Page 69 - Modelling in Transport Phenomena A Conceptual Approach

50 CHAPTER 3. INTERPHASE TRANSPORT

at the wall, NA, ly=ol is

(3.3-1)

where Jiul is the molecular (or, diffusive) molar flux at the wall. For low mass
y=O
transfer rates Eq. (3.3-1) can be simplified to3

(3.3-2)

and the rate of moles of species A transferred, ?i~, from one side of the plate to
the flowing stream is
?i~ 1" 1" NA,dxdz (3.3-3)
=
Evaluation of NA, requires the determination of the concentration gradient at the
wall. Since this is almost impossible to obtain, in an analogous manner to the
definition of the heat transfer coefficient, the convection mass tmnsfer weflcient,
kc, is defined by4
1 NA, = kc (CAW - CA,) 1 (3.3-4)

The mass transfer coefficient has the units of m/s. It depends on the fluid flow
mechanism, fluid properties (density, viscosity, diffusion coefficient) and flow ge-
ometry.
Substitution of Eq. (3.3-4) into Eq. (3.3-3) gives the rate of moles of species A
transferred as

where (kc) is the mass transfer coefficient averaged over the area of the plate and
is defined by

1" 1" kc dxdz 1
L
w
(kc) = = ~1 1 kddz (3.3-6)
1" 1" dxdz

3Note that VI; is the molar average velocity defined by
- CAVA, +CBVBu
v-
C
At the wall, Le., y = 0, VB, = 0 due to no-slip boundary condition. However, VA, # 0 as a result
of the transfer of species A from the surface to the flowing stream. Therefore, vI;lV=o # 0 .
4Equation (3.3-4) may be called Newton's law of mass transfer as suggested by Slattery (1999).