Combined effects of lateral heating and thermo-diffusion on convection bifurcations in a porous enclosure subject to vertical thermal and solutal gradients

Abstract

The present study deals with double diffusive convection within a horizontal well packed porous layer of finite aspect ratio where thermo-diffusion has a predominant effect on the convective flow stability. The porous layer is subject to vertical thermal and solutal gradients and a lateral heating flux. The investigation is focused on a special situation where the lateral heat flux is balanced by the horizontally induced Soret mass flux, which allows a possible equilibrium state (motionless state) that becomes unstable under certain conditions. The aim of the present investigation is to study the flow stability and to develop some universal correlations for the flow intensity and heat transfer, which is valid for any aspect ratio independently of the governing parameters. The correlations were constructed from the parallel flow assumption valid for an infinite aspect ratio enclosure but can be used for a finite aspect ratio. To this end, numerical simulations are performed to support the investigation and to calibrate the correlations. By using a linear stability analysis, based on a finite element method, the onset conditions for the stationary convection and over stabilities are investigated with the focus on the effect of the lateral heating magnitude on the stability thresholds. In general, the thermo-diffusion problem balanced by a lateral heating effect is found to exhibit a rich variety of different bifurcation phenomena and complex unsteady flow patterns near criticality.