Search

We consider a saturated porous medium of Darcy type with an exothermic reaction occurring on the domain boundary. In this model the reaction is the main driving force behind convection and we establish continuous dependence of the solution on the reaction terms.

The problem is considered of thermal convection in a saturated porous medium contained in an infinite vertical channel with differentially heated sidewalls. The theory employed allows for different solid and fluid temperatures in the matrix. Nonlinear energy stability theory is used to derive a Rayleigh number threshold below which convection will not occur no matter how large the initial data. A generalized nonlinear analysis is also given which shows convection cannot occur for any Rayleigh number provided the initial data is suitably restricted.