Radiative convection with a fixed heat flux

We have determined the marginal stability curve of convective instability i n the usual Rayleigh-Benard configuration with radiative transfer and a fix ed total heat flux at the boundaries instead of a fixed temperature. In the Milne-Eddington approximation, radiative transfer introduces a new length scale and breaks the invariance of the Boussinesq equations under an arbitr ary temperature shift, which occurs when the heat flux is fixed at the boun daries. The convergence to the limits where the non-radiative cases are exp ected is studied in this approximation. Then, using a second-order perturba tive calculation, we show that the presence of radiation can change qualita tively the instability pattern: there is a range of optical parameters wher e the Cahn-Hillard equation is not anymore the one appropriate to describe the instability near the threshold. (C) 2001 Published by Elsevier Science B.V.