Extension of the M² and the Thin-Wing-Expansion Methods to Magnetohydrodynamics

Abstract

On the basis of a reduced equation for steady, two-dimensional flow of a perfectly conducting gas with an aligned magnetic field, the M²⁻ expansion method as well as the thin-wing expansion method is extended to include the effect of a magnetic field.
General formulae obtained by both methods remain unchanged, except that the parameters involved should be read as given in the paper.
The transonic thin-airfoil theory is also modified for magneto-hydro-dynamical flow and it is found that the same similarity rule for the flow past a slender body holds for both non-magnetic and magnetic cases with the proper alteration of the parameters.