Analysis of Rayleigh-Bénard convection with thermal volumetric radiation using Lattice Boltzmann Formulation

Abstract

The interactions between Transient Rayleigh-Bénard convection and volumetric radiation are investigated by means of the lattice Boltzmann method (LBM) performed for a two dimensional participating Rayleigh-Bénard cell. Given that, the analysis of the transient convection-radiation finds applications in combustion chambers, rocket propulsion systems, the design of reactors, heat pipes, etc. in this paper, we extended the mesoscopic Lattice Boltzmann model for analyzing the coupled engineering problem Rayleigh-Bénard Convection with thermal radiation. In order to highlight and assess the aim and the computational advantage of computing the radiative information too using the LBM and to demonstrate the workability of the LBM to a such coupled problem in two dimensional media, first, transient Rayleigh-Bénard convection is solved using the lattice Boltzmann method (LBM) and then are compared with those available in the literature. The coupled transient case, Rayleigh-Bénard convection-radiation in participating media is extended, where LBM, is used, both to calculate the volumetric radiative information needed for the energy equation, which is solved using the LBM. Results of this recent approach LBM-LBM work are compared with those available in the literature. In all cases, good agreement has been obtained. Indeed, the recent numerical approach is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer in presence of volumetric radiation in participating medium. The steady state stream-functions, isotherms and pressure distribution were compared with results available in the literature. It is found that the recent approach provides accurate results and it is computationally more efficient than others CFD numerical methods which approve the workability of this recent approach and this make it a new potential computational tool for solving a large class of engineering problems.

Keywords

• heat transfer
• lbm
• rte
• transient rb convection
• volumetric radiation
• participating media