Modeling of Free Convection Heat Transfer to a Supercritical Fluid in a Square Enclosure by the Lattice Boltzmann Method

During the last decade, a number of numerical computations based on the finite volume approach have been reported, studying various aspects of heat transfer near the critical point. In this paper, a lattice Boltzmann method (LBM) has been developed to simulate laminar free convection heat transfer to a supercritical fluid in a square enclosure. The LBM is an ideal mesoscopic approach to solve nonlinear macroscopic conservation equations due to its simplicity and capability of parallelization. The lattice Boltzmann equation (LBE) represents the minimal form of the Boltzmann kinetic equation. The LBE is a very elegant and simple equation, for a discrete density distribution function, and is the basis of the LBM. For the mass and momentum equations, a LBM is used while the heat equation is solved numerically by a finite volume scheme. In this study, interparticle forces are taken into account for nonideal gases in order to simulate the velocity profile more accurately. The laminar free convection cavity flow has been extensively used as a benchmark test to evaluate the accuracy of the numerical code. It is found that the numerical results of this study are in good agreement with the experimental and numerical results reported in the literature. The results of the LBM-FVM (finite volume method) combination are found to be in excellent agreement with the FVM-FVM combination for the Navier–Stokes and heat transfer equations.