Interaction between natural convection and radiation in a square cavity heated from below

The radiation effect of gray surfaces on multiple steady-state solutions obtained in a square enclosure filled with air has been investigated numerically, by a finite-difference procedure. The bottom and top surfaces of the cavity are, respectively, heated and cooled at constant temperatures, while its vertical walls are adiabatic. Parameters of the problem are the Rayleigh number (10(3) less than or equal to Ra less than or equal to 2.5 x 10(6)) and the surface emissivity (0 less than or equal to epsilon less than or equal to 1). The results obtained show that surface radiation alters significantly the existence range of the solution and the average heat transfer through the horizontal walls of the cavity. The parameter a is found to reduce considerably the critical Rayleigh number characterizing the transition toward the oscillatory convection.