Two-dimensional Flow of an Ideal Gas with Small Electric Conductivity past a Thin Profile

Abstract

Two dimensional flow of an ideal gas with small electric conductivity past a thin profile is investigated. The applied uniform magnetic field is assumed to make a small angle with the uniform flow at infinity. The usual thin wing expansion technique is applied and the linearized equation is derived. The linearized equation is solved for the case of flow past a symmetric profile using an approximate method similar to that of Oseen in the theory of viscous flow, and the first order effects of the conductivity and of the angle of inclination are examined. The subsonic as well as the supersonic flow cases are considered, and the lift and the drag due to the magnetic field are obtained. In the subsonic case, the lift vanishes while the drag is positive for any profile. In the supersonic case, the lift is found to be negatively proportional to the angle of inclination, while the drag is not affected by the presence of the magnetic field. An intuitive explanation of the results is also included.