dp=57.0; #Particle size in micrometer
rhos=940.0; #Density of solids in kg/m**3
Cps=828.0; #Specific heat capacity of the solid in J/kg K
ks=0.20; #Thermal conductivity of solids in W/m k
kg=0.035; #Thermal concuctivity of gas in W/m k
umf=0.006; #Velocity at minimum fluidization condition in m/s
ephsilonmf=0.476;#Void fraction at minimum fluidization condition
do1=0.0254; #Outside diameter of tube in m
L=1;
uo=[0.05,0.1,0.2,0.35];#Superficial gas velocity in m/s
nw=[2.,3.1,3.4,3.5]; #Bubble frequency in s**-1
g=9.81; #Acceleration due to gravity in square m/s**2
#CALCULATION
dte=4.*do1*L/2.*L; #Hydraulic diameter from Eqn.(6.13)
db=(1+1.5)*0.5*dte; #Rise velocity of the bubble
ubr=0.711*(g*db)**0.5; #Rise velocity of bubble from Eqn.(6.7)
phib=0.19;#From Fig.(15) for ks/kg=5.7
ke=ephsilonmf*kg+(1-ephsilonmf)*ks*(1/((phib*(ks/kg))+(2/3.0)))
#Effective thermal conductivity of bed from Eqn.(3)
n=len(uo);
i=0;
ub = [0,0,0,0]
delta = [0,0,0,0]
h = [0,0,0,0]
while i<n:
ub[i]=uo[i]-umf+ubr; #Velocity of bubbles in bubbling beds in Eqn.(6.8)
delta[i]=uo[i]/ub[i];#Fraction of bed in bubbles from Eqn.(6.29)
h[i]=1.13*(ke*rhos*(1-ephsilonmf)*Cps*nw[i]*(1-delta[i]))**0.5;
#Heat transfer coefficinet from Eqn.(18)
i=i+1;
#OUTPUT
print 'Superficial gas velocity(m/s)',
print '\tHeat transfer coefficient(W/m**2 k)'
i=0;
while i<n:
print '%f'%uo[i],
print '\t\t\t%f'%h[i]
i=i+1;
dp=80.; #Particle size in micrometer
rhos=2550.; #Density of solids in kg/m**3
Cps=756.; #Specific heat capacity of the solid in J/kg K
ks=1.21; #Thermal conductivity of solids in W/m k
kg=[0.005,0.02,0.2]; #Thermal concuctivity of gas in W/m k
ephsilonmf=0.476; #Void fraction at minimum fluidization condition
#CALCULATION
delta=0.5*(0.1+0.3);#For a gently fluidized bed
nw=3.;#Bubble frequency in s**-1 from Fig.(5.12) at about 30cm above the distributor
n=len(kg);
i=0;
x = [0,0,0]
while i<n:
x[i]=ks/kg[i];#To find different values of ks/kg
i=i+1;
phib=[0.08,0.10,0.20];#From Fig.(15) for different values of ks/kg
i=0;
ke = [0,0,0]
h1 =[0,0,0]
while i<n:
ke[i]=ephsilonmf*kg[i]+(1-ephsilonmf)*ks*(1/((phib[i]*(ks/kg[i]))+(2.0/3)))
#Effective thermal conductivity of bed from Eqn.(3)
h1[i]=1.13*(ke[i]*rhos*(1-ephsilonmf)*Cps*nw*(1-delta))**0.5;#Heat transfer coefficinet from Eqn.(18)
i=i+1;
#OUTPUT
print 'Thermal conductivity of Gas(W/m K))',
print '\tMax. heat transfer coefficient(W/m**2 k)'
i=0;
while i<n:
print '%f'%kg[i],
print '\t\t\t\t%d'%h1[i]
i=i+1;
rhos=2700.; #Density of solids in kg/m**3
Cps=755.; #Specific heat capacity of the solid in J/kg K
ks=1.2; #Thermal conductivity of solids in W/m k
kg=0.028; #Thermal concuctivity of gas in W/m k
ephsilonmf=0.476; #Void fraction at minimum fluidization condition
dp1=10E-3; #Particle size for which h=hmax in m
hmax=250.; #Max. heat transfer coefficient in W/m**2 K
nw=5.; #Bubble frequency in s**-1
delta=0.1; #Fraction of bed in bubbles
deltaw=0.1; #Fraction of bed in bubbles in wall region
dp=2E-3; #Diameter of particle in m
#CALCULATION
x=ks/kg;
phib=0.11;
phiw=0.17;
ke=ephsilonmf*kg+(1-ephsilonmf)*ks*(1/((phib*(ks/kg))+(2.0/3)));
#Effective thermal conductivity of bed from Eqn.(3)
hpacket=1.13*(ke*rhos*(1-ephsilonmf)*Cps*nw/(1-deltaw))**0.5;
#Heat transfer coefficient for the packet of emulsion from Eqn.(11)
ephsilonw=ephsilonmf;#Void fraction in the wall region
kew=ephsilonw*kg+(1-ephsilonw)*ks*((phiw*(ks/kg)+(1.0/3))**-1);
#Effective thermal conductivity in the wall region with stagnant gas from Eqn.(4)
y=(2*kew/dp1)+(hmax*hpacket)/(((1-deltaw)*hpacket)-hmax);
#Calculating the term alphaw*Cpg*rhog*uo from Eqn.(16) by rearranging it
h=(1-deltaw)/((2*kew/dp+y*(dp/dp1)**0.5)**-1+hpacket**-1);
#Heat transfer coeeficient from Eqn.(11) by using the value of y
#OUTPUT
print 'The heat transfer coefficient for paricle size of %fm = %fW/m**2 K'%(dp,h);
import math
#Variable declaration
Hf=4.0; #Height of freeboard in m
uo=2.4; #Superficial gas velocity in m/s
ho=350.0; #Heat transfer coefficient at the bottom of freeboard region in W/m**2 K
hg=20.0; #Heat transfer coefficient in equivalent gas stream, but free of solids in W/m**2 K
#CALCULATION
zf=[0,0.5,1,1.5,2,2.5,3,3.5,Hf];#Height above the top of the dense bubbling fluidized bed
hr=0;#Assuming heat transfer due to radiation is negligible
a=1.5/uo;#Since decay coefficient from Fig.(7.12), a*uo=1.5s**-1
n=len(zf);
i=0;
h = []
while i<n:
h.append((hr+hg)+(ho-hr-hg)*math.exp(-a*zf[i]/2.0));#Heat transfer coefficient from Eqn.(24) for zf=Hf
i=i+1;
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)
#OUTPUT
print 'The required relationship is h(W/m**2 K) vs. zf(m) as in Fig.(9a)'
print 'Height above the dense bubbling fluidized bed(m))',
print '\tHeat transfer coefficient(W/m**2 k)'
i=0;
while i<n:
print '%f'%zf[i],
print '\t\t\t\t\t\t%f'%h[i]
i=i+1;
print '\nThe mean heat transfer coefficient for the 4-m high freeboard =%d W/m**2 K'%hbar