AI 中文总结
本研究验证横向磁场中对流的准二维（Q2D）模型适用性，对比三维计算结果明确其有效条件，发现其可正确预测特定腔室流动特性，并提出其在导电边界腔室的扩展方向。
AI 中文摘要
本研究探讨横向加热矩形盒在横向磁场中自然对流的准二维（Q2D）模型的适用性。为此，将Q2D模型的结果与完全三维计算结果进行对比，计算对象为方形横截面矩形盒、长径比（长度与高度之比）为8的水平细长矩形盒，且宽高比（宽度与高度之比）在1至10之间变化。研究指出，Q2D模型在特定条件下有效，这些条件包括展向边界的热学和电学完全绝缘，以及相对于展向中平面的反射对称性。结果表明，在这些条件下，Q2D模型对于方形横截面盒及水平细长腔室，无论宽高比如何，均能给出定量正确的结果。针对壁面完全导电的盒所得到的三维结果，在宽高比逐渐增大时呈现渐近行为，但这与修正后的Q2D模型的预测不符。研究还表明，当Q2D模型适用时，它可正确预测三维流动的稳态-振荡转变。研究建议，应探索Q2D模型在展向边界完全导电的腔室中的扩展方向。
英文摘要
In this study we examine applicability of the quasi-two-dimensional (Q2D) model of natural convection in a laterally heated rectangular box subject to a transverse magnetic field. For this purpose, results obtained using the Q2D model are compared with fully three-dimensional calculations for rectangular boxes with a square cross-section and horizontally elongated ones with the length to height ratio 8. The width to height ratio is varied from 1 to 10. It is argued that the Q2D model is valid under certain conditions, which include perfect thermal and electrical insulation of the spanwise boundaries and reflection symmetry with respect to the spanwise midplane. It is shown that under these conditions, the Q2D model yields quantitatively correct results for boxes with square cross-section, as well as for horizontally elongated cavities, independently on the width to height ratio. Three-dimensional results obtained for boxes with perfectly conducting walls exhibit asymptotics at gradually increasing width ratio, which, however, does not agree with the predictions of an amended Q2D model. It is shown also that when is applicable, the Q2D model can correctly predict steady-oscillatory transition of three-dimensional flows. It is proposed to seek for extensions of the Q2D model for cavities with perfectly conducting spanwise boundaries.
