MHD stability of natural convection in rectangular cavity

We present the results of a three-dimensional numerical investigation of the effect of a magnetic field on the stability of laminar natural convection in a metal liquid. A rectangular cavity with a free top surface container of Gallium is subject to a horizontal temperature gradient and a uniform magnetic field is applied separately in two directions. Computations are carried out for the cavity 5 x 1 X 1 (length to height to width). The model equations are solved by a finite volume method. The validation of the numerical method was achieved by comparison with both experimental data found in literature. Results show that natural convection is suppressed with an imposed magnetic field and the magnetic damping effect increases with an increase in the field strength. We present stability diagrams showing the dependence of the critical Grashof number on the Hartmann number. It is shown that a longitudinal magnetic field provides the strongest stabilization effect.