On the motion past thin airfoils of incompressible fluids with conductivity tensor

Abstract

This note is a study of the problem of the steady motion of an inviscid incompressible fluid past thin airfoils, the Hall effect being taken into account. The case of crossed fields (one of the most important in aerodynamics) is studied in detail. The results for the cases of aligned fields and Alfvén motion are also given. The general solution is represented by a continuous superposition of plane waves. The boundary conditions determine the solution by means of a Fredholm-type integral equation which may be solved with the aid of the method of successive approximations. If the parameter of the magneto-hydrodynamic interaction ( S ) \left ( S \right ) is equal to zero, one obtains the known solution of classical aerodynamics. The equation is solved explicitly for Alfvén motion.