Darcy number influence on natural convection around porous cylinders in an enclosure using Darcy- Brinkman-Forchheimer model: LBM study

Abstract

We evaluated numerically the combined impact of Darcy and Rayleigh number changes on natural convection around two vertically arranged hot porous cylinders of different diameters in a square enclosure. Numerical simulations are conducted by implementing lattice Boltzmann technique using the D2Q9 model. The Darcy-Brinkman-Forchheimer equations for porous medium are solved with a single-domain approach. The influence of Darcy number (10−6≤Da≤ 10−2) on rate of heat transfer from cylinders is described for 104≤Ra≤ 106 by altering the cylinder diameter from 0.1 to 0.4L. With increment of cylinder size, Ra and Da, heat transfer rates are found to improve. At Ra = 106, the highest enhancement occurs for D = 0.1L. On lower Rayleigh numbers (Ra = 104) as well as Darcy numbers (Da = 10−6), doubling the diameter of the cylinder increases heat transport by 41.5%. Consequently, when the diameter is multiplied by four, the improvement is 211%. At Ra = 106, the rate of augmentation from D = 0.2L–0.3L is lower than for the case when D = 0.1L and 0.2L. At D = 0.4L maximal transfer of heat arises when the cylinder is extremely permeable (i.e., Da = 10−2). This study has applications in the thermal management of a bank of electronic components.