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 ΔT∗=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 ΔT∗: Nuh decreases with ΔT∗ while Nuc increases with ΔT∗.