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Magnetohydrodynamic flow of an incompressible fluid through a plane channel with slowly varying walls and a magnetic field applied transverse to the channel is investigated in the high Reynolds number limit. It is found that the magnetic field can first influence the hydrodynamic flow when the Hartmann number reaches a sufficiently large value. The magnetic field is found to suppress the steady and unsteady viscous flow near the channel walls unless the wall shapes become large.
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