Lattice Boltzmann method for natural convection in a square cavity with a heated chip

The buoyancy-driven gas flow (air) confined within an enclosed square-section cavity with isothermal walls is investigated numerically using the lattice Boltzmann method (LBM). The right side of the enclosure is partially heated by a hot chip, while, the left one is completely kept at cold temperature. However, the horizontal walls and apart from the chip are kept adiabatic. The buoyancy effect induced by the gravity acceleration, related to the convection force, is evaluated through the Rayleigh number in the range of 10³-10⁶(laminar regime). Wall heating-ratio effect on the flow properties such as temperature and velocity profiles. The heat transfer is analyzed through the Nusselt number for different chip lengths. Results show that the wall heat ratio has an interesting effect on flow behavior. Results show good agreement with those of full natural convection simulation in the literature and their experimental data.

I. Introduction

Several industrial systems involving gas flows at different scales of applications are in growth use. In the last few decades, lattice Boltzmann method was successfully used as a mesoscopic approach based on both continuum and kinetic descriptions of flows. Hence, LBM has become a recent powerful computational fluid dynamics (CFD) tool. Its popularity is mainly because the method can be extended to other applications unlike the Navier-Stokes based solvers restricted to the pure macroscopic description of flows.