On an analogy between plane finite elastic deformations and certain magnetohydrodynamic flows

Abstract

The governing non-linear coupled partial differential equations for certain steady magnetohydrodynamic flows are shown to be similar in form to those arising for plane strain finite elastic deformations of a neo-Hookean or Mooney material. Based on this analogy new results are obtained for the magnetohydrodynamic system. Firstly a restricted form of Adkins' reciprocal theorem is given and secondly two new classes of exact solutions are obtained. One of these includes as a special case a known class of spiral flows for geometries wherein the magnetic field and fluid velocity are everywhere inclined at a constant angle.