Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convection.