Page 105 - Modelling in Transport Phenomena A Conceptual Approach

4.3. FLOW PAST A SINGLE SPHERE 85

Steinberger-Treybal correlation
The correlation originally proposed by Steinberger and Treybal (1960) includes a
correction term for natural convection. The lack of experimental data, however,
makes this term very difficult to calculate in most cases. The effect of natural
convection becomes negligible when the Reynolds number is high and Steinberger-
Treybal correlation reduces to
I Sh = 0.347 Re$62 Sc1I3 I (4.3-36)

Equation (4.3-36) is recommended for liquids when

2000 5 Rep 5 16,900

4.3.3.1 Calculation of the mass transfer rate
Once the average mass transfer coefficient is estimated by using correlations, the
rate of mass of species d transferred is calculated as

(4.3-37)

Example 4.8 A solid sphere of benzoic acid (p = 1267 kg/ m3) with a diameter of
12 mm is dropped in a long cylindrical tank filled with pure water at 25 "C. If the
height of the tank is 3 m, determine the amount of benzoic acid dissolved from the
sphere when it reaches the bottom of the tank. The saturation solubility of benzoic
acid in water is 3.412 kg/ m3.

Solution

Physical properties
p = 1000 kg/ m3
For water (a) at 25°C (298K) : ,LL = 892 x kg/m. s
DAB = 1.21 x 10-~ m2/ s
The Schmidt number is

sc = -
P
PDAB
- 892 x = 737
-
(1000)(1.21 x 10-9)
Assumptions
1. Initial acceleration period is negligible and the sphere reaches its terminal
velocity instantaneously.