Stability of convection induced by selective absorption of radiation in a fluid overlying a porous layer

Abstract

A linear stability analysis for the onset of convection induced by selective absorption of radiation in a two-layer system is presented. The system comprises a layer of fluid which lies above a porous layer saturated with the same fluid. The model for selective absorption of radiation is based on a similar one introduced by Krishnamurti [Dyn. Atmos. Oceans, 27, 367 (1997)] for a viscous fluid. Both the upper and lower surfaces are assumed to be fixed and it is found that the heating direction between both plates has a strong effect on the onset of convection. If the system is heated from below, the instability seems to have a bimodal nature in which convection may be dominated by fluid layer or by porous layer. While if heating from above, only one instability mode may exist in which convection is dominated by porous layer. Results for the stability characteristics with respect to the variations of depth ratio (the ratio of the depth of fluid layer to that of porous layer), strength of radiative heating, and Lewis number are also demonstrated in detail.