Page 411 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 391

It is important to note that although the local concentration, CA, the bulk
concentration, CA~, and the wall concentration, CA,, may change along the axial
direction, the ratio given in Eq. (9.539) is independent of the axial coordinate4,
i.e.,

(9.540)
Equation (9.540) indicates that

Example 9.10 Consider the flow of a fluid with constant physical properties.
Show that the mass transfer coeficient is constant when the concentration profile
is fully developed.

Solution

For a fully developed concentration profile, the ratio given in Eq. (9.5-39) depends
only on the radial coordinate r, i.e.,

CA - cAb
= f (r)
- cAb
Differentiation of Eq. (1) with respect to T gives

which is valid at all points within the flow field. Evaluation of Eq. (2) at the surface

On the other hand, the molar flux of species A at the pipe surface is expressed as

41n the literature, the condition for the filly developed concentration profile is also given in
the form

Note that