Multiple steady states in a confined porous medium with localized heating from below

TLDR: In this paper, the authors considered a two-dimensional rectangular cavity whose portion of the bottom surface is isothermally heated, the upper surface is cooled at a constant temperature, and all other surfaces are adiabatic.

Abstract: Natural convection flow induced by localized heating from below in a horizontal porous layer is investigated numerically. The geometry considered is a two-dimensional rectangular cavity whose portion of the bottom surface is isothermally heated, the upper surface is cooled at a constant temperature, and all other surfaces are adiabatic. Parameters of the problem are the cavity aspect ratio A, dimensionless length of heat source B, dimensionless position of heat source e with respect to the vertical line of symmetry of the cavity, and Rayleigh number R based on cavity width. Three main convective modes are studied—conduction and single- and double-cell convection—and their features are described in detail. Maximum stream function and global Nussett numbers are presented as functions of the external parameters. Multiplicity of solutions is explored for an aspect ratio of unity. The existence of two steady-state solutions for a given set of the governing parameters is demonstrated.