Liquid metal MHD flow in a duct whose cross section changes from a rectangle to a trapezoid

Abstract

This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross-sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided that the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and the electric currents are concentrated in boundary layers adjacent to the sides and in the sides. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers and sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow.