Page 717 - Bird R.B. Transport phenomena

§22.5 Mass Transfer and Chemical Reactions 697

(i) For small values of c Bx /c A0 , or for equal diffusivities,

Ha = (22.5-11)
be АО
(ii) For large values of c Bx /c A

Ha = (22.5-12)

(Hi) For all values ofc Boo /c AO (approximate),

ac B (22.5-13)
be
Equation 22.5-11 is particularly useful, since it is accurate for the common situation of nearly
equal diffusivities as well as for small c /c . Equation 22.5-13 is useful because it is valid for
A0
Boo
both large and very small values of ac %b /bc %i) . In addition, the exact solution always
BS
AS
Boo
A0
lies in the space between the curve of Eq. 22.5-13 and those portions of the curves of Eqs. 22.5-
11 and 12 that are closest to it. This is shown in Fig. 22.5-2, where these bounding approxima-
tions are compared to the exact solution.
We next note that we can replace the diffusivity ratio by the corresponding ratio of non-
reactive Sherwood numbers,
where the superscript 0 denotes the observed Sherwood number in the absence of chemical
reaction. We may thus obtain a set of model-insensitive bounding solutions

L A0

Sh°
(22.5-15)
bcWSh8
These equations have been shown 7 to provide convenient bounds for laminar and turbulent
boundary layers as well as the penetration model of Example 20.1-2. They thus form a highly
model-insensitive correlation and are widely useful.

100
- i
2 \
/ I
A /

I sq. 22.5-12 /
10
— 2
txa^i
sc )lution У Fig. 22.5-2. Model-
(Eq 22.5-10) insensitive correlations
Eq 22.5-IK for absorption with
1 _ uL! E- 4 i iq.2 2.5-13 rapid chemical reaction,
1 1 II 4_-
|
1
N
derived
from the pene-
1
0.01 0.1 1 1 1 IN 100 tration model, for the
10
Stoichiometric ratio, ac Boo /bc AQ case that 9) = 2ЯЬ .
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