Interaction between chemical reaction and natural convection in porous media

Natural convection in porous media has received much attention in the last decades. Most of the work, however, has been devoted to the case of a global driving force resulting from thermal or concentration gradients applied to the boundaries of the system. As changes in the density lead to natural convection, chemical reactions can provide a distributed driving force for secondary flows. The conditions for the onset of natural convection are represented by the critical value of the thermal Rayleigh number. The critical value is found by performing a linear stability analysis of the basic reaction regime. Results are reported for the onset of both oscillatory and monotonic instabilities. The stability of the convective modes is studied by using a variational approach and deriving a set of spectral equations by means of a truncated mode interaction. The initial-value problem is analyzed by continuation routines and bifurcation diagrams are drawn. These diagrams constitute a valuable tool in the design of heterogeneous reacting systems. The numerical solution of the full governing equations serves to corroborate the predictions of the simplified model as well as to illustrate the effects of natural-convection phenomena on systems with chemical reaction. © 1989.