Darcy number effects on natural convection around a porous cylinder in L-shaped enclosure using Lattice Boltzmann method

This study numerically evaluates fluid flow and natural convection heat transfer of a porous square cylinder in an L-shaped enclosure using the Lattice Boltzmann method. Three layouts along vertical and horizontal centrelines are explored, investigating the effects of Rayleigh number (Ra) (10³ ≤ Ra ≤ 10⁶), Darcy number (Da) (10^-6 ≤ Da ≤ 10^-2), and cylinder size. Results show that increasing Rayleigh numbers enhances heat transfer, with higher Mean Nusselt number (Nu_Mean) values observed. Doubling the cylinder's width at Da = 10^-6 increases Nu_Mean by 46.5%, and tripling the width results in a 118% enhancement. Higher Rayleigh values enhance buoyant forces' intensity, improving heat transfer; for example, at Ra = 10⁵ and Da = 10^-2, there is a 42% increase in Nu mean for a cylinder with a 0.6 L side length compared to Ra = 10³. Optimal cylinder orientation significantly maximizes convective heat transfer, especially at high Rayleigh and Darcy numbers. This study provides valuable insight for optimizing the orientation of electronic blocks in compact L-shaped enclosures for better thermal management.