A numerical study of thermal radiation effects on MHD flow and heat transfer in the presence of an external magnetic field in a cubic differentially heated cavity is carried out. The improved projection scheme, which is based on the spectral methods, is used to deal with the coupling of the velocity and the pressure. The radiative transfer equation is angularly discretized by the discrete ordinates method with an SPAP(N) quadrature scheme, and all the governing equations are solved by the Chebyshev collocation spectral method using the same grid. The results are presented in graphical and tabulated form. The isothermal surfaces, the projection of streamlines and isotherms on the three different mid-plane of the cubic cavity, comparative results of heat transfer rate, and three-dimensional transverse flow show the effects of the Hartmann number, the optical thickness and the conduction radiation interaction parameter on flow and heat transfer process. (C) 2015 Elsevier Ltd. All rights reserved.