Natural convection of an electrically conducting and radiating fluid in the presence of an external magnetic field is investigated numerically. The two opposing side walls are differentially heated with a temperature difference specified, while the top and bottom walls are insulated. The coupled momentum and energy equations associating with the electromagnetic retarding force as well as the buoyancy force terms are solved by an iterative procedure using the SIMPLER algorithm based on control volume approach. Steady-state conditions are assumed. The finite-volume method is utilised to solve the radiation transport adopting the same computational grid as used in solving the flow field, with which the radiating fluids in an enclosure are assumed to be radiatively opaque, transparent and participating, respectively. After validating the numerical procedures, the changes in the buoyant flow patterns and temperature distribution affected by combined radiation and a magnetic field are focused mainly. Comparative results for the velocity profiles and the heat transfer rates are presented too. Based on the results of this study, it was found that the radiation played a significant role in developing the hydromagnetic free convective flow in a differentially heated enclosure. (C) 2009 Elsevier Ltd. All rights reserved.