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首页> 外文期刊>Fluid mechanics research >Unsteady MHD Hartmann-Couette Flow Due to Time Dependent Movement of the Plate of a Darcian Channel with Hall Current and Ion-Slip Effects
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Unsteady MHD Hartmann-Couette Flow Due to Time Dependent Movement of the Plate of a Darcian Channel with Hall Current and Ion-Slip Effects

机译：由于具有霍尔电流和离子滑移效应的达尔卡河通道板的时变运动，导致不稳定的MHD Hartmann-Couette流动

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摘要

Unsteady MHD Hartmann-Couette flow of a viscous, incompressible and electrically conducting fluid within parallel plate porous Darcian channel with Hall current and ion-slip effects is carried-out. Fluid flow within the channel is induced due to time dependent movement of the upper plate of the channel and by a constant pressure gradient applied along the axis of the plates of the Darcian channel. Fluid flow within the Darcian channel is permeated by a uniform transverse magnetic field, which is fixed relative to the stationary plate. Laplace transform technique is used to obtain an exact solution of the governing equations. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. To highlight the transient approach to the final steady state flow and the effects of Hall current, ion-slip, magnetic field, permeability and suction/injection, asymptotic behavior of the solution is analyzed for small and large values of time. It is noticed that, at the starting stage, secondary velocity is independent of permeability and there are no flows in the secondary flow direction in the absence of Hall current. At the final stage, fluid flow is in quasi-steady state. Steady state flow executes spatial oscillations in the flow-field whereas unsteady state flow exhibits spatial as well as inertial oscillation in the flow-field. Inertial oscillations in the flow-field are due to presence of Hall current. Numerical values of primary and secondary fluid velocities and that of shear stress at the moving plate of the Darcian channel due to primary and secondary flows are represented graphically for various values of pertinent flow parameters.
机译：在具有霍尔电流和离子滑移效应的平行板多孔达西通道内，进行了粘性，不可压缩且导电的流体的非稳态MHD Hartmann-Couette流。通道内的流体流动是由于通道的上板的时间依赖性运动以及沿达西通道的板的轴线施加的恒定压力梯度引起的。 Darcian通道内的流体流被均匀的横向磁场渗透，该磁场相对于固定板是固定的。拉普拉斯变换技术用于获得控制方程的精确解。还导出了由于一次和二次流动而在移动板上的剪切应力的表达式。为了突出最终稳态流动的瞬态方法以及霍尔电流，离子滑移，磁场，磁导率和吸力/注入的影响，分析了溶液的渐近行为，无论时间大小如何。注意到，在开始阶段，次级速度与渗透率无关，并且在没有霍尔电流的情况下，在次级流动方向上没有流动。在最后阶段，流体流动处于准稳态。稳态流在流场中执行空间振荡，而非稳态流在流场中表现出空间以及惯性振荡。流场中的惯性振荡是由于霍尔电流的存在。对于相关流动参数的各种值，用图形表示了一次和二次流体速度的数值，以及由于一次和二次流动而在Darcian河道运动板处的切应力的数值。

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