Page 49 - Modelling in Transport Phenomena A Conceptual Approach

30 CHAPTER 2. MOLECULAR AND CONVECTIVE TRANSPORT

0 Entering and/or leaving conduits,
0 Exchange of mass between the system and its surroundings through the
boundaries of the system, Le., interphase transport.

When a mass of species i enters and/or leaves the system by a conduit(s), the
characteristic velocity is taken as the average velocity of the flowing stream and it
is usually large enough to neglect the molecular flux compared to the convective
flux, Le., PQ >> 1. Therefore, &. (2.4-9) simplifies to
mi = ( volume ) ( velocity ) ( !Z ) (2.4-10)
Average
Mass of i

(2.411)

Summation of Eq. (2.411) over all species leads to the total mass flow rate, k,
entering and/or leaving the system by a conduit in the form
- 1 (2.412)

In terms of molar basis, Eqs. (2.4-11) and (2.412) take the form
I hi = ci (v)A = ci Q I (2.4 13)

I
17i = c(v)A = CQ (2.414)

On the other hand, when a mass of species i enters and/or leaves the system as
a result of interphase transport, the flux expression to be used is dictated by the
value of the Peclet number as shown in &. (2.48).

Example 2.4 Liquid t3 is flowing over a vertical plate as shown in Figure 2.7.
The surface of the plate is coated with a material A which has a very low solubility
in liquid B. The concentration distribution of species A in the liquid is given by
Bird et al. (1960) as

where CA, is the solubility of A in B, q is the dimensionless parameter defined by

and r(4/3) is the gamma function defined by