Page 311 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WTHOUT CONVECTION 291

Multiplication of Eqs. (8.421) and (8.423) by H- and H+, respectively, and the
addition of these equations with l3q. (8.422) gives

8.4.2 Diffusion in Cylindrical Coordinates

Consider one-dimensional diffusion of species A in the radial direction through a
hollow circular pipe with inner and outer radii of R1 and R2, respectively, as shown
in Figure 8.29.

1 -

1 -NArl*

E

Figure 8.29 Diffusion through a hollow cylinder.

Since XA = xA(r), Table C.8 in Appendix C indicates that the only non-zero molar
flux component is NA, and it is given by
dXA
NA, = Ji, = - CDAB - (8.425)
dr
For a cylindrical differential volume element of thickness AT, as shown in Figure
8.29, Equation (8.41) is expressed in the form
(AN&)Ir - (ANAv)Ir+& = 0 (8.426)