Magnetic convection

磁场已被用于各种制造过程，如半导体材料的克佐拉尔斯基晶体生长和/或连续铸钢过程，因此可以通过平息熔融材料的对流来期望更高质量的固化产品。这是因为液态金属的普朗特数低至0.01。振荡对流是液态金属中常见的现象，它会导致凝固产物的结构不均匀。为了避免这些现象，有时在没有详细了解热、质量和动量传递等输运现象的相关机制的情况下，在试错基地中使用强磁场。在本研究计划中，对磁场的影响进行了精确的建模和精确的数值分析。第一个考虑的系统是查克拉尔斯基晶体生长过程中的熔体对流。所考虑的系统是在高H的圆柱形坩埚中熔化的InSb金属，直径为1.25H，直径为0.625H的晶棒。对晶棒进行冷却，对自由表面进行辐射冷却。然后，在没有磁场的情况下，即使在轴对称坩埚中，也计算了单个单侧对流滚动。在水平横向磁场作用下，计算了自由表面上的稳定对流，在垂直磁场平面上气流上升，在平行磁场平面上气流下降。这使得自由表面上的椭圆温度等高线期望提供椭圆截面的单晶棒。通过查阅文献，我们发现Kajigaya等人在水平磁场中制备了GaAs的椭圆截面单晶棒。这意味着他们的实验报告有力地支持了目前的理论分析，并对单晶棒的生长给出了理论解释。作为第二个研究课题，对磁化力引起的对流进行了研究。其中之一是关于氧气从垂直管道的顶部和底部开口流出的对流和扩散过程，垂直管道位于一个强度为12特斯拉的超导磁体孔中。竖管直径50mm，长600mm，管内充入纯氧气体。在时间为零时，打开管道的顶部和底部开口，使氧气自然通风。氧气的平均分子量略大于周围空气的平均分子量，在没有磁场的情况下，氧气会快速流出。随着磁场强度的增大，垂直管道中高处氧的平均浓度逐渐降低。在12特斯拉时，2000秒后氧的浓度下降到初始浓度的30%。用质量和动量平衡方程模拟了目前的现象，并进行了数值求解。计算得到的中高度瞬态氧气浓度与前人的实验结果吻合较好，从而保证了模型方程的正确性。详细的图形可视化阐明了上述特点。当管道中的氧气下半部分从底部开口流出，管道上半部分充满空气时，磁化力作用将氧气拉回管道的中心高度，使高浓度的氧气长期保持在管道的中间高度。管道中高度处的氧气浓度随着扩散逐渐降低。除此之外，还有大量的研究结果。它们分别是：直克拉尔斯基晶体生长中的尖形磁场、旋转磁场、塞贝克对流和超导磁体孔内由磁化力引起的准非引力场。少

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 analyzes 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, … More 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 analyzes 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 located1 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