Page 317 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WITHOUT CONVECTION 297

Since the temperature is constant and there is no volume change due to reaction,
the pressure and hence the total molar concentration, c, remains constant. Under
these conditions, from Table C.8 in Appendix C, the components of the molar flux
become’
NA, = -VAB - (8.4-45)
aCA
dr
(8.4-46)

Substitution of Eqs. (8.445) and (8.4-46) into Eq. (8.444) gives the governing
equation for the concentration of species A as

(8.4-47)

The boundary conditions associated with Eq. (8.447) are

(8.4-48)

(8.4-49)
at z =O CA = CA, (8.4-50)

(8.4-51)

The term ICs in EQ. (8.449) is the first-order surface reaction rate constant. In
writing Q. (8.4-51) it is implicitly assumed that no reaction takes place on the
surface at z = L. Since there is no mass transfer through this surface, = 0.
As we did in Section 8.2.4, this complicated problem will be solved by making
use of the area averaging technique. The area-averaged concentration for species
A is defined by

JdlrJdRcArdrd6 1 2~ R
-
(CA) = I” - ZJd Jd CArdrdO (8.452)
12“ r drd6

Although the local concentration, CA, is dependent on T and z, the area-averaged
concentration, (cA), depends only on z.
Area averaging is performed by integrating Eq. (8.447) over the crosssectional
area of the pore. The result is

‘From the stoichiometry of the reaction, the molar average velocity is zero.