Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls

Abstract

In this article, a comprehensive numerical investigation of the natural convection in a hydro-dynamically as well as thermally anisotropic porous enclosure with insulated side walls is presented. The two different cases, (I) same heat flux on the top as well as bottom walls and (II) heat flux on the top wall being negative of the heat flux on the bottom wall, are considered. A non-Darcy model that includes Darcy and Brinkman terms have been adopted and the coupled governing equations are solved numerically by SIMPLER algorithm. The influence of periodicity parameter and anisotropy parameters on the flow dynamics as well as heat transfer rate has been addressed. It has been found from our rigorous numerical experiments that the structure of streamlines and isotherms for Case I is multicellular and depends on the value of periodicity parameter (N) as well as media permeability, whereas the same for Case II is unicellular. In general, the profile of local heat transfer rate under Case I possesses $(N-1)$ points of singularity inducing hyperbolic temperature contour. In contrast to Case I, the profile of local heat transfer rate under Case II is found to be free from points of singularity.

Additional information

Funding

One of the authors, Harish Chandra, is grateful to M.H.R.D India for providing financial support (MHRD Grant No.: OH-31-23-200428) during the preparation of this article.