Numerical Analysis of Heat Transfer by Natural Convection and Radiation in Participating Fluids Enclosed in Square Cavities

The influence of thermal radiation on natural convection in a participating fluid contained in a square cavity is studied numerically. The radiative transfer process is solved from the PI approximation. The Navier-Stokes equations are solved by a finite difference scheme integrated over control volumes. A numerical study of the so-called window problem (thermally driven cavity) shows the influence of thermal radiation on this reference problem for Rayleigh numbers in the range of 103-107 and Planck numbers varying from 1 to 0.05. The isotherms, streamlines, and heat lines show an increase of the dynamical effects in the central part of the cavity and a significant modification of the boundary layers. Results obtained from the simulation of an isotropically scattering medium are given.