Unsteady flow of an electrically conducting Bingham fluid in a plane magnetohydrodynamic channel

The influence of a sudden change in the external magnetic field on the flow of an electrically conducting Bingham fluid in a two-dimensional channel is considered. It is demonstrated that a method of independent descriptions of the flow in plastic and viscous regions can be used for studying magnetohydrodynamic flows of the Bingham fluid. An exact equation is derived for the position of the plastic flow region boundary as a function of time and magnetic field induction. It is shown that the corresponding Cauchy problem has a unique asymptotically stable solution. Results of numerical integration for some values of parameters are presented; these result confirm the qualitative conclusions.