Steady Two-Dimensional Channel Flow of an Incompressible Perfect Fluid with Small Electric Conductivity in the Presence of Nonuniform Magnetic Fields

Abstract

This paper deals with the steady two-dimensional channel flows of an incompressible perfect fluid with small electric conductivity in the presence of nonuniform magnetic fields generated by a system of electric currents and magnetic poles. The flow and the magnetic fields are calculated for small values of electric conductivity of the fluid. The velocity distribution is found, with in the order of our approximation, to depend only on the distribution of the magnitude of the magnetic field. The numerical calculations are performed for one case of the geometrical parameter which represents the position of the currents or of the magnetic poles, and the results are shown graphically. The analytical expressions for the pressure difference between infinities down- and up-stream and the velocity distribution at the infinity downstream also presented.