THERMOCAPILLARY CONVECTION IN A CYLINDRICAL LIQUID-METAL FLOATING-ZONE WITH A STRONG AXIAL MAGNETIC-FIELD AND WITH A NON-AXISYMMETRICAL HEAT-FLUX

This paper treats the steady three-dimensional thermocapillary convect ion in a cylindrical liquid-metal zone between the isothermal ends of two coaxial solid cylinders and surrounded by an atmosphere. There is a uniform steady magnetic field which is parallel to the common centre lines of the liquid zone and solid cylinders, and there is a non-axisy mmetric heat flux into the liquid's free surface. The magnetic field i s sufficiently strong that inertial effects and convective heat transf er are negligible, and that viscous effects are confined to thin bound ary layers adjacent to the free surface and to the liquid-solid interf aces. With an axisymmetric heat flux, the axisymmetric thermocapillary convection is confined to the thin layer adjacent to the free surface , but with a non-axisymmetric heat flux, there is an azimuthal flow in side the free-surface layer from the hot spot to the cold spot with th e circulation completed by flow across the inviscid central core regio n. This problem is related to the magnetic damping of thermocapillary convection for the floating-zone growth of semiconductor crystals in S pace.