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

采用Czochralski法制备了金属硅和砷化镓等半导体材料作为集成电路衬底。这一过程是在高温下进行的，以便原料多晶硅在自然对流中熔化。晶体棒和坩埚在外加磁场作用下旋转，使晶体成分均匀，以抑制紊流。这些引力场和磁场使流场变得复杂，使人们难以理解体流特性。本文从理论和实验两方面对这些对流场进行了分析。在解析方法中，导出了动量、能量、质量和磁感应平衡方程的二维数学模型。在pr=0.054、prm=1和Ha=1 ~ 10^3、Ra=10^4 ~ 10^6范围内进行了样本计算。在强磁场作用下，许多水平浅涡在垂直外磁场作用下是稳定的。当外磁场为水平横向时，发现对流模式由同心垂直卷胞组成。实验装置由有机玻璃制成，其垂直一侧均匀加热，另一侧在等温条件下冷却。当实验液态金属在稳定对流中对流时，外加磁场被施加。传热速率随磁场强度的增大而减小。然而，均匀热流条件与理论等温条件不同，为今后的工作推迟了定量比较。

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.