Three-dimensional computation of natural convection in the presence of magnetic field (cubic enclosure)

Abstract

Buoyancy-driven magneto hydrodynamic flow in a liquid-metal filled cubic enclosure is investigated by three dimensional numerical simulations. The enclosure is heated and cooled along two opposite vertical walls, all other walls being adiabatic. A uniform magnetic field is applied orthogonally to the gravity vector and to the temperature gradient (i.e., parallel to the isothermal walls). The Prandtl number is = 0.019 (characteristic of Galium); the Rayleigh number is made to vary from 103 to 107, the Hartmann number between 30 to 120 and the electrical conductance of the walls between 0 and 1. The Navier–Stokes equations, for the electrical potential, are solved by a finite volume method using the CFD package CFX-4 with some necessary adaptations. Steady-state conditions are assumed. In all cases, a three-dimensional flow with complex secondary motions and a complex current pattern is established. The results show that the dynamic and temperature fields are strongly affected by variations of the magnetic field intensity and the angle of inclination. Numerical simulations are carried out considering different combinations of Grashof and Hartmann numbers to study their effects on the streamlines, the isotherms and the Nusselt number. Wall electrical conductivity enhances damping by changing the distribution of the induced electric current to one which augments the magnitude of the Lorentz force.