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

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.

Automated summary

In this study, 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 is numerically evaluated. The numerical simulations are conducted using the lattice Boltzmann technique and the D2Q9 model. It is found that heat transfer rates improve with an increase in cylinder size, Ra, and Da.