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Analysis and control of shear flow over a rotating plate in the presence of magnetic field
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-02-06 , DOI: 10.1002/zamm.201800044 Motahar Reza 1 , G. P. Raja Sekhar 2
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-02-06 , DOI: 10.1002/zamm.201800044 Motahar Reza 1 , G. P. Raja Sekhar 2
Affiliation
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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.
中文翻译：
磁场作用下旋转板上剪切流的分析与控制
研究了在存在横向磁场的情况下，不可压缩的粘性导电流体流过均匀旋转的无限不可渗透平板的剪切流。假定流动受Navier-Stokes方程控制，并加上外加磁场。分析相应方程的解。注意，由于在旋转板上的剪切流，该问题没有轴对称解。但是有趣的是，这个问题对于次级速度分量没有唯一的解决方案。值得注意的是，针对该问题的Navier-Stokes方程接受一个参数系列的解。在边界层内部，外部剪切流的动量传递主要由压力梯度决定。沿x轴的次级速度分量是由于剪切和平移引起的速度的线性组合。但是，应注意的是，剪切力的贡献占主导。可以看出，初级和次级速度分量可以通过施加的磁场来控制。还发现由流体施加在板上的扭矩受所施加的磁场影响，但与外部流中的剪切无关。
更新日期：2020-02-06
中文翻译：
磁场作用下旋转板上剪切流的分析与控制
研究了在存在横向磁场的情况下，不可压缩的粘性导电流体流过均匀旋转的无限不可渗透平板的剪切流。假定流动受Navier-Stokes方程控制，并加上外加磁场。分析相应方程的解。注意，由于在旋转板上的剪切流，该问题没有轴对称解。但是有趣的是，这个问题对于次级速度分量没有唯一的解决方案。值得注意的是，针对该问题的Navier-Stokes方程接受一个参数系列的解。在边界层内部，外部剪切流的动量传递主要由压力梯度决定。沿x轴的次级速度分量是由于剪切和平移引起的速度的线性组合。但是，应注意的是，剪切力的贡献占主导。可以看出，初级和次级速度分量可以通过施加的磁场来控制。还发现由流体施加在板上的扭矩受所施加的磁场影响，但与外部流中的剪切无关。
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