Accurate meso-scale simulation of mixed convective heat transfer in a porous media for a vented square with hot elliptic obstacle: An LBM approach

Abstract

In the present study, heat and fluid flow of water in a vented cavity with elliptical hot obstacle is numerically investigated using Lattice Boltzmann Method (LBM). This flow is assumed to be laminar, 2D and incompressible. The main purpose in this work is to investigate the effect of utilizing porous medium on mixed convective heat transfer in an obstructed vented cavity. The simulations are performed for Richardson number of 0.1, 1 and 10, porosity of 0.5, 0.7 and 0.9, and solid-to-fluid conductivity ratios of 10, 33.3, 66.7 and 100. The results are presented by streamlines, temperature contours, and Nusselt number curves. Results show that by increasing Richardson number, due to the dominance of natural convective heat transfer compared with that of the forced case, the heat penetration in fluid layers in all areas of the cavity is increased. Moreover, as the Richardson number increases, due to limitation of forced heat transfer, the temperature gradients in the cavity rise and the growth of thermal boundary layer becomes significant. This behavior has an undesirable effect on heat transfer of hot obstacle especially around the cavity outlet and right side of the obstacle. By decreasing the cavity porosity, the areas around the hot obstacle will experience higher heat penetration into the fluid and consequently the heat transfer is reduced. In this study, the highest Nusselt number is obtained for Richardson number of Ri=0.1 and porosity of Po=0.5 and the increase in Richardson number and porosity coefficient results in reduced Nusselt number in all areas around the hot obstacle. The porosity changes have more significant effect on heat transfer in smaller Richardson numbers. This results in Nusselt number higher about 79% in best condition at conductivity ratio of 33.33 (Ri=0.1) while it changes the Nusselt number about 17.4% at conductivity ratio of 10 (Ri=10).