MRT-lattice Boltzmann computations of natural convection and volumetric radiation in a tilted square enclosure

A numerical analysis is carried out for natural convection while in an asymmetrically heated square cavity containing an absorbing emitting medium. The numerical approach adopted uses a hybrid thermal lattice Boltzmann method (HTLBM) in which the mass and momentum conservation equations are solved by using multiple relaxation time (MRT) model and the energy equation is solved separately by using the finite difference method (FDM). In addition, the radiative transfer equation (RTE) is treated by the discrete ordinates method (DOM) using the S8 quadrature to evaluate the source term of the energy equation. The effects of parameters such as the Rayleigh number Ra, the optical thickness τ and the inclination angle φ, are studied numerically to assess their impact on the flow and temperature distribution.The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in the absence of the radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in temperature and velocity gradients along both thermally active walls.

► A coupled natural convection and gray gas radiation was studied numerically. ► The dynamic and thermal fields are computed by hybrid scheme (HTLBM-MRT and FDM). ► The radiative source term is evaluated by the discrete ordinates method (DOM). ► In pure natural convection, the cavity core is thermally stratified. ► Temperature and velocity gradients at vertical walls are increased by radiation.