Page 407 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TWSFER WITH CONVECTION 387

Since v, # v,(z), the integral on the left-side of Eq. (9.515) can be rearranged as

Substitution of Eq. (9.514) into Eq. (9.516) yields

(9.517)

where Q is the volumetric flow rate.
On the other hand, since ~CA/~T = 0 as a result of the symmetry condition at
the center of the tube, the integral on the right-side of Eq. (9.515) takes the form

(9.518)

Substitution of Eqs. (9.5-17) and (9.518) into Eq. (9.515) gives the governing
equation for the bulk concentration in the form

(9.519)

The solution of Eq. (9.519) requires the boundary conditions associated with the
problem to be known.

Constant wall concentration
If the inner surface of the pipe is coated with species A, the molar flux of species
A on the surface can be represented by

(9.520)

It is implicitly implied in writing Eq. (9.520) that the concentration increases in
the radial direction. Substitution of E'q. (9.520) into Eq. (9.519) and rearrange-
ment yields

dCAb = TD I' kc dz (9.521)
CAW - CAb