Hydromagnetic flow in a cavity under a uniform magnetic field is studied numerically. The cavity is comprised of four radiatively active surfaces. Due to large temperature difference inside a cavity, the radiative interaction between walls is taken into account. The coupled momentum and energy equations are solved by SIMPLER algorithm while the radiant heat exchanges are obtained by the finite volume method for radiation. A Wide range of Grashof numbers is examined as a controlling parameter. Resultant flow and heat transfer characteristics are investigated as well.