BOUNDARY-LAYERS IN MAGNETIC CZOCHRALSKI CRYSTAL-GROWTH

The magnetohydrodynamic boundary layer at the crystal-melt interface and the free surface of the melt, in Czochralski crystal growth, is examined. The cases of a uniform axial magnetic field, and a radial magnetic field are considered separately. Authors first establish the governing equations in the boundary-layer approximation, on the assumption that the Reynolds number based on the speed at the edge of the rotating crystal is large. They discuss in detail the current density vector and its role in creating the Lorentz force at the edge of, and beyond, the boundary layer. For the second case, where there is only a radial component of magnetic field in the boundary layer, they show that there is no direct hydromagnetic effect on the flow in the boundary layer unless a current passes between the melt and crystal.