Lattice Boltzmann Method Analysis of Natural Convection in a Closed Environment With a Square Heater Inserted in a Porous Cylinder

Abstract

In this work, a numerical study of the natural convection within a two-dimensional square cavity is presented. The cavity is equipped with a hot square block at its center with a side length of , and it is enveloped by a porous layer of cylindrical shape with a radius (r(p)) . The vertical walls are adiabatic, while the horizontal walls are maintained at a cold temperature. To describe the momentum equations in the porous matrix, the Brinkman-extended Darcy equation is applied, and the Boussinesq approximation is employed for the buoyancy term. The Lattice Boltzmann Method is utilized and validated by comparison with results from the literature. The novelty of this study lies in analyzing the combined effects of the porous layer geometry and thermal conductivity ratio on heat transfer performance, which has not been previously addressed in detail. The results obtained made it possible to study the structure of flow and heat transfers, as a function of the various parameters such as the Darcy number (Da), the Rayleigh number (Ra), the porosity of the porous medium as well as the thermal conductivity ratio (R-k) and the porous layer radius (r(p)) . Our results show that increasing the Rayleigh number markedly strengthens the convective flow, whereas higher Darcy numbers enhance the interaction between the fluid and the porous medium. In contrast, enlarging the porous layer radius leads to a reduction in the overall heat transfer rate. Notably, the most significant enhancement in the Nusselt number occurs at intermediate porosity values combined with a moderate thermal conductivity ratio. These outcomes offer valuable insights for optimizing cavity porous configurations in order to achieve more efficient natural convection heat transfer.