Multiple steady states for unicellular natural convection in an inclined porous layer

Abstract

Multiplicity of steady states in natural convection within an inclined porous material with parallel conductive isotherms is investigated. The different steady states are obtained analytically for unicellular convection in thin rectangular porous layers with uniform heating and cooling through opposite walls. The basis of the analytical approximation is an assumption of parallel flow over a large portion of the layer. The two cases of heat fluxes through side and end walls are both calculated and are seen to share some qualitatively similar features. At sub-critical Rayleigh numbers only one steady state exists for any tilt angle. For higher Rayleigh numbers and for small enough inclinations around bottom heating, however, multiple steady states exist, some of which are unstable. Numerical confirmation of the stable analytical results is also presented.