Influence of the parameters of a traveling magnetic field on the flow of a viscous conducting fluid

V. F. Tkachenko

Abstract
In this paper a solution is obtained for the motion of a conducting fluid in a plane duct when the tangential component of a traveling magnetic field is given at the duct boundaries with arbitrary amplitudes B₀₁ and B₀₂ and phase shift ϕ. The curl of the electromagnetic forces is calculated on the basis of an electrodynamic approximation, and it does not depend on the time or the coordinate in the direction of the phase velocity of the traveling field. This allows us to find a stationary solution of the equations of motion for the laminar flow of the fluid. An expression is obtained for the velocity profile, the average flow velocity, and the hydraulic drag coefficient. The dependence of the profile and the average velocity on the ratio of the ampli tudes h = B₀₂/B₀₁ and on the phase shift ϕ is investigated.