Numerical Modeling of Natural Convection Modes in a Cubic Differentially Heated Porous Cavity Under Rotation Conditions

This numerical study investigates natural convection phenomenon in a rotating porous cubical cavity, analyzing the coupled effects of rotation, temperature difference and porous medium characteristics on heat transfer dynamics. The governing equations, formulated using vector potential and vorticity variables, incorporate the extended Darcy-Brinkman model to account for porous media effects. A second-order finite difference method with successive over relaxation and Thomas algorithm solves the discretized system, validated against benchmark solutions for both hydrodynamic and thermal fields. The analysis explores a broad parameter space, including Taylor numbers, Rayleigh numbers, and porosities. Key findings reveal that two distinct regimes exist: buoyancy-dominated (low Ta) with oscillatory Nusselt numbers and rotation-dominated (high Ta) with stabilized Nu. Porosity-enhanced heat transfer persists across all Ta, although centrifugal forces modulate its efficiency, while Ra significantly intensifies convection only at low Ta, demonstrating rotational suppression of thermal effects. The results demonstrate that angular velocity and porosity can serve as effective control parameters for thermal management, with practical implications for rotating machinery and energy systems employing porous media. The study establishes a validated numerical framework to analyze three-dimensional convection in rotating porous environments. This study identifies optimal rotation-porosity configurations that enhance thermal efficiency in heat exchangers and passive cooling systems, outperforming conventional designs. The findings enable sustainable heat recovery in industrial applications and next-generation microelectronics thermal management, reducing energy consumption.