Analysis of the local non-equilibria on the heat transfer and entropy generation during thermal natural convection in a non-Darcy porous medium

Abstract

This paper addressed new and unique information on the influence of local thermal non-equilibrium (LTNE) effects on heat exchange and entropy generation during thermal-free convection in a non-Darcy porous domain. The simplest configuration was considered, which consisted of a square cavity in which the steady-thermal-free convection motion is generated by maintaining the vertical sidewalls at different and constant temperatures. The Darcy-Brinkman-Forchheimer design has been adopted. The governing equations, which include the two energy equations for the fluid and solid phases, along with momentum equations in their dimensionless form, are solved using the finite volume computational approach. Due to the application of two different heat transport equations under the LTNE modeling technique, sources of entropy generation owing to thermal diffusion in the fluid phase and in the solid phase in addition to the entropy generation owing to viscous dissipation were identified. Maps of the distribution pattern of LTNE sources were also visualized. Furthermore, to assess and compare the thermal diffusion irreversibility in the two components of the porous structure, for the first time, we introduced and examined a new parameter (Ty), which is the ratio of the thermal entropy generation rate in the fluid phase to that in the solid phase.