{ "metadata": { "name": "", "signature": "sha256:69d28aca1d8ec525f15842df275d6e6c6108139c968df651029692a500222ce7" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 11 : Particle to Gas Mass and Heat Transfer" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", "For more information, type 'help(pylab)'.\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 1, Page 265\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "db=0.37; #Equilibrium bubble size in cm\n", "dp=0.028; #Particle size in cm\n", "rhos=1.06; #Density of solids in g/cc\n", "ephsilonmf=0.5; #Void fraction at minimum fluidization condition\n", "phis=0.4; #Sphericity of solids\n", "gammab=0.005; #Ratio of volume of dispersed solids to that of bubble phase\n", "rhog=1.18E-3; #Density of air in g/cc\n", "myu=1.8E-4; #Viscosity of gas in g/cm s\n", "D=0.065; #Diffusion coefficient of gas in cm**2/s\n", "Sc=2.35; #Schmidt number\n", "etad=1; #Adsorption efficiency factor\n", "y=1;\n", "umf=1.21; #Velocity at minimum fluidization condition in cm/s\n", "ut=69; #Terminal velocity in cm/s\n", "g=980; #Acceleration due to gravity in square cm/s**2\n", "uo=[10,20,30,40,50];#Superficial gas velocity in cm/s\n", "\n", "#CALCULATION\n", "n=len(uo);\n", "i=0;\n", "Rept=(dp*ut*rhog)/myu;\n", "Shstar=2+(0.6*(Rept**0.5)*(Sc**(1/3)));#Sherwood no. from Eqn.(1)\n", "Kbc=4.5*(umf/db)+5.85*((D**0.5*g**0.25)/db**(5/4));#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", "ubr=0.711*(g*db)**0.5;#Rise velocity of the bubble\n", "x = [0,0,0,0,0]\n", "Shbed = [0,0,0,0,0]\n", "Rep = [0,0,0,0,0]\n", "while i" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 2, Page 267" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.optimize import fsolve \n", "import math \n", "\n", "#INPUT\n", "umf=0.12 #Velocity at minimum fluidization condition in cm/s\n", "uo=40.; #Superficial gas velocity in cm/s\n", "ub=120; #Velocity of the bubble in cm/s\n", "D=0.7; #Diffusion coefficient of gas in cm**2/s\n", "abkbe1=1.; #Bubble-emuslion interchange coefficient for non absorbing particles(m=0)\n", "abkbe2=18.; #Bubble-emuslion interchange coefficient for highly absorbing particles(m=infinity)\n", "g=980.; #Acceleration due to gravity in square cm/s**2\n", "\n", "#CALCULATION\n", "#For non absorbing particles m=0,etad=0\n", "Kbc=(ub/uo)*(abkbe1);\n", "dbguess=2;#Guess value of db\n", "def solver_func(db): #Function defined for solving the system\n", " return abkbe1-(uo/ub)*(4.5*(umf/db)+5.85*(D**0.5*g**0.25)/(db**(5/4.)));#Eqn.(10.27)\n", "\n", "d=fsolve(solver_func,dbguess)\n", "#For highly absorbing particles m=infinity, etad=1\n", "M=abkbe2-(uo/ub)*Kbc;\n", "#For intermediate condition\n", "alpha=100.;\n", "m=10.;\n", "etad=1./(1+(alpha/m));#Fitted adsorption efficiency factor from Eqn.(23)\n", "abkbe3=M*etad+(uo/ub)*Kbc;\n", "\n", "#OUTPUT\n", "print 'For non absorbing particles:\\tDiameter of bubble=%fcm\\tBubble-cloud interchange coefficient=%fs**-1'%(d,Kbc);\n", "print 'For highly absorbing partilces:\\tM=%f'%(M);\n", "print 'For intermediate condition:\\tFitted adsorption efficiency factor:%f\\tBubble-emuslion interchange coefficient:%fs**-1'%(etad,abkbe3);\n", "\n", "#====================================END OF PROGRAM ======================================================" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For non absorbing particles:\tDiameter of bubble=6.010032cm\tBubble-cloud interchange coefficient=3.000000s**-1\n", "For highly absorbing partilces:\tM=17.000000\n", "For intermediate condition:\tFitted adsorption efficiency factor:0.090909\tBubble-emuslion interchange coefficient:2.545455s**-1\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 3, Page 273\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "rhos=1.3; #Density of solids in g/cc\n", "phis=0.806; #Sphericity of solids\n", "gammab=0.001; #Ratio of volume of dispersed solids to that of bubble phase\n", "rhog=1.18E-3; #Density of air in g/cc\n", "Pr=0.69; #Prandtl number\n", "myu=1.8E-4; #Viscosity of gas in g/cm s\n", "Cpg=1.00; #Specific heat capacity of gas in J/g K\n", "ephsilonmf=0.45; #Void fraction at minimum fluidization condition\n", "kg=2.61E-4; #Thermal concuctivity of gas in W/cm k\n", "dp=0.036; #Particle size in cm\n", "umf=6.5; #Velocity at minimum fluidization condition in cm/s\n", "ut=150.; #Terminal velocity in cm/s\n", "db=0.4; #Equilibrium bubble size in cm\n", "etah=1; #Efficiency of heat transfer\n", "uo=[10.,20.,30.,40.,50.];#Superficial gas velocity in cm/s\n", "g=980.; #Acceleration due to gravity in square cm/s**2\n", "\n", "#CALCULATION\n", "Nustar=2+(((dp*ut*rhog)/myu)**0.5*Pr**(1./3));#Nusselt no. from Eqn.(25)\n", "Hbc=4.5*(umf*rhog*Cpg/db)+5.85*((kg*rhog*Cpg)**0.5*g**0.25/db**(5./4));#Total heat interchange across the bubble-cloud boundary from Eqn.(32)\n", "ubr=0.711*(g*db)**0.5;#Rise velocity of the bubble from Eqn.(6.7)\n", "n=len(uo);\n", "i=0;\n", "x = [0,0,0,0,0]\n", "Nubed = [0,0,0,0,0]\n", "Rep = [0,0,0,0,0]\n", "\n", "while i" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Example 4, Page 274\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "import math\n", "\n", "#Variable declaration\n", "rhog=1.2; #Density of air in kg/m**3\n", "myu=1.8E-5; #Viscosity of gas in kg/m s\n", "kg=2.6E-2; #Thermal concuctivity of gas in W/m k\n", "dp=1E-4; #Particle size in m\n", "rhos=8920; #Density of solids in kg/m**3\n", "Cps=390; #Specific heat capacity of the solid in J/kg K\n", "ephsilonf=0.5; #Void fraction of the fluidized bed\n", "umf=0.1; #Velocity at minimum fluidization condition in m/s\n", "uo=0.1; #Superficial gas velocity in m/s\n", "pi=3.14\n", "\n", "#CALCULATION\n", "to=0; #Initial temperature of the bed\n", "T=100; #Temperature of the bed\n", "t=0.99*T; #Particle temperature i.e. when it approaches 1% of the bed temperature\n", "mp=(pi/6)*dp**3*rhos; #Mass of the particle\n", "A=pi*dp**2; #Surface area of the particle\n", "Rep=(dp*uo*rhog)/myu; #Reynold's no. of the particle\n", "Nubed=0.0178; #Nusselt no. from Fig.(6)\n", "hbed1=(Nubed*kg)/dp; #Heat transfer coefficient of the bed\n", "t1=(mp*Cps/(hbed1*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(a)\n", "hbed2=140*hbed1;#Since from Fig.(6) Nup is 140 times Nubed\n", "t2=(mp*Cps/(hbed2*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(b)\n", "\n", "#OUTPUT\n", "print 'Case(a):Using the whole bed coefficient from Fig.(6)'\n", "print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.0fs'%t1\n", "print 'Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)'\n", "print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.2fs'%t2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Case(a):Using the whole bed coefficient from Fig.(6)\n", "\tTime needed for the particle approach 1 percentage of the bed temperature is 58s\n", "Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)\n", "\tTime needed for the particle approach 1 percentage of the bed temperature is 0.41s\n" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }