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Three-dimensional numerical calculations have been performed on liquid-metal magnetohydrodynamic (MHD) flow through a rectangular channel in the inlet region of the applied magnetic field, including a region upstream the magnetic field section. The continuity equation, the momentum equation including the Lorentz force term and the induction equation have been solved numerically. The induction equation is derived from Maxwell's equations and Ohm's law in electromagnetism. The discretization of the equations is carried out by the finite difference method, and the solution procedure follows the MAC method. Along the flow axis (i.e. the channel axis), the pressure decreases slightly as normal non-MHD flow, increases once, thereafter decreases sharply and finally decreases as fully-developed MHD flow. The sharp decrease in the pressure, resulting in a large pressure drop, in the inlet region is due to increase in the induced electric current in this region comparing with that in the fully-developed region. In the inlet region, the flow velocity distribution changes from a parabolic profile of a laminar non-MHD flow to a flat profile of a fully-developed MHD flow.

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