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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Analysis and control of shear flow over a rotating plate in the presence of magnetic field
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Analysis and control of shear flow over a rotating plate in the presence of magnetic field

机译：磁场存在下旋转板上剪切流的分析与控制

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摘要

Shear flow of an incompressible viscous electrically conducting fluid past a uniformly rotating infinite impermeable flat plate in the presence of transverse magnetic field is investigated. The flow is assumed to be governed by Navier-Stokes equations augmented with an applied magnetic field. Solutions of the corresponding equations are analyzed. It is noted that due to shear flow over a rotating plate, the problem has no axisymmetric solutions. But it is interesting to note that this problem has no unique solution for the secondary velocity components. It is remarkable to note that Navier- Stokes equations for this problem admit a one parameter family of solutions. Inside the boundary layer, the momentum transfer of the outer shear flow is dominated by the pressure gradient. The secondary velocity component along x-axis is a linear combination of velocity due to shear and translation. However, it is noted that the contribution from the shear dominates. It is observed that the primary and secondary velocity components can be controlled by the applied magnetic field. It is also found that the torque exerted by the fluid on the plate is influenced by the applied magnetic field but independent of the shear in the external flow.
机译：研究了不可压缩粘性导电流体在横向磁场作用下通过均匀旋转无限大不透水平板的剪切流动。假设流动由附加磁场的Navier-Stokes方程控制。分析了相应方程的解。值得注意的是，由于旋转板上的剪切流，该问题没有轴对称解。但有趣的是，对于二次速度分量，这个问题没有唯一的解决方案。值得注意的是，这个问题的Navier-Stokes方程允许一个单参数解族。在边界层内部，外部剪切流的动量传递受压力梯度控制。由于剪切和平移，沿x轴的二次速度分量是速度的线性组合。然而，值得注意的是，剪切的贡献占主导地位。观察到，一次和二次速度分量可以由外加磁场控制。还发现，流体施加在板上的扭矩受外加磁场的影响，但与外部流动中的剪切力无关。

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