Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method

The main purpose of this paper is to study, in a three-dimensional, differentially heated cavity, the phenomenon of radiation and natural convection in both transparent and participating media. The discrete ordinates method (DOM) is used to solve the radiative transfer equation. The Navier–Stokes equations (NSE), describing natural convection, are solved with a segregated SIMPLE-like algorithm. For non-participating media, the coupling between the radiative transfer and NSE is done via the radiative heat exchange between surfaces. For participating media, a source term is added in the energy equation. The local and mean heat flux as a function of the Rayleigh number is studied, for both transparent and participating media with different optical thicknesses. The effect of the Planck number on the heat flux is also analyzed for different values of the Rayleigh number. Also, a comparison between a purely two-dimensional case and the results obtained in the mid-plane of a long rectangular enclosure is presented.