Numerical Simulation of Three Dimensional Low Prandtl Liquid Flow in a Parallelepiped Cavity Under an external Magnetic Field

A numerical study has been carried out to investigate the three-dimen -sional buoyant flow in a parallelepiped box heated from below and partially from the two sidewalls (a configuration commonly used for solidification problems and crystal growth systems). Attention has been paid, in particular, to phenomena of symmetry breaking and transition to unsteady non-symmetric convection for a low Prandtl number fluid (Pr=0.01). The influence of an applied horizontal magnetic field on the stability properties of the flow has been also considered. Results obtained may be summarized as follows: In the absence of magnetic field and for relatively small values of the Rayleigh number (Ra), a steady and symmetric flow field is obtained with 3D effects limited to classical spiral flows in the third direction. When Ra is increased to its first critical value, the system bifurcates from the steady symmetric flow to a non-symmetric flow. The break in symmetry occurs with respect to the vertical mid-plane and the diagonal plane. The first critical value for which symmetry is broken has been found to behave as an increasing function of the magnetic field strength.