Multiple steady states for natural convection in a shallow porous cavity subject to uniform heat fluxes

Abstract

Multiplicity of steady states in natural convection within a shallow porous cavity, exposed to uniform heat fluxes on all sides, is investigated. Analytical solution for the stream function and temperature fields, in the central region of the cavity, is obtained using a parallel flow assumption. It is demonstrated that multiple steady states are possible, some of which are unstable. A finite difference method is used to obtain numerical solutions of the full governing equations. A good agreement is observed between the analytical predictions and the numerical simulations.