Page 314 - Modelling in Transport Phenomena A Conceptual Approach

294 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

where K is an integration constant.
If the surface concentrations axe specified, Le.,

at r=R1 XA=~A~
(8.440)
at r=R2 XA=XA~

the molar transfer rate and the concentration distribution of species A are given
in Table 8.10.

Table 8.10 Rate of transfer and concentration distribution for one-dimensional
diffusion in a hollow sphere for the boundary conditions given by Eq. (8.440).

Molar Transfer
Constant Concentration Distribution
Rate

1 1

Example 8.13 Consider the transfer of species A from a spherical drop or a
bubble of radius R to a stationary fluid.
a) Determine the molar rate of species A transferred to the fluid.
b) Determine the concentration distribution of species A within the fluid.
c) Determine the Sherwood number.

Solution

Assumptions
1. Steady-state conditions prevail.

2. The concentration at the surface of the sphere is constant at CA, .

3. The concentration of species A far from the sphere is CA,.