Page 613 - Bird R.B. Transport phenomena

§19.4 Use of the Equations of Change for Mixtures 593

Fig. 19.4-1. Condensation of a hot vapor A
on a cold surface in the presence of a non-
X X condensable gas B.
A ~ A8
Г stagnant gas
Boundary of
film

Direction of
movement of
condensable
vapor A
Cold
surface.

properties to be constant, evaluated at some mean temperature and composition. Neglect ra-
diative heat transfer.
(b) Generalize the result for the situation where both A and В are condensing on the wall,
and allow for unequal film thicknesses for heat and mass transport.

SOLUTION (a) To determine the desired quantities, we must solve the equations of continuity and en-
ergy for this system. Simplification of Eq. 19.1-10 and Eq. С of Table 19.2-1 for steady, one-
dimensional transport, in the absence of chemical reactions and external forces, gives
dN
Continuity of A: Al = 0 (19.4-1)
~dy

Energy: (19.4-2)

Therefore, both N Ay and e are constant throughout the film.
y
To determine the mole fraction profile, we need the molar flux for diffusion of A through
stagnant B:

(19.4-3)
Av
l - x A dy
Insertion of Eq. 19.4-3 into Eq. 19.4-1 and integration gives the mole fraction profile (see §18.2)

~4 /5 (19.4-4)
Here we have taken сЯЬ АВ to be constant, at the value for the mean film temperature. We can
then evaluate the constant flux N from Eqs. 19.4-3 and 4:
Ay
l-x
In A8 (19.4-5)

Note that N Ay is negative because species A is condensing. The last two expressions may be
combined to put the concentration profiles in an alternative form:
~ exp[(N /c® )y]
~
X A X A Ay AB (19.4-6)
- exp[(N /c® )8]
AB
Ay