Page 325 - Modelling in Transport Phenomena A Conceptual Approach

8.5. MASS TRANSPORT WITH CONVECTION 305

Solution
Assumptions

1. Pseudo-steady-state behavior.
2. The system is isothermal.

3. The total pressun? remains constant.
4. The mole fraction of species A at the top of the tube is zero.

5. No turbulence is observed at the top of the tube.
Analysis

System: Liquid in the tube
The inventory rate equation for mass of A gives

- Rate of moles of A out = Rate of accumulation of moles of A (1)

where pi is the density of species A in the liquid phase and A is the cross-sectional
area of the tube.
The rate of evaporation from the liquid surface, h~, can be determined from Eq.
(8.5-17). For A = constant and XA~ 0, Eq. (8.5-17) duces to
=
A CDAB
nA=-- 141 - XA,) (3)
L
It should be kept in mind that Eq. (8.5-17) was developed for a steady-state case.
For the unsteady problem at hand, the pseudo-steady-state assumption implies that
Eq. (3) holds at any given instant, i.e.,

Substitution of Eq. (4) into Eq. (2) gives
1
t
” I’LdL
-cDABI~(~-zA,) dt=- MA Lo

L2 = - 2 MA CDAB ln(1- ZA,) ] t+L?
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