Competition of localized thermal buoyancy and Lorentz forces in an electrolyte enclosed in a cavity

Abstract

We study the flow of an electrolyte inside a slender square cavity produced by two competing localized forces, the thermal buoyancy force produced by the heating of a central part of the horizontal bottom wall and a vertical downward Lorentz force. This force is produced by a constant horizontal electric current between the slender vertical walls and a couple of circular magnets with opposing polarization placed on the center of both square vertical walls. The flow inside the cavity is considered two dimensional and simulated using the lattice Boltzmann equation method. We find the map of the flow patterns and their transitions for a Grashof number Gr in the range 0≤Gr≤4×103 and a Chandrasekhar number Ch in 0≤Ch≤1×107. For Gr≤2×103, the plane Gr-Ch can be divided in three regions with sharp changes in the flow patterns and the average Nusselt number on the top wall and the average asymmetry. One region is dominated by the buoyancy force, another by the Lorentz force, and there is an intermediate one, where neither of these forces dominates. For larger Gr, there are no sharp transitions.