MHD duct flows under hydrodynamic “slip” condition

Three classic MHD problems are revisited assuming hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating wall: (1) Hartmann flow; (2) fully developed flow in a rectangular duct; and (3) quasi-two-dimensional (Q2D) turbulent flow. The first two problems have been solved analytically. Additionally to the Hartmann number (Ha), a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions of the paper is that the duct flows with the slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha >> 1 by factor (1+ S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers.