Page 417 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 397

Analysis
The Reynolds number is
Re=- D(V%)P
CL
- (6 x 10-2)(1.5 x 10-3)(1000) = 101 + Laminar flaw (1)
-
892 x
Note that the tern (D/L) Re Sc becomes
(+&=( ) (101)(737) = 2233

Since the concentration at the surface of the pipe is constant, the we of Eq. (9.5-73)
gives
Sh = 3.66 + 0.668 [(DIL) Re%]
1 + 0.04 [(D/L) ReScI2I3
0.0668 (2233)
= 3.66 + 1 + 0.04 (2233)2/3 = 22.7 (3)
- - (CAb)OUt] - [cA~ - (CAb)iTZ]
Considering the water in the pipe as a system, a macroscopic mass balance on
benzoic acid gives

(.D2/4)(v%) [(CAb)out - (CAb)in] = (@(kc)
-
Q AM ln cA~ (CAb)Wt 3
- ( CAb )in
~
\ /
(ACA)LM
(4)
Since (cA~)~~ Eq. (4) simplifies to
0,
=

Substitution of numerical values into Eq. (5) gives
{
(cA~)~~ 1 - exp - 4 (2)(22.7) I>
3.412
=
[ (6 x 10-2)(101)(737)
= 0.136kg/m3 (6)
Comment: One could also use Eq. (4.5-31) to calculate the Sherwood number,
%.e.,

Sh = 1.86 @~SC(D/L)]~/~
= 1.86 (2233)'13 = 24.3

which is not very much digerent jhm 22.7.