Thermocapillary convection in a cylinder with a strong non-uniform axisymmetric magnetic field

Abstract

This paper treats a surface-tension-driven liquid-metal flow in a cylinder with a steady externally applied non-uniform axisymmetric magnetic field. The top boundary consists of an annular free surface around a solid disk, modelling the Czochralski growth of silicon crystals. A radial temperature gradient produces a decrease of the surface tension from the disk edge to the vertical cylinder wall. The magnetic flux density is sufficiently large that inertial effects and convective heat transfer are negligible. First we present large-Hartmann-number asymptotic solutions for magnetic fields with either a non-zero or a zero axial component at the free surface. The asymptotic solutions indicate that a purely radial magnetic field at the free surface represents a singular limit of more general magnetic fields. Secondly we present numerical solutions for arbitrary values of the Hartmann number, and we treat the evolution of the thermocapillary convection as the axial magnetic field at the free surface is changed continuously from the full field strength to zero.

Melt‐Motion during the Czochralski Growth of Silicon Crystals with a Cusp Magnetic Field

“…As in our previous papers, 8 The isotherms and buoyant-convection streamlines in the core for Pe = 5 are presented in Fig. 2.…”

Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

“…The numerical results for magnetic field effects on thermocapillary flows in Czochralski configurations (see e.g. Khine & Walker 1994 and references therein) or infinite plane layers (e.g. Priede, Thess & Gerbeth 1994;Priede & Gerbeth 1995; see also the review in Wilson 1994) cannot be applied to the floating-zone problem owing to the different geometry.…”