Page 410 - Modelling in Transport Phenomena A Conceptual Approach

390 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

Integration of Eq. (9.5-34) gives the variation of the bulk concentration of species
A in the axial direction as

(9.535)

Therefore, the bulk concentration of species A varies linearly in the axial direction
as shown in Figure 9.19.

Z

Figure 9.19 Variation of the bulk concentration of species A with the axial
direction for a constant wall heat flux.

Evaluation of Q. (9.535) over the total length gives the bulk concentration of
species A at the exit of the pipe as

- 4 NAwL (9.536)
- + 'DAB Re Sc
The rate of moles of species A transferred is given by

nA = (CAbo,t - CAbi, 1 (9.537)

Substitution of &. (9.536) into Eq. (9.537) yields

T~A (TDL)NA, (9.538)
=
9.5.1.1 Fully developed concentration profile
If the ratio
(9.539)

does not vary along the axial direction, then the concentration profile is said to be
fully developed.