MHD flow in rectangular ducts with inclined non-uniform transverse magnetic field

This paper examines the three-dimensional liquid metal MHD flow in rectangular ducts with thin conducting walls and with an inclined non-uniform transverse magnetic field. The Hartmann number and interaction parameter are assumed to be large and the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined to thin boundary layers adjacent to the walls. Outside these layers, the governing equations are significantly simplified. For validation of the numerical solutions, exact analytical solutions are derived for the case of a rectangular duct of equal wall thickness and with a uniform magnetic field. Comparisons of the exact analytical and numerical solutions give excellent agreement. Variation of the fully developed flow pressure gradient with the wall conductance ratio, aspect ratio, and magnetic angle is discussed. Numerical solutions are presented for flow in the varying field region where the flow is perturbed due to three-dimensional effects. The three-dimensional pressure drop, i.e. in excess of the locally fully developed pressure, is presented and its implication to a fusion blanket is discussed. The velocity distributions are also presented.