Nature convection in porous enclosures: The application of the two-energy equation model

The present investigation is concerned with the numerical simulation of a fluid-saturated porous medium emplaced inside a square enclosure. The flow field is modeled using the generalized form of the momentum equation by accounting for the viscous effects and the inertial effects as well. In addition, the local fluid and solid temperatures were both accounted for separately by employing the two-energy equation model. The sensitivity of the Darcy number and Grashof number values on the momentum and energy transport processes are highlighted in the range of 10^-5 < Da < 10^-1 and 10⁴ < Gr < 10⁶, respectively. Furthermore, Nusselt number formulation, based on the overall energy balance, was developed for the two-energy equation model. Finally, an assessment of the local thermal equilibrium condition was carried out to weigh its significance over the range of flow conditions and porous configurations considered in the analysis.