Stability and Instability of Darcy–Bénard Problem in Bidispersive Porous Medium with an Exothermic Boundary Reaction

The Darcy–Bénard problem in a bidisperse porous medium with an exothermic reaction at the lower boundary is investigated. The layer is saturated with a non-isothermal liquid containing a concentration of the reactive chemical, and the porous medium is of the Darcy type. The linear instability problem is given a thorough study. The nonlinear stability problem is studied in a case that is believed to be physically relevant, and the stability threshold is compared directly to that found by linear instability theory. The Chebyshev collocation method provides the foundation for the numerical techniques we use, and the QZ algorithm is used to solve the associated finite-dimensional generalized matrix eigenvalue problem. It is demonstrated that there is a region where sub-critical instability can arise.