Liquid metal MHD flow and heat transfer in a rectangular duct with perfectly conducting walls perpendicular to the applied magnetic field

Abstract

Several technological applications involve the flow of liquid metals in ducts under a magnetic field, for instance, the coolants of fusion reactors. In this paper, using a magnetohydrodynamic MHD formulation based on the electric potential, we obtain an analytical solution for the flow of a liquid metal in a rectangular duct with two insulating walls and two perfectly conducting walls perpendicular to the applied uniform magnetic field. As the Hartmann number increases, the flow displays high velocities in the boundary layers attached to the insulating walls and a quasi-stagnant flow at the core. The effect of this flow pattern on the forced convection heat transfer is then explored numerically considering a uniform heat flux on either the conducting or insulating walls. Compared to the hydrodynamic case, the MHD flow enhances the heat transfer as the Hartmann number increases only in the case when the heat flux is applied at the insulating walls where high velocities are present. The increase of the local Nusselt number as the Péclet number grows indicates an efficient heat removal from the heated wall.