The study on the natural convection heat transfer of liquid metals under the magnetic and gravitational fields

金属硅、砷化镓等半导体材料是用直拉法制备的集成电路衬底材料。该过程在高温下进行，使得进料多晶硅通过自然对流熔化。在外部磁场下，晶体棒和坩埚都旋转以具有均匀的晶体成分，从而抑制湍流。这些重力场和磁场使流场变得复杂，并且使得难以理解整体流动特性。本文从理论和实验两个方面对这一对流场进行了分析，在解析方法中，建立了动量、能量、质量和磁感应强度平衡方程的二维数学模型。在pr=0.054、prm=1以及Ha=1 ~ 10^3、Ra=10^4 ~ 10^6的范围内进行了样本计算。在强磁场下，许多水平浅涡在垂直外磁场下是稳定的。当外加磁场为水平横向时，对流模式由同心垂直滚动单元组成，实验装置由有机玻璃制成，其垂直一侧均匀加热，另一侧壁在等温条件下冷却。当实验液态金属在稳态对流中对流时，外加磁场。实验结果表明，随着磁场强度的增加，传热速率降低。然而，均匀热流条件与理论等温条件不同，定量比较被推迟到未来的工作。

The semiconducting materials such as metalic silicon and Gallium Arsenide are made by Czochralski method for substrates for integrated circuits. This process is undertaken under a high temperature so that feed poly silicon is melted with natural convection. Both a crystal rod and a crucible are rotated to have a uniformity of crystal component under an external magnetic field to suppress the turbulent flow. These gravitational and magnetic fields make the flow field complicated and make it difficult to understand the bulk flow characteristics. in this research, both theoretical and experimental analyses were carried out to clarify these convection fields.In the analytical approach, two-dimensional mathematical model was derived for the balance equations of momentum, energy, mass and magnetic induction. Sample computations were carried out for pr=0.054, prm=1 and for the range of Ha=1 to 10^3 and Ra=10^4 to 10^6. Under a strong magnetic field, many horizontal shallow vortices were found to be stable under a vertical external magnetic field. When the external magnetic field was horizontally transverse, the mode of convection was found to consist of concentric vertical roll cells.The experimental apparatus was made of plexiglass whose one vertical side was uniformly heated and an opposing wall was cooled at an isothermal condition. When the experimental liguid metal convected in a steady convection, the external magnetic field was impressed. The heat transfer rate was found to decrease with an increase in the strength of magnetic field. However, the uniform heat flux condition is different from the theoretical isothermal condition and quantitative comparison was deferred for the future work.