Page 427 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSE'ER WTH CONVECTION 407

(9.5-143)

It is customary to write Eq. (9.5143) in terms of dV = Adz rather than dz, so
that Eq. (9.5143) becomes
d(e ca) =air (9.5-144)
-
dV
Equation (9.5-144) can also be expressed in the form

(9.5-145)

where ni is the molar flow rate of species i.
The variation of the number of moles of species i as a function of the molar
extent of the reaction is given by Eq. (5.3-10). It is also possible to express this
equation as
it( = ni, + ai 6 (9.5 146)
Let us assume that the rate of reaction has the form

(9.5147)

Substitution of Eq. (9.5-147) into Eq. (145) gives

(9.5148)

Integration of Eq. (9.5-148) depends on whether the volumetric flow rate is constant
or not.

9.5.3.1 Constant volumetric flow rate

When steady-state conditions prevail, the mass flow rate is constant. The volu-
metric flow rate is the mass flow rate divided by the total mass density, i.e.,

m
Q=- (9.5-149)
P
For most liquid phase reactions the total mass density, p, and hence the volumetric
flow rate are constant.
For gas phase reactions, on the other hand, the total mass density is given by
the ideal gas equation of state as

PM
p=- (9.5-150)
RT