Rayleigh-Bénard stability of a solidifying porous medium (Q1962519)

This paper considers the problem of Rayleigh-Bénard instability of a liquid layer undergoing a phase transition within a porous medium. The porous medium is saturated with the liquid in all pores or in the interparticle space of the medium, thus leaving no space for a vapor, gas, or for other liquids within the medium. A linear stability analysis is performed to determine the effects of medium characteristics and phase change on the conditions for incipient instability in a range of thermal boundary conditions. The authors show that the presence of a solidification boundary destabilizes the system. As the solid thickness increases, the system becomes less stable as is ascertained by a decrease in the Rayleigh number marking the onset of convection. Also, as the solid thickness is increased, the nondimensional wave number decreases, thus rendering smaller convection cells. The number of cells is directly related to the solidification rate, and hence to the heat transfer rate. As the cell size decreases, a greater heat transfer rate should be expected. A very important conclusion is that, in comparison to the classical Bénard problem or that of solidification of a pure liquid layer, the presence of the porous medium renders the porous Lapwood model more stable than the bulk liquid analog.