The onset of convection in a porous layer with multiple horizontal solid partitions

Abstract

The principal objective of the present paper is to investigate the onset of convection in a horizontal layer heated from below which consists of distinct porous sublayers which are separated by solid heat-conducting partitions. Each of the porous sublayers are identical as are the solid partitions. The present analysis employs linearised stability theory and a dispersion relation is derived from which neutral curves may be computed. For two-layer configurations the dispersion relation may be written explicitly, but for larger numbers of sublayers a simple systematic numerical procedure is used to compute the dispersion relation which, while it may also be written analytically, rapidly becomes increasingly lengthy as the number of sublayers increases. It is found that neutral curves are always unimodal and each has a well-defined single minimum. We attempt to give a comprehensive physical understanding of the effect of the number of layer, the relative thickness of the partitions and the conductivity ratio on the onset of convection and the form taken by the onset modes. Our results are compared with those of Rees and Genç (2011) [1] who considered the special case where the partitions are infinitesimally thin.