Page 75 - Modelling in Transport Phenomena A Conceptual Approach

56 CHAPTER 3. INTERPHASE TRANSPORT

3.5 TRANSPORT ANALOGIES

Existing analogies in various transport processes depend on the relationship be-
tween the dimensionless numbers defined by Eqs. (3.410)-(3.412). In Section 3.1.1
we showed that
Lch
sfRe=T
1
(3.51)
On the other hand, substitution of Eqs. (3.2-11) and (3.3-11) into Eqs. (3.411)
and (3.412), respectively, gives
NU= - (3.52)
Lch
6t
and
Lch
Sh= - (3.53)
6,
Examination of Eqs. (3.51)-(3.5-3) indicates that
Interphase flux - Characteristic length (3.54)
-
Molecular flux Effective film thickness
Comparison of Eqs. (3.49) and (3.54) implies that
Diffusivity
Effective film thickness = (3.55)
Transfer coefficient
Note that the effective film thickness is the thickness of a fictitious film which would
be required to account for the entire resistance if only molecular transport were
involved.
Using Eqs. (3.51)- (3.53), it is possible to express the characteristic length as

Substitution of Nu = StH RePr and Sh = StM Re Sc into Eq. (3.56) gives
1
- f6 = StH Pr6t = StM sc6c (3.57)
2
3.5.1 The Reynolds Analogy

Similarities between the transport of momentum, energy and mass were first noted
by Reynolds in 1874. He proposed that the effective film thicknesses for the transfer
of momentum, energy and mass are equal, i.e.,
6 = St = 6, (3.58)
Therefore, 3. (3.57) becomes

f
- = StH Pr = StM sc (3.59)
2