Thermal fluid flow in a porous rectangular cavity driven by differential heating and uniform heat fluxes

Abstract

This paper investigates the complex dynamics of thermal fluid flowwithin a porous rectangular cavity, subjected to a hybrid thermal environment consisting of differential heating on the top wall and uniform heat fluxes on the vertical boundaries. The study aims to characterize the interaction between buoyancy-driven convection and localized heat input within a saturated porous medium, modeled using the Darcy model. The governing equations are described by the continuity equation, the momentum equation, and the energy equation. The equations were made dimensionless. Three dimensionless parameters are introduced, namely the Darcy-Rayleigh number (the porous medium conductivity parameter), the heat flux parameter, and the geometric aspect ratio (the cavity shape parameter).Numerical solutionswere conducted by using the finite-difference method. Special attention is paid to finding an analytical solution for a small Darcy-Rayleigh number by using the asymptotic expansion method. Our simulation results show that the interaction between these boundary conditions creates complex, multi-cellular flow patterns and directly impacts heat transfer efficiency, offering insights for thermal management applications. Furthermore, the study provides a comprehensive mapping of the temperature distribution and streamline patterns, offering critical insights into heat transfer optimization.