| Research Abstract |
The magnetic field has been employed for various manufacturing processes such as Czochralski crystal growth of semi-conducting material and/or continuous steel casting processes so that higher quality of solidified products can be expected by calming the convection of molten materials. This is because the Prandtl number of liquid metal is as low as 0.01. The oscillatory convection is common for liquid metal and causes nonuniform structure in the solidified product. To avoid these phenomena sometimes strong magnetic field has been employed in trial and error bases without detailed understanding on the related mechanism of transport phenomena such as heat, mass and momentum transfer. In the present research program, an exact modeling on the effect of magnetic field and acurate numerical analyses were carried out.
The first system considered is melt convection in a Czochralski crystal growth process. The system considered is molten metal of InSb in a cylindrical crucible with H in height,
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1.25H in diameter with a crystal rod of 0.625H in diameter. The crystal rod is cooled and the free surface is radiatively cooled. Then, without a magnetic field, a single one-sided convection roll was computed even in an axi-symmetric crucible. With a horizontal lateral magnetic field, a stable convection over a free surface was computed with rising flow in a perpendicular plane of a magnetic field and downward flow in a parallel plane. This caused elliptic temperature contours over a free surface to expect to provide an elliptic cross-sectional single crystal rod. By making a literature survey, we found a report by Kajigaya et al. to have manufactured an elliptic cross sectional single crystal rod of GaAs in a horizontal magnetic field. This means present theoretical analyses are strongly supported by their experimental report and to give theoretical explanation for their growing of a single crystal rod.
As a second research subject, the convection due to magnetizing force was studied. One of them is about the convection and diffusion process of oxygen gas flowing out from top and bottom openings of a vertical pipe located in a bore of a super-conducting magnet as strong as 12 Tesla. The vertical pipe is 50 mm in diameter and 600 mm in length and is filled with pure oxygen gas. At time zero, top and bottom openings of the pipe are opened and natural ventilation of oxygen gas is resulted. The average molecular weight of oxygen gas is slightly larger than that of ambient air to result in quick flowing out of oxygen gas in the case of no magnetic field. As the magnetic strength was increased, the average concentration of oxygen at a mid height of the vertical pipe was found to decrease more and more gradually. At 12 Tesla, the concentration of oxygen decreased to 30 % of the initial one after 2000 seconds. Present phenomena was modeled by balance equations for mass and momentum and numerically solved. Then the resulted transient concentration of oxygen gas at a mid height agreed quite well with previous experiments to assure the model equations. Detailed graphic visualization clarified above characteristics. When bottom half of oxygen gas in the pipe flows out from a bottom opening with the top half of the pipe filled with air, then magnetizing force works to pull back the oxygen gas into the central height of the pipe and high concentration of oxygen gas was kept at the mid-height for a long time. The concentration of oxygen gas at a mid-height of the pipe decreased gradually with diffusion.
There are extensive research results other than this. They are the cusp-shaped magnetic field in a Czochralski crystal growth, the rotational magnetic field, Seebeck convection and quasi non-gravitational field due to magnetizing force in a bore of a super-conducting-magnet. Less
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