Page 307 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WlTHOUT CONVECTION 287

where K is an integration constant. The determination of LA and K requires two
boundary conditions. Depending on the type of the boundary conditions used, the
molar transfer rate of species A as well as the concentration distribution of species
A as a function of position are determined from Eq. (8.412).
If the surface concentrations are specified, i.e.,

at z=O XA=XA,
(8.413)
at z=L XA=XA,
the molar transfer rate and the concentration distribution of species A are given
in Table 8.8.
Table 8.8 Rate of transfer and concentration distribution for one-dimensional
diffusion in rectangular coordinates for the boundary conditions given by
Eq. (8.413).
Molar Transfer
Constants Concentration Distribution
Rate

JXA,
None

JXA, Jo 1
f" dz
-
DAB
10 A0

A

JXA,
DAB
A

Example 8.12 Two large tanks are connected by a truncated conical duct as
shown in Figure 8.27. The diameter at z = 0 is 6mm and the diameter at
z = 0.2m is 10mm. Gas compositions in the tanks are given in terms of mole
percentages. The pressure and temperature throughout the system are latm and
25 "C, respectively, and DAB = 3 x m2/ s.