Linear stability analysis of convection in a solid partitioned inhomogeneous multilayered porous structure

Abstract

We investigate the effect of varying permeability on the onset of convection in a system of multi-layered porous medium when heated from below. Here, the interface between any two porous sublayers is a thick solid conducting plate. The porous sublayers are inhomogeneous with respect to their permeability. Results for the homogeneous case are validated against those from the literature. The solvability condition is produced for a general [Formula: see text] layered inhomogeneous system to study the neutral curves. Detailed results are presented for a two layered and a three layered configuration. The effect of the involved parameters such as permeability ratio, thermal conductivity ratio, and thickness ratio on the onset of convection is analyzed using linear stability analysis. The critical values of Rayleigh number and the corresponding wave number increased with the increase in the thermal conductivity of the solid partitions, irrespective of the change in the permeability of porous sublayers. Multicellular sublayer flow circulation strength is amplified by the conductivity of the solid interfaces. Higher modes are also examined for varying permeability ratio and thermal conductivity ratio. A different flow pattern is observed for mode 3 when the permeability ratio is either very much less than one or much greater than one. Onset of the convection is sensitive to the increasing number of inhomogeneous porous sublayers of the layered porous system.