In this paper a steady laminar 2D Poiseuille flow between twoplates with chemical reactions on the upper wall is considered. Thisis a typical configuration in flow chambers (like the BIACORE one), which are used for the determination of the rate constants of reversiblereactions between biological macromolecules. As the chamber thicknessis small compared to its length, simplifications are possible, so,some asymptotic limits of mass conservation equation coupled with thewall chemistry are presented. We obtain a system with a large Péclet number. The small effects of the flow on thechemical reaction, which depend on the combination of the Damköhler and Péclet numbers, are highlighted. The results of these equationsare favorably cross compared with the asymptotic (Lévêque)solution or with the simplified solutions (integral methods) found in the literature. The final result is that, due to the fact that theexchange coefficient is shown to be nearly constant, the simplifiedintegral method is derived in a more rigorous way and its area of useis improved.