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

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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.