Lattice Boltzmann Analysis of 2-D Natural Convection Flow and Heat Transfer within Square Enclosure including an Isothermal Hot Block

Abstract

In the present investigation, physics of natural convection flow and heat transfer in closed enclosure including an isothermal heat block are analyzed by double population approach of lattice Boltzmann method (LBM). The sidewalls are isothermally cooled at a constant temperature while the upper and bottom walls are considered to be adiabatic except for the rectangular block heated at a uniform temperature. The simulations were performed for a Prandtl number fixed to 0.71. Main attention has been focused on the effects of Rayleigh number (103 ≤ Ra ≤ 106 ), position (0.1 ≤ xc ≤ 0.4), length (0.1 ≤ a ≤ 0.6) and height (0 ≤ b ≤ 0.4) of the active block upon dynamic and thermal fields of fluid. It is found that the present approach of thermal LB model D2Q4-D2Q9 produces similar results by comparison with former predictions. Besides, the computational results show that the parameters governing the problem have a considerable effects on the flow patterns and the temperature repartition and consequently on the heat transfer rate. By increasing Rayleigh number, average Nusselt number along upper and lateral surfaces of the heater increases causing an enhancement of convective mode in enclosure. A weakening of heat transfer rate is obtained with increasing position, length as well as height of hot source.