Effects of a rotating magnetic field on the thermocapillary instability in the floating zone process

Abstract

This paper presents a linear stability analysis for the thermocapillary convection in the floating zone process with a rotating magnetic field (RMF). For every case with a RMF, there is a transition from a steady, axisymmetric flow to a periodic, nonaxisymmetric flow at a critical value of Re, the Reynolds number for the thermocapillary convection. As Tm, the magnetic Taylor number for the RMF, is increased from zero, the critical value of Re first decreases to a minimum and then increases as the azimuthal flow velocity becomes strong enough to damp the radial and axial flow velocities. Critical modes for some values of Tm involve azimuthal wave velocities which are greater than the maximum azimuthal flow velocity, while critical modes for other values of Tm could be nonaxisymmetric patterns which are convected by the azimuthal flow velocity. Results are presented for three values of the Prandtl number.