Page 478 - Modelling in Transport Phenomena A Conceptual Approach

458 CHAPTER io. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

As in Section 8.4, our analysis will be restricted to the application of Eq. (10.3-1)
to diffusion in solids and stationary liquids. The solutions of almost all imaginabIe
diffusion problems in different coordinate systems with various initial and boundary
conditions are given by Crank (1956). As will be shown later, conduction and
diffusion problems become analogous in dimensionless form. Therefore, solutions
given by Carslaw and Jaeger (1959) can also be used for diffusion problems.
The Biot number is given by Eq. (7.1-14) as

(Difference in driving force),,lid
Bi = (10.3-2)
(Difference in driving force)flusd

In the case of mass transfer, when BiM << 1 the internal resistance to mass transfer
is negligible and the concentration distribution is considered uniform within the
solid phase. When BiM >> 1, the external resistance to mass transfer is considered
negligible and the concentration in the fluid at the solid surface is almost the same
as in the bulk fluid.

10.3.1 Mass Tkansfer Into a Rectangular Slab
Consider a rectangular slab of thickness 2L as shown in Figure 10.4. Initially
the concentration of species A within the slab is uniform at a value of CA,. At
t = 0 the surfaces at z = f are kept at a concentration of CA~. To calculate the
L
amount of species A transferred into the slab, it is first necessary to determine the
concentration distribution of species A within the slab as a function of position
and time. -4 Az IC
i IN

NAZ IZ Iz+&

Figure 10.4 Mass transfer into a rectangular slab.