Numerical study of the Rayleigh-Bénard convection in two-dimensional cavities heated by elliptical heat sources using the lattice Boltzmann method

This study aims to investigate numerically the Rayleigh-Bénard Convection using an in-house Fortran 90 code based on the lattice Boltzmann method. The bottom wall is equipped with two hot circular/elliptical sources and the right wall is open. The non-linear coupled differential governing equations are formulated using the lattice Boltzmann equation associated with the Boussinesq approximation. The simulations are conducted for (103 ≤ Ra ≤ 106) and Pr = 0.7 (corresponding to air). The code verification showed a good reliability of the present mesoscopic numerical approach. Several configurations related to the size and shape of the heaters were studied. It was found that elliptically shaped heat sources provide higher heat transfer rates compared to circular sources.