Two-dimensional channel flow of liquid metal in the presence of progressing alternating transverse magnetic field

Abstract

The flow of an electrically conducting incompressible fluid through a two-dimensional channel in the presence of a progressing alternating transverse magnetic field is solved by the method of matched asymptotic expansions for large Reynolds number and small magnetic Reynolds number, under the assumption of sufficiently small channel height compared with the wavelength of the alternating magnetic field. The velocity distribution in the boundary layer consists of a Hartmann type monotonous profile as in a uniform magnetic field and an oscillatory profile characteristic of an alternating magnetic field. In the core region, the alternating Lorentz force is almost canceled by the corresponding variation of pressure and there is a little oscillation in the fluid velocity. However, in the boundary layer, the oscillatory fluid motion appears with appreciable amplitude, as a result of the unbalance between the alternating pressure gradient and the Lorentz force.