Stability of a free convection density-extremum flow in a porous medium

The relative stability of the multiple steady states of laminar free convection flows in a porous medium saturated with cold, pure water along a vertical, isothermal, planar surface is investigated. Two distinct regions of numerically computed multiple steady-state solutions for flow conditions in which the internal temperature range spans a density maximum (0 < R < 1 2, where R is a temperature ratio parameter) have been reported in the literature. Stability analysis of these steady states is performed by linearizing the time-dependent equations about the steady-state solutions and by considering only amplification or decay of perturbations with time. The results obtained indicate that all but one of the multiple steady states at each R are unstable with respect to time. Relative merits and demerits of the approach used in this study over the conventional hydrodynamic stability analysis are discussed.