Influence of secondary flows on the stability of chemically reacting systems

A model is presented for convection and chemical reacton in porous media. An irreversible chemical reaction of arbitrary order is considered. Reactant depletion allows for basic solutions in either the kinetic or the diffusion regime. The cases of forced flow parallel to the lateral walls of the cavity and a closed system are addressed. A linear stability analysis of the basic states is performed and critical values of the thermal Rayleigh number for the onset of natural convection are determined. A dispersion relation is derived and a graphical representation of the linear stability analysis results is provided for typical values of the system parameters. Analytical predictions are verified by results obtained by numerical integration of the complete set of nonlinear partial differential equations. The effect of natural convection is discussed when the basic state is either in the kinetic or in the diffusion regime. For large gradients, associated with the diffusion regime, chemical reaction can drive free convection even for low values of the Rayleigh number. In forced flow systems, natural convection can change substantially the flow pattern of the system.