# NUMERICAL COMPUTATION FOR CZOCHRALSKI CONVECTION OF LIQUID METAL IN A CUSP MAGNETIC FIELD

**Akihiro Arimura**

Institute of Advanced Material Study, Kyushu University, Kasuga Koen 6-1, Kasuga 816, JAPAN

**Hiroyuki Ozoe**

Institute of Advanced Material Study, Kyushu University, Kasuga, Japan; and Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China

## Abstract

Numerical computations were carried out for a Czochralski bulk flow of liquid metal in a rotating crucible with a rotating crystal rod under a cusp shape magnetic field. This cusp-shape magnetic field was proposed by Hoshikawa et al. for the best way to control the concentration of oxygen in the melt of silicon. Due to the rotational system and axially symmetric cusp magnetic field, the mathematical model equations were assumed to be given by a two-dimensional cylindrical coordinate system. The height and radius for the melt zone were assumed to be equal and divided into 20 equal grid sizes. Sample computations were carried out for Gr=10^{6}, Pr=0.01, Ha=0 to 1000. Re_{1}=580 (a crystal rod), Re_{2}=0 or −348 (a crucible). At Ha=1000, the average velocity decreased to 1/30 of that at Ha=0 to give almost conductive isotherms. The magnetic induction profile and magnetic vector potential were obtained in a cusp shape. The distribution of the local Nusselt number at a solidifying interface gave a larger value in a center of a crystal rod at Ha=1000 in contrast to that at Ha=0 for which a larger value was given near an edge of a crystal rod.