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A numerical investigation was conducted to examine free convection heat transfer within a square cavity containing a fluid-saturated porous layer at the bottom under laminar flow conditions. The enclosure's left and right walls experienced heating and cooling, while the top and bottom walls remained adiabatic. The study explored the influence of the Darcy number, porosity number, and dimensionless thickness of the porous layer on heat transmission. This investigation utilized a FORTRAN computation program alongside the finite volume method, effectively solving the equations governing flow and heat exchange within porous materials through natural convection. The flow pattern is determined by the Navier–Stokes equations in the fluid region and the Darcy–Brinkman–Forchheimer formula in the porous region. The energy equation was employed to compute the thermal field. The increase in the Darcy number results in both an increase in heat transfer rate due to enhanced fluid flow through pores and an intensification of fluid flow patterns. Higher porosity leads to higher heat transfer rates due to greater fluid penetration and an increased surface area for heat exchange. The thicker porous layer reduces heat transfer rate due to increased resistance to fluid flow and decreased contact area.
Fenni et al. (Wed,) studied this question.