Here we've assumed that only the bottom wall has deposition, due perhaps to it being hot. To treat this problem we first need some nomenclature. We will assume that the gas velocity is the same everywhere. Once the diffusion front reaches the reactor walls, what happens depends on the shape and relative rates of diffusion, convection, and reaction. The net flux into a control volume arises from the derivative in x of the concentration, since the velocity is fixed.
H is the ratio of the volume of a segment of the reactor to the surface area.
Thus the characteristic time for consumption of reactants. The final case is when diffusion in the y-direction is slow compared to the reaction. The characteristic behavior exhibited in each regime is a useful guideline in more complex geometries where no analytic solution is possible.