Unsteady free convection with volumetric-radiation using LBM

Abstract

In the last decade, coupled convection and radiative engineering problems has emerged as a major area of study in the engineering applications and sciences. The present paper deals with a transient (steady and unsteady) combination between free convection and volumetric radiation in a closed enclosure in thermal incompressible fluid flows in a bi-dimensional, differentially heated enclosure with emitting, scattering and absorbing volume. In the equation of energy, the radiative heat flux was simulated using the CVFEM, (Control- Volume-Finite-Element-Method) in the RTE (Radiative Transfer Equation). The Navier–Stokes equations which describe natural convection were solved with a D2Q9 temperature and velocity flow distributions using Lattice Boltzmann BGK Method. Separate particle distribution functions in the LBM were used to calculate the density, velocity and thermal fields. The obtained findings in the current work were compared with literature and good validation are demonstrated. The streamlines, the horizontal and vertical velocities, midline temperature, and the isotherms were highlighted and discussed under various parameters such as Rayleigh number, convection radiation number, in both steady and also unsteady cases. The LBM-CVFEM was ascertained to be a reliable numerical technique for future engineering applications dealing with transient coupling heat transfer problems.