Page 312 - Modelling in Transport Phenomena A Conceptual Approach

292 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

Dividing Eq. (8.426) by AT and taking the limit as Ar 40 gives

lim (ANA, I+ - (ANA, Ir+Ar =O (8.427)
Ar-0 AT

(8.428)

Since flux times area gives the molar transfer rate of species A, +LA, it is possible
to conclude that
ANA, = constant = li~ (8.429)
Note that the area A in Eq. (8.429) is perpendicular to the direction of mass flux,
and is given by
A = 2xrL (8.430)

Substitution of Eqs. (8.425) and (8.430) into Eq. (8.429) and integration gives
/A. \ I
(8.431)

where K is an integration constant.
If the surface concentrations are specified, Le.,

at T=R~ XA=XA,
(8.432)
at r=R2 XA=XA~
the molar transfer rate and the concentration distribution of species A are given
in Table 8.9.

Table 8.9 Rate of transfer and concentration distribution for onedimensional
diffusion in a hollow cylinder for the boundary conditions given by Eq. (8.432).

Molar Transfer
Constant Concentration Distribution
Rate

None

DAB