A diffusion problem with chemical reaction

A substance is subjected to cylindrical Poiseuille flow, diffusion and a chemical reaction. In this paper the stationary state will be considered. It is assumed that the axial component of the diffusion can be neglected. Then the problem can be reduced to an eigenvalue problem determining an orthogonal set of eigenfunctions. Also a simplified model will be considered where the cylindrical wall is replaced by a flat wall. This problem can be solved by means of Laplace transformation. An explicit solution for the concentration at the wall has been obtained.