Effect of surface radiation on the natural-convection stability in a two-dimensional enclosure with diffusely emitting boundary walls

A transient interaction of natural convection with thermal radiation of gray surfaces of a square cavity filled with air is investigated numerically. The effect of radiation on the flow field, temperature distribution, and onset of oscillatory instability of flow is predicted. A complete study of stability of some value of Rayleigh number is performed for emissivity epsilon varying from 0 to 1. The finite-element and the fractional step time methods are used to solve the two-dimensional time-dependent Navier-Stokes and energy equations. The results are reduced in terms of the time-series averages Nusselt number and velocity component near vertical walls and at the center of the cavity. The Grashof number is varied up to 5 x 10(7) to determine the new critical values of regime flow for different values of emissivity.