Analysis of the Coupled Effects of Thermal Conductivity, Emissivity, and Rayleigh Number on the Thermal Behavior of a Porous Cavity

This study presents a numerical investigation of coupled heat transfer in a partitioned two-dimensional cavity containing two porous zones interacting with the main fluid region. The Darcy–Forchheimer–Brinkman model is used to describe the momentum transport and fluid–porous medium interactions by accounting for viscous diffusion, permeability resistance, and inertial effects inside the porous layers, while the thermal behavior is governed by the combined effects of conduction, natural convection, and surface radiation. The numerical results show that the introduction of porous media significantly weakens buoyancy-driven flow, leading to attenuated circulation cells, straighter and more parallel isotherms, and a clear reduction in the convective Nusselt number along the heated walls. It is also demonstrated that increasing the effective thermal conductivity of the porous medium enhances heat conduction through the solid matrix and modifies the overall flow structure by redistributing the temperature gradients between the fluid and the porous zones. The Rayleigh number is identified as the primary parameter controlling the transition between conduction-dominated and convection-dominated regimes, with low values corresponding to diffusion-controlled heat transfer and higher values promoting stronger convection even in the presence of porous obstacles. In addition, radiative heat transfer is found to be mainly governed by wall emissivity and the thermal properties of the cavity boundaries, and higher emissivity markedly increases the radiative contribution to the total Nusselt number by reinforcing surface-to-surface thermal exchanges, which partially compensates for the attenuation of convection induced by the porous layers. These findings provide valuable physical insight and practical guidelines for the thermal design and optimization of passive systems incorporating porous materials such as solar distillers, thermal insulation components, and energy storage devices operating under combined heat transfer modes.