Onset of convection in a horizontal porous layer driven by catalytic surface reaction on the lower wall

The onset of convection in a horizontal layer filled with a fluid-saturated porous medium is studied in this paper. On the lower wall there is an exothermic surface reaction, described by the Arrhenius kinetics, while the upper wall is subjected to uniform temperature and concentration. The problem, cast in dimensionless form, is governed by three dimensionless parameters pertaining to the exothermic reaction and the Lewis number. Once the basic state is solved, a linearized stability analysis is then performed and the resulting eigenvalue problem is solved using a conventional shooting method. One determines numerically the critical Rayleigh and wave numbers at the onset of convection, for various values of the problem parameters.