Abstract
Numerical computations were carried out for natural convection of liquid metal in a rectangular enclosure in the presence of uniform magnetic fields. A vertical wall is heated and an opposing vertical wall is cooled while the other four walls are adiabatic. When all walls are electrically insulated, in the vicinity of the walls perpendicular to the applied magnetic field, Hartmann layers develop in which a large amount of electric current density passes and significant Lorentz force acts. In the present report, since the velocity and current density profiles are exponential within the Hartmann layers and uniform in the core flow when the electromagnetic force is large enough to neglect the inertial force, theoretical values for the velocity and current density at the layers are derived and these are used for the boundary conditions for the core flow. The numerical results with employing the Hartmann layers modeling agree well with the theoretical solution and previous experimental data.
