Three-Dimensional Free Convective Heat Transmission Flow of Copper–Water Nanofluid in a Glass Bead Permeable Matrix within a Right Trapezoidal Cavity in Consideration of Thermal Non-Equilibrium Conditions

This work focuses on the impacts of varying penetrability and porosity through the natural convective heat transmission flow of copper–water in a glass bead permeable matrix within a right trapezoidal cavity in consideration of thermal non-equilibrium conditions among the permeable medium, nanoparticles, and the base fluid using the Darcy–Brinkman–Forchheimer model. The model equations are simulated using the Galerkin weighted residual finite element strategy. We analyze the influences of the various model factors particularly, the critical Rayleigh number, the porosity factor, the nanoparticles volume fraction, the interface heat transmission parameters, and the bead diameter in the realms of flow and heat. Furthermore, we investigate the effects of the aspect ratios of the trapezoidal cavity and various thermal boundary situations on the rate of heat transmission for base fluid, nanoparticles, and porous matrix in detail. The results show that the critical Rayleigh number for the commencement of local thermal nonequilibrium states reduced with the enhancement of the bead diameter and the porosity parameter. The average Nusselt number in the base fluid, nanoparticles, and solid matrix increased with the increase of the bead diameter for about 11.7%, 11.6%, and 1.4%, respectively, when it rises from 0.4 to 0.6. The trapezoidal cavity exhibits the greatest heat transmission rate for the base fluid, nanoparticles, and solid matrix in comparison with the cube and the rectangular cavity.