A theory of thin airfoils and slender bodies in fluids of finite electrical conductivity with aligned fields

Abstract

The steady incompressible flow of a non-viscous conducting fluid about thin airfoils and slender bodies is studied for the case of a uniform applied magnetic field aligned with the undisturbed fluid stream. Solutions are found, subject to the restriction of small perturbations to the applied field. This condition determines an upper limit on the range of conductivity to which the solution are applicable. Certain results for larger values of conductivity are presented and discussed.The lift on airfoils is calculated, including the possibility of magnets and externally driven currents inside the airfoil, and a magnetohydrodynamic analogue to the Kutta condition is discussed. Drag formulae are presented for airfoils and slender bodies, and the distribution of internal currents and magnets for zero drag is shown. Optimum drag airfoils and bodies are discussed briefly.