5.1.1 Main Task

In the previous chapter, we considered convective-diffusive transport in long ( x direction) and thin ( y direction) flows. This implied that although convective fluxes were significant in both x and y directions, significant diffusion fluxes occurred only in the y direction; diffusion fluxes in the x direction are negligible. We now turn our attention to flows in which diffusive fluxes are comparable in both x and y directions. Thus, the general transport Equation (1.25) may be written ^[1] as

(5.1)

where

(5.2)

In Equation 5.2, the first term on the right-hand side represents the convective flux whereas the second term represents the diffusive flux. Note that suffix f is attached to the velocity appearing in the convective flux; the significance of this suffix will become clear in a later section. In Equation 5.1, r stands for radius. This makes the equation applicable to axisymmetric flows governed by equations written in cylindrical polar coordinates. When plane flows are considered, r=1 and Equation 1.25 is readily recovered. By way of reminder, we note that ? may stand for 1, u _i ( i=1, 2), u ₃ (velocity in the x ₃ direction), ? _k , T or h, and e and ?, and ? _eff is the effective exchange coefficient (see Equation 4.89).

Flows with comparable convective-diffusive fluxes in each direction occur routinely in most practical...