Three-dimensional numerical calculations were performed on the magnetohydrodynamic (MHD) flow through a rectangular channel with sudden expansion. The sudden expansion is in the direction of the applied magnetic field. The continuity equation, the momentum equation and the induction equation, derived from Maxwell's equations and Ohm's law, were solved numerically. The discretization of the equations is carried out by the finite difference method, and the solution procedure follows the MAC method. A base case calculation was carried out for a Hartmann number of 100, a Reynolds number of 1000, a magnetic Reynolds number of 0.001, an aspect ratio of 1 and an expansion ratio of 2, simulating conditions typical to experimental scales and conditions. The loss coefficients for the expansions with aspect ratios larger than 1 or smaller than 1 become smaller than that in the base case (i.e. the aspect ratio of 1). A flow channel with a small aspect ratio has the advantage of decreasing the pressure drops both in the fully-developed flow and in the flow through the expansion. On the other hand, the loss coefficients for the expansions with expansion ratios larger than 3 become larger than that in the base case (i.e. the expansion ratio of 2).
