About modeling a layered viscous conductive fluid flow in a region changing in time

The flow of a viscous conductive incompressible fluid in a time-varying region is investigated. Based on the model of a layered fluid flow, a class of exact solutions of the equations of magnetohydrodynamics in the region moving in time is considered. We study the change in the structure of a fluid flow as a result of a volume effect by a magnetic field and the movement of the boundary of the flow region. Heat dissipation effect due to internal friction and Joule heating is considered. The presented results are relevant in connection with the study of optimization problems of controlling the dynamics of an incompressible fluid and the creation of the domestic technology “digital field”.