Numerical Modeling of Non-Boussinesq Natural Convection in a Square Cavity Containing a Porous Layer

Numerical simulations were conducted to study the fluid flow and heat transfer through a partially filled square enclosure with a horizontal porous layer at the bottom. The vertical walls of the enclosure were subjected to uniform heating and cooling at specified temperatures [Formula: see text] and [Formula: see text], respectively. The problem formulation was based on the Darcy–Brinkman model, which took into account density variation using the Mach number law approximation and incorporated variable properties. Based on the developed code, a parametric study of fluid flow and heat transfer inside the cavity was carried out to examine the effects of temperature difference, medium permeability, and Darcy number. Additionally, the variation of the Nusselt number on the hot and cold walls was provided to demonstrate the overall nature of heat transfer within the enclosure. The results of this study highlight that fluid flow and heat transfer are influenced by the temperature difference between the vertical walls and the characteristic parameters of the porous layer.