Abstract

The stability of magnetized flows of a nonuniformly rotating layer of an electrically conducting nanofluid is investigated with regard to the effects of Brownian diffusion and thermophoresis. In the absence of a temperature gradient, new types of magnetorotational instability (MRI) are considered in axial, azimuthal, and helical magnetic fields in thin layers of a nanofluid. The increments and development regions of these instabilities are obtained depending on the angular velocity profile (Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, stationary regimes of nonuniformly rotating convection in axial and helical magnetic fields are studied. Expressions are obtained for the critical Rayleigh numbers Ra_st, and neutral stability curves are plotted depending on the angular velocity profile, the profile of the external azimuthal magnetic field (the magnetic Rossby number Rb), and the radial wavenumber k. Conditions for stabilization and destabilization of stationary convection in axial and helical magnetic fields are found.

中文翻译：

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导电纳米流体非均匀旋转层中的水磁不稳定性

摘要

关于布朗扩散和热泳的影响，研究了导电纳米流体的非均匀旋转层的磁化流的稳定性。在没有温度梯度的情况下，在纳米流体薄层中的轴向、方位角和螺旋磁场中考虑了新型磁旋转不稳定性 (MRI)。这些不稳定性的增量和发展区域取决于角速度分布（Rossby 数 Ro）和径向波数k。在存在温度和纳米颗粒浓度梯度的情况下，研究了轴向和螺旋磁场中非均匀旋转对流的静止状态。获得临界瑞利数 Ra _{st 的}表达式和中性稳定性曲线根据角速度分布图、外部方位角磁场分布图（磁性罗斯比数 Rb）和径向波数k绘制。找到了在轴向和螺旋磁场中稳定对流的稳定和不稳定的条件。