Heat transfer by simultaneous radiation and natural convection through an optically thick fluid over a heated vertical plate has been studied with first-order momentum and thermal non-continuum boundary conditions. The radiant heat flux was treated using the Rosseland diffusion approximation. By solving the local non-similarity two-equation model, numerical solutions were obtained to examine the slip effects on the interaction between radiation and natural convection for a range of rarefied conditions and radiation effects. Results including slip velocity, temperature jump, skin friction, and heat transfer rate are presented graphically and discussed. In addition, an integral correlation is presented for the average Nusselt number as a function of the non-continuum conditions, radiation-conduction parameter, and flow properties. (C) 2015 Elsevier Ltd. All rights reserved.