Melt motion in a Czochralski crystal puller with an axial magnetic field: Uncertainty in the thermal constants
1988; Elsevier BV; Volume: 87; Issue: 1 Linguagem: Inglês
10.1016/0022-0248(88)90340-5
ISSN1873-5002
Autores Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoFor a Czochralski silicon puller with a uniform axial magnetic field of at least 0.2 T (2000 G), the melt velocities are so small that the inertial effects can be neglected and viscous effects are confined to thin layers. Analytical solutions of the momentum equation are possible and provide physical insights into the melt motions. The asymptotic analysis for strong magnetic fields is used to treat the effects of changing the values of the thermal conductivity, coefficient of volumetric expansion and thermal gradient of surface tension. With a particular choice for the characteristic velocity, the dimensionless streamfunctions for the melt motions are relatively independent of the thermal conductivity and depend on the thermal expansion coefficient and surface tension gradient only through a single parameter reflecting the ratio of these two thermal constants. Variations with magnetic field strengths from 0.2 to 1.7 T are discussed as well.
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