The paper studies the free convection flow of a compressible Boussinesq fluid under the simultaneous action of buoyancy and transverse magnetic field while the Rosselant approximation has been invoked to describe the radiative flux in the energy equation. The viscosity of the fluid v and its thermal conductivity k in this model are assumed to be functions of temperature. Under suitable non-dimensionalization the governing non-linear, coupled, partial differential equations are solved employing a perturbation technique based on the assumption that the fluid flow field is made up of a steady part and a transient. Results obtained which compare favourably well with published data show, that the skin friction for a compressible fluid is lower than that for an incompressible fluid. (c) 2006 Elsevier Ltd. All rights reserved.