Free convective heat transfer flow in a glass bead porous medium varying permeability and sinusoidal wall temperature

This study examines the effects of varying permeability and sinusoidal wall temperature fluctuations on the temporal heat transfer flow driven by natural convection inside a rectangular enclosure filled with a glass bead porous medium under local thermal nonequilibrium conditions for both the working fluid and the porous medium. The fluid’s thermal conductivity is assumed to be variable, and a Darcy–Brinkman–Forchheimer model is used to describe the fluid flow. The Galerkin-type finite element method simulates the constitutive equations governing the flow and heat transfer. The simulation explores the influence of different model parameters on the flow and thermal fields. The results indicate that at a steady state ( \(\tau = 1.0\) $\tau =1.0$ ), when glass bead diameter Dp increased from 0.01 to 1.0, the values of \(\overline{{{\text{Nu}}_{{\text{f}}} }}\) $\overline{{\text{Nu}}_{\text{f}}}$ and \(\overline{{{\text{Nu}}_{{\text{s}}} }}\) $\overline{{\text{Nu}}_{\text{s}}}$ decreased by 48.8% and 26%, respectively. Besides, the value of the Nusselt number for the fluid increased by 280.61%, whereas the Nusselt number for the solid increased by 266.55% with the increase of the wave frequency n from 1 to 4. Furthermore, these physical quantities increased by 629.71% and 91.405% when the wave amplitude B rose from 0.1 to 1.