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Correlations for mass transfer coefficients
Sc 

DAB
;......Sh 
kc L
D AB
;.... Re 
u L

Sc: Schmidt number=
momentum diffusivity (/) /mass diffusivity (DAB)
Sh: Sherwood number=
Molecular mass transport resistance (L/DAB) /
Convective mass transfer resistance (1/kc)
L: characteristic length or diameter
kc: mass transfer coefficient
u∞: bulk fluid velocity
Flow past single sphere
Suspended particles; flow of gas past single sphere
Froessling Eq. (WWWR 30.9):
Sh  2  0.552 Re1/ 2 Sc1/ 3
for 2<Re<800;
0.6<Sc<2.7
If stagnant fluid: Sh=2 (exact solution)
Use physical properties of fluid
e.g. evaporation of water from falling water droplet into air;
Suspended particles; flow of liquid past single sphere
Brian and Hales Eq. (WWWR 30.7):
2 / 3 1/ 2
Sh  ( 4  1.21PeAB
) ;
PeAB  Re Sc
for PeAB<10,000
e.g. Dissolution of drug from tablet into flowing liquid
Flow past a flat plate
Laminar flow on flat plate, (Re uses L=total length of
plate): eq. 28.21
• ReL< 2E5
Sh  0.664 Re L
1/ 2
1/ 3
Sc
Turbulent flow on flat plate, eq. 28-26:
ReL>2E5
Sh  0.0365 Re L
Sc 

DAB
;......Sh 
kc L
D AB
0.8
Sc
u L
;.... Re 

e.g. chemical vapor deposition reactor;
1/ 3
Flow inside tubes
Laminar flow in tubes, mass transfer to
inside wall of pipe )(eq. 30-19 WWWR),
10<Re<2000:
1/ 3
D

Sh  1.86 Re Sc 
L

Turbulent flow in tubes, liquid (eq. 30-18
WWWR),
2000<Re<35,000
1000<Sc<2260
Sh  0.023 Re 0.83 Sc1/ 3
e.g. absorption/stripping columns
Sc 

DAB
;......Sh 
kc L
D AB
u L
;.... Re 

Flow normal to single cylinder
Eq. (30-16)
400<ReD<25,000
0.6<Sc<2.6
0.56
kc Sc
u
 0.281Re
0.4
D
e.g. humidification process—water drips vertically down
Outside walls of vertical cylinders and air flows horizontally
Across outside of cylinders; mass transfer of water into air
stream
Many more correlations available in McCabe and Smith
And WWWR
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