Melting of a Solid in Porous Medium Induced by Free Convection of a Warm Dissimilar Fluid

Buoyancy-driven flow from a vertical flat plate in porous medium was investigated first by Cheng and Minkowycz. Their results were extended later to the case of cold water natural convection by Ramilison and Gebhart. In two recent studies Epstein and Cho and Kazmierczak et al. studied theoretically the effect of forced and natural convection, respectively, on the phenomenon of melting from a flat plate embedded in porous medium. The present study pertains to a different class of melting problems in porous medium. Unlike the above studies where both the solid and the liquid phase are of the same substance, here melting from a vertical flat plate is initiated by a warm fluid that is dissimilar to the solid phase it surrounds. Therefore, the liquid in the melt layer is dissimilar to the warm liquid outside the melt layer. Of particular interest to the present study is the case where the density difference between the melt and the ambient fluid is considerably greater than that caused by thermal expansion. Hence, the buoyancy force responsible for the motion in the melt layer originates from differences in material densities and not, as is customarily assumed, from temperature differences. Regarding the warm ambient fluidmore » responsible for the initiation and continuation of the melting phenomenon, it is assumed that the temperature gradients existing in the vicinity of the interface between the ambient fluid and the melt region drive a natural convection flow inside the ambient fluid near the melt/ambient fluid interface. This flow is taken into account and its effect on the melting phenomenon is thoroughly investigated. The main application of the basic research reported in this paper is in geophysical heat transfer where melting of the type studied here may occur, resulting in the spreading of pollutants.« less