LBM study of natural convection heat transfer from a porous cylinder in an enclosure

Natural convection heat transfer from a porous cylinder put at various positions in a square, cooled enclosure, with air as the working fluid, is investigated in this work. The following setups are taken into account: The hot cylinder is placed in the middle of the enclosure, near the bottom, top, right sides, along diagonal as top-diagonal and bottom-diagonal. The cylinder and the enclosure walls are kept hot and cold, respectively. The lattice Boltzmann method is used to perform a numerical analysis for Rayleigh number \(10^{4}\le \) Ra \(\le 10^{6}\) and Darcy number \(10^{-6}\le \) Da \(\le 10^{-2}\). The results are plotted as streamlines, isotherms, and local and mean Nusselt number values. The amount of heat transported from the heated porous cylinder is determined by varying Ra, Da, and the cylinder location. Even at a lower Rayleigh number (\(10^{4}\)), the average Nusselt number grows by nearly 70 % as the cylinder moves from the centre to the bottom and 105% as it moves to bottom-diagonal location when \({Da}=10^{-2}\). At Ra \(=10^{6}\) and Da \(=10^{-2}\), the heat transfer rate of the cylinder located near the corner of the enclosure at the bottom wall increases by approximately 33% when compared to the case of the cylinder in the centre. Convective effects are more noticeable when the cylinder is positioned towards the enclosure’s bottom wall. This research is applicable to electronic cooling applications in which a collection of electronic components is arranged in a circular pattern inside a cabinet.