Page 408 - Modelling in Transport Phenomena A Conceptual Approach

388 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

Since the wall concentration, CA, , is constant, integration of Eq. (9.5-21) yields

(9.522)

in which (kc)z is the average mass transfer coefficient from the entrance to the
point z defined by

(kc), = 1’ kc dz (9.5-23)
0
If Eq. (9.522) is solved for CA~, the result is

(9.524)

which indicates that the bulk concentration of species A varies exponentially with
the axial direction as shown in Figure 9.18.

Z

Figure 9.18 Variation of the bulk concentration of species A with the axial
direction for a constant wall concentration.

Evaluation of Eq. (9.5-22) over the total length, L, of the pipe gives

(9.525)

where

(9.526)

If Eq. (9.525) is solved for C A ~ the ~result is
,
~
~