计及Hall和离子滑移电流的旋转流体在与时间相关初值条件下的MHD Couette流动

Time-Dependent MHD Couette Flow of a Rotating Fluid With Hall and Ion-Slip Currents

考虑Hall和离子滑移电流的影响,在旋转系统中研究导电流体非稳定的MHD Couette流动.在小数值磁场Reynolds数假定下,推导出基本的控制方程,使用著名的Laplace变换技术,数值地求解该基本方程.分两种情况:磁场相对于流体或者移动平板固定时,得到速度和表面摩擦力统一的闭式表达式.用图形讨论了问题的不同参数,对速度和表面摩擦力的影响.所得结果显示,主流速度u和次生速度v随着Hall电流而增大.离子滑移电流的增大,也会导致主流速度u的增大,但会使次生速度v减小.还给出了旋转、Hall和离子滑移参数的综合影响,确定了次生运动对流体流动的贡献.

The unsteady MHD Couette flow of an electrically conducting fluid in a rotating system was investigated taking Hall and ion-slip currents into consideration. The derived funda- mental equations on the assumption of small magnetic Reynolds number were solved analytical- ly by employing the well known Laplace transform technique. A unified closed form expressions for the velocity and the skin friction for the two different cases of the magnetic field being fixed to either the fluid or to the moving plate were obtained. The effects of the various parameters of the problem on the velocity and the skin friction were discussed through graphs. The result obtained revealed that the primary and the secondary velocities increases with Hall current. An increase in the ion-slip also led to an increase in the primary velocity but decreases the secondary velocity. It has also been shown that the combined effect of the rotation, Hall and ion-slip parameters determine the contribution of the secondary motion in the fluid flow.