Page 632 - Bird R.B. Transport phenomena

2
Chapter 0

Concentration Distributions

with More Than One

Independent Variable

§20.1 Time-dependent diffusion
§20.2° Steady-state transport in binary boundary layers
§20.3* Steady-state boundary layer theory for flow around objects
§20.4* Boundary layer mass transport with complex interf acial motion
§20.5* Taylor dispersion in laminar tube flow

Most of the diffusion problems discussed in the preceding two chapters led to ordinary
differential equations for the concentration profiles. In this chapter we use the general
equations of Chapter 19 to set up and solve some diffusion problems that lead to partial
differential equations.
A large number of diffusion problems can be solved by simply looking up the solu-
tions to the analogous problems in heat conduction. When the differential equations and
the boundary and initial conditions for the diffusion process are of exactly the same form
as those for the heat conduction process, then the heat conduction solution may be taken
over with appropriate changes in notation. In Table 20.0-1 the three main heat transport
equations used in Chapter 12 are shown along with their mass transport analogs. Many
solutions to the nonflow equations may be found in the monographs of Carslaw and
1
Jaeger and of Crank. 2
Because the diffusion problems described by the equations in Table 20.0-1 are analo-
gous to the problems of Chapter 12, we do not discuss them extensively here. Instead,
we focus primarily on problems involving diffusion with chemical reactions, diffusion
with a moving interface, and diffusion with rapid mass transfer.
In §20.1 we discuss a variety of time-dependent diffusion problems. In §20.2 we pre-
sent some steady-state boundary layer problems involving binary mixtures. This is fol-
lowed by two boundary layer analyses for more complicated systems: the diffusion in
steady flow around arbitrary objects in §20.3, and the diffusion in flows with complex in-
terfacial motion in §20.4. Finally, in §20.5 we explore an asymptotic solution to the "Tay-
lor dispersion" problem.

1
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd edition, Oxford University Press
(1959).
2
J. Crank, The Mathematics of Diffusion, 2nd edition, Clarendon Press, Oxford (1975).
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