diff options
Diffstat (limited to 'Fluidization_Engineering/ch13.ipynb')
| -rw-r--r-- | Fluidization_Engineering/ch13.ipynb | 313 |
1 files changed, 313 insertions, 0 deletions
diff --git a/Fluidization_Engineering/ch13.ipynb b/Fluidization_Engineering/ch13.ipynb new file mode 100644 index 00000000..06efb739 --- /dev/null +++ b/Fluidization_Engineering/ch13.ipynb @@ -0,0 +1,313 @@ +{ + "metadata": { + "name": "ch13" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Chapter 13 : Heat Transfer between Fluidized Beds and Surfaces" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 1, Page 331\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#h on a Horizontal Tube Bank\n", + "\n", + "#Variable declaration\n", + "dp=57.0; #Particle size in micrometer\n", + "rhos=940.0; #Density of solids in kg/m**3\n", + "Cps=828.0; #Specific heat capacity of the solid in J/kg K\n", + "ks=0.20; #Thermal conductivity of solids in W/m k\n", + "kg=0.035; #Thermal concuctivity of gas in W/m k\n", + "umf=0.006; #Velocity at minimum fluidization condition in m/s\n", + "ephsilonmf=0.476;#Void fraction at minimum fluidization condition\n", + "do1=0.0254; #Outside diameter of tube in m\n", + "L=1;\n", + "uo=[0.05,0.1,0.2,0.35];#Superficial gas velocity in m/s\n", + "nw=[2.,3.1,3.4,3.5]; #Bubble frequency in s**-1\n", + "g=9.81; #Acceleration due to gravity in square m/s**2\n", + "\n", + "\n", + "#CALCULATION\n", + "dte=4.*do1*L/2.*L; #Hydraulic diameter from Eqn.(6.13)\n", + "db=(1+1.5)*0.5*dte; #Rise velocity of the bubble\n", + "ubr=0.711*(g*db)**0.5; #Rise velocity of bubble from Eqn.(6.7)\n", + "phib=0.19;#From Fig.(15) for ks/kg=5.7\n", + "ke=ephsilonmf*kg+(1-ephsilonmf)*ks*(1/((phib*(ks/kg))+(2/3.0)))\n", + " #Effective thermal conductivity of bed from Eqn.(3) \n", + " \n", + "n=len(uo);\n", + "i=0;\n", + "ub = [0,0,0,0]\n", + "delta = [0,0,0,0]\n", + "h = [0,0,0,0]\n", + "while i<n:\n", + " ub[i]=uo[i]-umf+ubr; #Velocity of bubbles in bubbling beds in Eqn.(6.8)\n", + " delta[i]=uo[i]/ub[i];#Fraction of bed in bubbles from Eqn.(6.29)\n", + " h[i]=1.13*(ke*rhos*(1-ephsilonmf)*Cps*nw[i]*(1-delta[i]))**0.5;\n", + " #Heat transfer coefficinet from Eqn.(18)\n", + " i=i+1;\n", + "\n", + "#OUTPUT\n", + "print 'Superficial gas velocity(m/s)',\n", + "print '\\tHeat transfer coefficient(W/m**2 k)'\n", + "i=0;\n", + "while i<n:\n", + " print '%f'%uo[i],\n", + " print '\\t\\t\\t%f'%h[i]\n", + " i=i+1;\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Superficial gas velocity(m/s) \tHeat transfer coefficient(W/m**2 k)\n", + "0.050000 \t\t\t270.297375\n", + "0.100000 \t\t\t323.421769\n", + "0.200000 \t\t\t315.487604\n", + "0.350000 \t\t\t292.370761\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 2, Page 332\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Effect of Gas Properties on h\n", + "\n", + "#Variable declaration\n", + "dp=80.; #Particle size in micrometer\n", + "rhos=2550.; #Density of solids in kg/m**3\n", + "Cps=756.; #Specific heat capacity of the solid in J/kg K\n", + "ks=1.21; #Thermal conductivity of solids in W/m k\n", + "kg=[0.005,0.02,0.2]; #Thermal concuctivity of gas in W/m k\n", + "ephsilonmf=0.476; #Void fraction at minimum fluidization condition\n", + "\n", + "#CALCULATION\n", + "delta=0.5*(0.1+0.3);#For a gently fluidized bed\n", + "nw=3.;#Bubble frequency in s**-1 from Fig.(5.12) at about 30cm above the distributor\n", + "n=len(kg);\n", + "i=0;\n", + "x = [0,0,0]\n", + "while i<n:\n", + " x[i]=ks/kg[i];#To find different values of ks/kg\n", + " i=i+1;\n", + "\n", + "phib=[0.08,0.10,0.20];#From Fig.(15) for different values of ks/kg\n", + "i=0;\n", + "ke = [0,0,0]\n", + "h1 =[0,0,0]\n", + "while i<n:\n", + " ke[i]=ephsilonmf*kg[i]+(1-ephsilonmf)*ks*(1/((phib[i]*(ks/kg[i]))+(2.0/3)))\n", + " #Effective thermal conductivity of bed from Eqn.(3)\n", + " \n", + " h1[i]=1.13*(ke[i]*rhos*(1-ephsilonmf)*Cps*nw*(1-delta))**0.5;#Heat transfer coefficinet from Eqn.(18)\n", + " i=i+1;\n", + "\n", + "#OUTPUT\n", + "print 'Thermal conductivity of Gas(W/m K))',\n", + "print '\\tMax. heat transfer coefficient(W/m**2 k)'\n", + "i=0;\n", + "while i<n:\n", + " print '%f'%kg[i],\n", + " print '\\t\\t\\t\\t%d'%h1[i]\n", + " i=i+1;\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thermal conductivity of Gas(W/m K)) \tMax. heat transfer coefficient(W/m**2 k)\n", + "0.005000 \t\t\t\t324\n", + "0.020000 \t\t\t\t567\n", + "0.200000 \t\t\t\t1157\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3, Page 332\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Effect of Particle Size on h\n", + "\n", + "#Variable declaration\n", + "rhos=2700.; #Density of solids in kg/m**3\n", + "Cps=755.; #Specific heat capacity of the solid in J/kg K\n", + "ks=1.2; #Thermal conductivity of solids in W/m k\n", + "kg=0.028; #Thermal concuctivity of gas in W/m k\n", + "ephsilonmf=0.476; #Void fraction at minimum fluidization condition\n", + "dp1=10E-3; #Particle size for which h=hmax in m\n", + "hmax=250.; #Max. heat transfer coefficient in W/m**2 K \n", + "nw=5.; #Bubble frequency in s**-1\n", + "delta=0.1; #Fraction of bed in bubbles\n", + "deltaw=0.1; #Fraction of bed in bubbles in wall region\n", + "dp=2E-3; #Diameter of particle in m\n", + "\n", + "#CALCULATION\n", + "x=ks/kg;\n", + "phib=0.11;\n", + "phiw=0.17;\n", + "ke=ephsilonmf*kg+(1-ephsilonmf)*ks*(1/((phib*(ks/kg))+(2.0/3)));\n", + "#Effective thermal conductivity of bed from Eqn.(3)\n", + "\n", + "hpacket=1.13*(ke*rhos*(1-ephsilonmf)*Cps*nw/(1-deltaw))**0.5;\n", + "#Heat transfer coefficient for the packet of emulsion from Eqn.(11)\n", + "\n", + "ephsilonw=ephsilonmf;#Void fraction in the wall region\n", + "\n", + "kew=ephsilonw*kg+(1-ephsilonw)*ks*((phiw*(ks/kg)+(1.0/3))**-1);\n", + "#Effective thermal conductivity in the wall region with stagnant gas from Eqn.(4)\n", + "\n", + "y=(2*kew/dp1)+(hmax*hpacket)/(((1-deltaw)*hpacket)-hmax);\n", + "#Calculating the term alphaw*Cpg*rhog*uo from Eqn.(16) by rearranging it\n", + "\n", + "h=(1-deltaw)/((2*kew/dp+y*(dp/dp1)**0.5)**-1+hpacket**-1);\n", + "#Heat transfer coeeficient from Eqn.(11) by using the value of y \n", + "\n", + "#OUTPUT\n", + "print 'The heat transfer coefficient for paricle size of %fm = %fW/m**2 K'%(dp,h);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The heat transfer coefficient for paricle size of 0.002000m = 194.873869W/m**2 K\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4, Page 334\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Freeboard Heat Exchange\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Hf=4.0; #Height of freeboard in m\n", + "uo=2.4; #Superficial gas velocity in m/s\n", + "ho=350.0; #Heat transfer coefficient at the bottom of freeboard region in W/m**2 K\n", + "hg=20.0; #Heat transfer coefficient in equivalent gas stream, but free of solids in W/m**2 K\n", + "\n", + "#CALCULATION\n", + "zf=[0,0.5,1,1.5,2,2.5,3,3.5,Hf];#Height above the top of the dense bubbling fluidized bed\n", + "hr=0;#Assuming heat transfer due to radiation is negligible\n", + "a=1.5/uo;#Since decay coefficient from Fig.(7.12), a*uo=1.5s**-1 \n", + "n=len(zf);\n", + "i=0;\n", + "h = []\n", + "while i<n:\n", + " h.append((hr+hg)+(ho-hr-hg)*math.exp(-a*zf[i]/2.0));#Heat transfer coefficient from Eqn.(24) for zf=Hf\n", + " i=i+1;\n", + "\n", + "hbar=(hr+hg)+2*(ho-hr-hg)*(1-math.exp(-a*Hf/2.0))/(a*Hf);#Mean heat transfer coefficient for the 4-m high freeboard from Eqn.(26)\n", + "\n", + "#OUTPUT\n", + "print 'The required relationship is h(W/m**2 K) vs. zf(m) as in Fig.(9a)'\n", + "print 'Height above the dense bubbling fluidized bed(m))',\n", + "print '\\tHeat transfer coefficient(W/m**2 k)'\n", + "i=0;\n", + "while i<n:\n", + " print '%f'%zf[i],\n", + " print '\\t\\t\\t\\t\\t\\t%f'%h[i]\n", + " i=i+1;\n", + "\n", + "print '\\nThe mean heat transfer coefficient for the 4-m high freeboard =%d W/m**2 K'%hbar\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required relationship is h(W/m**2 K) vs. zf(m) as in Fig.(9a)\n", + "Height above the dense bubbling fluidized bed(m)) \tHeat transfer coefficient(W/m**2 k)\n", + "0.000000 \t\t\t\t\t\t350.000000\n", + "0.500000 \t\t\t\t\t\t302.263958\n", + "1.000000 \t\t\t\t\t\t261.433158\n", + "1.500000 \t\t\t\t\t\t226.508723\n", + "2.000000 \t\t\t\t\t\t196.636271\n", + "2.500000 \t\t\t\t\t\t171.085009\n", + "3.000000 \t\t\t\t\t\t149.229857\n", + "3.500000 \t\t\t\t\t\t130.536154\n", + "4.000000 \t\t\t\t\t\t114.546583\n", + "\n", + "The mean heat transfer coefficient for the 4-m high freeboard =208 W/m**2 K\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |