The effect of the direction of external horizontal magnetic fields on the linear stability of natural convection of liquid metal in an infinitely long vertical rectangular enclosure is numerically studied. A vertical side wall is heated and the opposing vertical wall is cooled both isothermally, whereas the other two vertical walls are adiabatic. A uniform horizontal magnetic field is applied either in the direction parallel or perpendicular to the temperature gradient. In this study, the height of the enclosure is so long as to neglect the top and bottom effects where returning flow takes place, and thus the basic flow is assumed to be a parallel flow and the temperature field is in heat conduction state. The Prandtl number is limited to the value of 0.025 and horizontal cross-section is square. The natural convection is monotonously stabilized as increase in the Hartmann number when the applied magnetic field is parallel to the temperature gradient. However, when the applied magnetic field is perpendicular to the temperature gradient, it is once destabilized at a certain low Hartmann number, but it is stabilized at high Hartmann numbers.

中文翻译：

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均匀水平磁场方向对长垂直矩形外壳自然对流线性稳定性的影响

数值研究了外部水平磁场方向对无限长垂直矩形外壳内液态金属自然对流线性稳定性的影响。垂直侧壁被加热，相对的垂直壁被等温冷却，而另外两个垂直壁是绝热的。在平行或垂直于温度梯度的方向上施加均匀的水平磁场。在本研究中，围护结构的高度只要忽略回流发生的顶部和底部效应，因此假设基本流动为平行流动，温度场处于热传导状态。Prandtl 数限制为 0.025 的值，并且水平横截面为正方形。当外加磁场平行于温度梯度时，自然对流随着哈特曼数的增加而单调稳定。但是，当外加磁场垂直于温度梯度时，它在一定的低哈特曼数下一度不稳定，但在高哈特曼数下稳定。