Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body

In this paper, a numerical investigation of laminar convective flows in a differentially heated, square enclosure with a heat-conducting cylinder at its center, is carried out. The flow and the temperature are computed using respectively the lattice Boltzmann equation and finite-difference with suitable coupling to take natural convection into account. The investigation is performed for Pr = 0.71, Rayleigh numbers of Ra = 103 - 106 and temperature-difference ratio of Δ T* = 0 - 50. The average hot and cold walls Nusselt numbers, the flow and temperature fields are presented and discussed. For a constant Ra, the average Nusselt number at the hot and cold walls (Nuh and Nuc) vary linearly with Δ T*: Nuh decreases with Δ T* while Nuc increases with Δ T*. © 2006 Elsevier SAS. All rights reserved.