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In the currently proposed helium-cooled lead lithium blanket design, the liquid metal serves mainly to breed tritium, and the heat flux is removed by helium flowing at high pressure in channels grooved in the walls. The use of a separate coolant has the advantage that the liquid metal can flow in the blanket with smaller velocities compared to those required in self-cooled blanket concepts. As a result, the buoyant convective flow caused by nonuniform thermal conditions and gravity may be comparable or even exceed the forced flow foreseen for tritium removal. Therefore, the knowledge of buoyancy-driven magnetohydrodynamic flows becomes fundamental to understand how the liquid metal circulates in the blanket. In this paper, the main characteristics of magnetoconvective duct flows are described. Effects of the direction of the temperature gradient with respect to the orientation of the applied magnetic field and the influence of electric conductivity of walls on the flow structure are investigated numerically.