*a/100 \t\t\t#kg/h, rate of vaporization\n", "W2_ = W2/3600 \t\t\t#kg/s\n", "Q = W2_*Lv \t\t\t#W,heat load\n", "A = Q/(h*Te) \t\t\t#m**2, area of heat transfer\n", "l = A/(math.pi*d) \t\t\t#m, required length of tube\n", "#from table 6.2\n", "Tl = 0.393\n", "\n", "# Results\n", "print \"The total tube length is %.3f m\"%(Tl)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.5 Page No : 195" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total rate of condensation is 33.08 kg/h\n" ] } ], "source": [ "from scipy.optimize import fsolve \n", "import math \n", "\n", "# Variables\n", "rhol = 483. \t\t\t#kg/m**3, density of liquid propane\n", "mul = 9.1*10**-5 \t\t\t#P ,vismath.cosity of liquid propane\n", "kl = 0.09 \t\t\t#W/m K, thermal conductivity of liquid propane\n", "Lv = 326. \t\t\t#kj/kg. enthalpy of vaporization\n", "Cpl = 2.61 \t\t\t#kj/kg K, specific heat of liquid propane\n", "T1 = 32.\n", "T2 = 25. \t\t\t#C, surface temp.\n", "p1 = 11.2\n", "rhov = 24.7 \t\t\t#kg/m**3, density of vapour\n", "g = 9.8\n", "h = 0.3\n", "\n", "#Calculation\n", "Lv1 = Lv+0.68*Cpl*(T1-T2)\n", "#h = 0.943*(g*Lv1*10**3*rhol*(rhol-rhov)*kl**3/(mul*L*(T1-T2)))**(1/4)\n", "#Q = h*(L*1)*(T1-T2)\n", "#m = Q/(Lv1*10**3) = 1.867*10**-2*L**(3/4)\n", "Ref = 30.\n", "#from the relation 4*m/mu = Re\n", "L = (Ref*mul/(4*1.867*10**-2))**(4./3)\n", "m = 1.867*10**-2*L**(3./4) \t\t\t#rate of condensation for laminar flow\n", "#from eq. 6.32\n", "#Nu1 = h_/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1/3) = Ref/(1.08*(Ref)**(1.22)-5.2)\n", "Lp = h-L \t\t\t#length of plate over which flow is wavy\n", "A = Lp*1 \t\t\t#m**2 area of condensation\n", "\n", "\n", "def f(h1): \n", " return h1/kl*(mul**2/(rhol*(rhol-rhov)*g))**(1./3)-(29.76+0.262*h1)/(1.08*(29.76+0.262*h1)**(1.22)-5.2)\n", "h1 = fsolve(f,1000)\n", "m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n", "Ref1 = 4*m2/mul\n", "m2 = m+h1*A*(T1-T2)/(Lv1*10**3)\n", "\n", "# Results\n", "print \"Total rate of condensation is %.2f kg/h\"%(m2*3600)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.6 Page No : 199" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rate of condensation is 45.7 kg/h \n", "Rate of condensation is 1052 kg/h \n", "thus there will be increase in the calculated rate of heat transfer and in rate of condensation as 1.188 percent\n" ] } ], "source": [ "import math\n", "\n", "# Variables\n", "#data fot TCE\n", "T1 = 87.4 \t\t\t#C, normal boiling point\n", "T2 = 25. \t\t\t#C, surface temp.\n", "Lv = 320.8 \t\t\t#kj/kg, heat of vaporization\n", "cp = 1.105 \t\t\t#kj/kg C, specific heat\n", "mu = 0.45*10**-3 \t\t\t#P. liquid vismath.cosity\n", "k = 0.1064 \t\t\t#W/m C, thermal conductivity\n", "rhol = 1375. \t\t\t#kg/m**3, liquid density\n", "rhov = 4.44 \t\t\t#kg/m**3, density of vapour\n", "Tm = (T1+T2)/2. \t\t\t#C, mean film temp.\n", "d = 0.0254 \t\t\t#m, outside diameter of tube\n", "l = 0.7 \t\t\t#m, length\n", "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", "\n", "# Calculations and Results\n", "#(a) from eq. 6.34\n", "Lv1 = Lv+0.68*cp*(T1-T2)\n", "h = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(mu*d*(T1-T2)))**(1./4)\n", "A = math.pi*d*l \t\t\t#m**2, area of tube\n", "Q = h*A*(T1-T2) \t\t\t#W, rate of heat transfer\n", "m = (Q/Lv1)/1000 \t\t\t#kg/s rate of condensation\n", "print \"Rate of condensation is %.1f kg/h \"%(m*3600)\n", "\n", "#(b) from eq. 6.35\n", "N = 6. \t\t\t#No. of tubes in vertical tire\n", "h1 = 0.728*(g*Lv1*10**3*rhol*(rhol-rhov)*k**3/(N*mu*d*(T1-T2)))**(1./4)\n", "TN = 36. \t\t\t#total no. of tubes\n", "TA = TN*math.pi*d*l \t\t\t#m**2, total area\n", "Q1 = h1*TA*(T1-T2) \t\t\t#W, rate of heat transfer\n", "m1 = (Q1/Lv1)/1000. \t\t\t#kg/s rate of condensation\n", "print \"Rate of condensation is %.0f kg/h \"%(m1*3600)\n", "#from chail's corelation\n", "h2 = (1+0.2*cp*(T1-T2)*(N-1)/(Lv1))\n", "print \"thus there will be increase in the calculated rate of\\\n", " heat transfer and in rate of condensation as %.3f percent\"%(h2)\n", "\n", "# note : rounding off error." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.7 Page No : 201" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fraction of input vapour condensed is 52.7\n" ] } ], "source": [ "import math\n", "\n", "# Variables\n", "Gv = 20. \t\t\t#kg/m**2 s, mass flow rate of benzene\n", "di = 0.016 \t\t\t#m, tube diameter\n", "muv = 8.9*(10**-6) \t\t\t#P, vismath.cosity\n", "Lv = 391. \t\t\t#kj/kg., enthalpy of vaporization\n", "cpl = 1.94 \t\t\t#kj/kg C, specific heat\n", "Tv = 80. \t\t\t#C, normal boiling point of benzene\n", "Tw = 55. \t\t\t#C, wall temp.\n", "g = 9.8 \t\t\t#m/s**2, gravitational consmath.tant\n", "rhol = 815. \t\t\t#kg/m**3, density of benzene\n", "rhov = 2.7 \t\t\t#kg/m**3, density of benzene vapour\n", "kl = 0.13 \t\t\t#W/m C, thermal conductivity\n", "mu = 3.81*10**-4 \t\t\t#P, vismath.cosity of benzene\n", "l = 0.5 \t\t\t#m, length of tube\n", "\n", "#calculation\n", "Rev = di*Gv/muv \t\t\t#Reynold no. of vapour\n", "#from eq. 6.38\n", "Lv1 = Lv+(3./8)*cpl*(Tv-Tw)\n", "#heat transfer corfficient , h\n", "h = 0.555*(g*rhol*(rhol-rhov)*kl**3*Lv1*10**3/(di*mu*(Tv-Tw)))**(1./4)\n", "Aavl = math.pi*di*l \t\t\t#m**2, available area\n", "Q = Aavl*h*(Tv-Tw) \t\t\t#W, rate of heat transfer\n", "m = Q/(Lv1*10**3) \t\t\t#kg/s, rate of condensation of benzene\n", "Ratei = Gv*(math.pi/4)*di**2 \t\t\t#kg/s rate of input of benzene vapour\n", "n = m/Ratei \n", "\n", "# Results\n", "print \"fraction of input vapour condensed is %.1f\"%(n*100)\n", "\n", "# note : rouding off error." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }