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3.6 T ed Beds w o-Phase Fix 165

A typical v alue of Sh is 1000 and 1 for liquids and gases, respecti Thus, . ely v Sh numbers
are considerably lower for gases, about one order of magnitude, for the same Re p number
(Perry and Green, 1999). Ho v er , we k in gases is much higher due to the higher f D f values.
v
For both gas and liquid–solid systems, the Dwiedi and Upadhay equation could be
used (Smith, 1981):
0.458 dG  p  0.407
j j or   (3.354)
D H


k f 23
j D Sc (3.355)
u
s

h  c
 23
p
j f   (3.356)
H
cu s  f 
p
where:
G u , the fluid mass superficial velocity, kg/m 2 s
s
h f the heat transfer coef W/m icient, f 2 K
c p the specific heat capacity of the fluid, J/kg K
the thermal conductivity of the fluid, W/m K.
f
The above equations hold for Re p 10. ge At temperatures abo v e about 400 °C and for lar
particles ( 0.25 in), heat transfer by radiation maybe signif en into icant and should be tak
account.
For all the equations presented,
kd fp
Sh (3.357)
D f

du ps
Re
(3.358)
p

Sc (3.359)
D
f
where:
Re p the particle Reynolds number
Sh the Sherwood number
Sc the Schmidt number
u s the superficial v elocity
D f the dificient of the solute in the liquid phase fusion coef f
d p the particle diameter
the liquid kinematic viscosity .