Channel flow with rapidly reacting walls

Channel Flow with Soluble or Rapidly Reacting Walls... 

Channel Flow with Soluble or Rapidly Reacting Walls 67 with the function satisfying the recursion relation... 

For the fully developed velocity profile the mathematical problem again reduces to the solution of the steady form of the convective diffusion equation for the solute concentration. In contrast to the diffusion equation treated in the channel flow problem with soluble or rapidly reacting walls, it is necessary to include here the lateral convection term to account for the product removal through the membrane walls, putting... 

Levich (1962) showed that a similarity solution exists to the problem as posed. We present his solution in a somewhat different form with the aim of paralleling our earlier treatments of convective diffusion layers and, in particular, the developing diffusion layer in a channel flow with a rapidly reacting wall. In direct analogy with Eq. (4.3.4) we introduce the new dependent variable... 

The differential equation may be seen to be exactly the same as Eq. (4.3.7) governing the developing diffusion layer in channel flow, with the boundary conditions the same as those appropriate to the case of a rapidly reacting wall, for which the solution is given by Eq. (4.3.19). 

As the reacting gas flows down the channel, it interacts with the channel walls, decomposes, and leaves a film on these walls. If the wall deposit is rapid and heavy, the reactants will deplete so that the gas composition will vary with x. Although this is a technologically important case, it requires a two-dimensional (partial differential equations) description. For the present problem, we will assume that depletion is slow enough for us to neglect, and gas composition will not be a function of x. 

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