On the theory of Heiser and Shercliff experiment. Part 1: MHD flow in an open channel in strong uniform magnetic field

Magnetohydrodynamic (MHD) flows of viscous incompressible fluid in strong magnetic fields parallel to a free surface of fluid are investigated. The problem of flow in an open channel due to a moving side wall in uniform magnetic field is considered, and treated by means of matched asymptotic expansions method. The flow region is divided into various subregions and leading terms of asymptotic expansions as M tends towards infinity (M is the Hartmann number) of solutions of correspondent problems in each subregion are obtained. An exact analytic solution of equations governing the free-surface layer of thickness of order M to the minus 1/2 power is obtained.