Convection induced by the selective absorption of radiation for the Brinkman model

Convection induced by the selective absorption of radiation in a porous medium is studied analytically and numerically using the Brinkman model. Both linear instability analysis and nonlinear stability analysis are employed. The thresholds show excellent agreement so that the region of potential subcritical instabilities is very small, demonstrating that linear theory is accurate enough to predict the onset of convective motion. A surprising result shows that the critical Rayleigh number increases linearly as lambda (Darcy number x Brinkman coefficient/dynamic viscosity of the fluid) increases.