Theoretical Approach to the Onset of Convection in a Porous Layer

Abstract

A new theory is proposed to determine the critical wave number and the critical Rayleigh number at the onset of convection. We consider a problem of the onset of instability in convection in a horizontal layer embedded in a fluid-saturated porous medium. The upper wall of the layer is maintained at uniform temperature and concentration. On the lower wall, an Arrhenius-type exothermic surface reaction and surface radiation are assumed to occur. The heat released from the surface reaction and surface radiation causes convection in the porous medium and thereby can lead instability in the system. Results showed that the new theory can reasonably predict the critical wave number and the critical Rayleigh number. Moreover the influences of the heat release parameter, the mass diffusion parameter, the activation energy parameter and the conduction–radiation parameter on the critical wave number and the critical Rayleigh number have been presented. In the presence of surface radiation there must have a maximum value of the heat release parameter and the activation energy parameter while there must a minimum value of the mass diffusion parameter for the onset of convection in a porous medium.