Steady longitudinal motion of an insulating cylinder in a conducting fluid

Abstract

AbstractA mathematical analogue between a special class of problems in steady magnetohydrodynamics and appropriate problems in the theory of the scattering of sound pulses is established and exploited. Rigorous asymptotic expansions for large Hartmann numberMare obtained for the exact solution of the prototype problem, the circular cylinder. Asymptotic expansions for largeMin the case of a cylinder whose cross-section is an arbitrary closed convex curve are obtained as a straightforward application of the theory of geometrical optics and Keller's geometrical theory of diffraction.