Page 480 - Modelling in Transport Phenomena A Conceptual Approach

460 CHAPTER 10. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

The physical significance and the order of magnitude of the terms in &. (10.3-7)
are given in Table 10.6.

Table 10.6 The physical significance and the order of magnitude of the terms in
Eq. (10.3-7).
Term Physical Significance Order of Magnitude

Rate of diffusion

- Rate of accumulation cAl - CA,
aCA
at of mass A t

Therefore, the ratio of the rate of diffusion to the rate of accumulation of mass A
is given by

Rate of diffusion - DAB (CA~ - CA,)/L~ DAB t
-
-
Rate of mass A accumulation (CAI - cAo L2 (10.3-10)
which is completely analogous to the Fourier number, Fo .
Introduction of the dimensionless quantities

e= CAI - CA (10.3-11)
CAI - CA,
z
E=, (10.3-12)

'DAB t
7-z- (10.3-13)
L2
reduces Eqs. (10.3-7) and (10.3-8) to
ae =-
a2e
-
87- at2 (10.3-14)
at r=O e=i
at E=l e=o (10.3-15)
at E=-1 e=O
Note the Eqs. (10.3-14) and (10.3-15) are identical waUh Eqs. (10.2-14, and (10.2-
15). Therefore, the solution given by Eq. (10.2-32) is also valid for this case,
i.e.,
00
00
+
(10.3-16)
;)
s [(n + ;) 74 (10.3-16)
[(n
s
74
n=O
n=O