Theory of thin airfoils in fluids of high electrical conductivity

Abstract

Steady, plane flow of incompressible fluid past thin cylindrical obstacles is treated with two different orientations of the undisturbed, uniform magnetic field; namely, parallel and perpendicular, respectively, to the undisturbed, uniform stream. In the first case, the flow of an infinitely conducting fluid is shown to be irrotational and current-free except for surface curents at the walls of the obstacles. With large but finite conductivity the surface currents are replaced by thin boundary layers of large current density.In the second case, for infinite conductivity the flow field is made up of an irrotational current-free part and a system of waves involving currents and vorticity extending out from the body. For large, finite conductivity these waves attenuate exponentially with distance from the body.In both cases the forces on sinusoidal walls and on airfoils are calculated. In the second case positive drag occurs.