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

A study of the effect of an externally imposed magnetic field on the axisym metry-breaking instability of an axisymmetric convective flow, associated w ith crystal growth from bulk of melt, is presented. Convection in a vertica l cylinder with a parabolic temperature profile on the sidewall is consider ed as a representative model. A parametric study of the dependence of the c ritical Grashof number Gr(cr) 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 Gr(cr)(Ha) corresponding to the axisymmetric-three-dimensional transition for increas ing values of the axial magnetic field is obtained. The calculations are do ne using the spectral Galerkin method allowing an effective and accurate th ree-dimensional stability analysis, it is shown that at relatively small va lues of Ha the axisymmetric flow tends to be oscillatory unstable. After th e magnitude of the magnetic field (Ha) exceeds a certain value the instabil ity switches to a steady bifurcation caused by the Rayleigh-Benard mechanis m. (C) 2001 Elsevier Science B.V. All rights reserved.