Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration

A study of the effect of an externally imposed magnetic field on the axisymmetry-breaking instability of an axisymmetric convective flow, associated with crystal growth from bulk of melt, is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. A parametric study of the dependence of the critical Grashof number Grcr on the Hartmann number Ha for fixed values of the Prandtl number (Pr=0.015) and the aspect ratio of the cylinder (A=height/radius=1, 2 and 3) is carried out. The stability diagram Grcr(Ha) corresponding to the axisymmetric}three-dimensional transition for increasing values of the axial magnetic field is obtained. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that at relatively small values of Ha the axisymmetric flow tends to be oscillatory unstable. After the magnitude of the magnetic field (Ha) exceeds a certain value the instability switches to a steady bifurcation caused by the Rayleigh–B! enard mechanism. # 2001 Elsevier Science B.V. All rights reserved. PACS: 81.10; 47.20; 47.65