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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.

We consider a saturated Darcy porous medium with an exothermic chemical reaction on the lower boundary. The Dufour effect is neglected, however the influence of the Soret effect is studied. It is found that increasing the Soret coefficient may be either linearly stabilising or destabilising, depending on the boundary parameters and Lewis number. When stationary convection occurs increasing the Soret coefficient has a stabilising effect. A switch from stationary to oscillatory convection occurs at a lower Lewis number for a greater Soret coefficient. Linearised perturbation equations are given and numerical results for the critical Rayleigh number are presented graphically and then discussed.

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.

The onset of instability in a porous medium of high porosity subject to a chemical surface reaction on the lower boundary and no slip conditions on both the upper and lower boundaries is studied. The equations are developed and then solved numerically to find the critical Rayleigh number. The influence that the boundary condition parameters and the Brinkman term have on the critical Rayleigh number is examined.

We develop a problem recently studied by Postelnicu in which a horizontal layer of porous material is subject to a chemical reaction at the base of the layer. The porous medium is of Darcy type and the layer is saturated with a non-isothermal liquid containing a concentration of the reacting chemical. The equations are developed and then it is shown that if the reaction parameter B of Postelnicu exceeds a critical value convection commences but as oscillatory convection, not stationary convection, as previously thought.