Page 106 - Modelling in Transport Phenomena A Conceptual Approach

86 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

2. The diameter of the sphere does not change appreciably. Thus, the Reynolds
number and the terminal velocity remain constant.
3. Steady-state conditions prevail.

4. Physical properties of water do not change as a result of mass transfer.
Analysis
To determine the terminal velocity of the benzoic acid sphere, it is necessary to
calculate the Archimedes number using Eq. (4.3-6):
Ar = D&IP(PP - P)
P2
- (12 x 10-3)3(9.8)(1000)(1267 - 1000) = 5,68
-
(892 x 10-6)2 106
The Reynolds number is calculated from Eq. (4.3-1.2):

-
- 5*68 lo6 [1+ 0.0579 (5.68 x 106)0.412] -la214 = 4056
18
Hence, the terminal velocity is

- (892 x 10-6)(4056)
- = 0.3 m/ s
(1000)(12 x 10-3)
Since the benzoic acid sphere falls the distance of 3 m with a velocity of 0.3 m/s,
then the falling time is
Distance
t=
Time
3
=--
0.3 - ‘Os
The Shemood number is calculated from the Steinberger- Beybal correlation, Eq.
(4.3-36), OB
Sh = 0.347Re$62 Sc1l3
= 0.347 (4056)0.62(737)1/3 = 541

The average mass transfer coefficient is

1.21 x 10-9
= (541) ( 12 ) = 5.46 x m/ s