Transient incompressible flows of Jeffrey fluids over a permeable, flat, and infinite plate have been investigated. The plate motion is an oscillatory translation along the x-axis. Using the Laplace transform and perturbation method, the analytical solution for the velocity field in the transform domain has been obtained. The velocity field in the real domain has been determined by using the numerical Stehfest’s algorithm for the Laplace transform inversion. To have a validation of the obtained solution, we have determined the analytical solution for the flow without transpiration. It was found that when the transpiration parameter approaches zero, the solution for the flow with transpiration tends to the solution corresponding to the case without perspiration. The influence of the system parameters on fluid motion has been investigated by numerical simulations and graphical illustrations prepared with the software package Mathcad.

中文翻译：

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Jeffrey 流体在渗透壁上的瞬态流动

已经研究了 Jeffrey 流体在可渗透的、平坦的和无限大的板上的瞬态不可压缩流动。板块运动是沿x的振荡平移-轴。利用拉普拉斯变换和微扰方法，得到了变换域速度场的解析解。实域中的速度场已通过使用数值 Stehfest 算法进行拉普拉斯变换反演确定。为了验证所获得的解决方案，我们已经确定了没有蒸腾作用的流动的解析解。发现当蒸腾参数趋近于零时，有蒸腾流的解趋于无汗流的解。系统参数对流体运动的影响已经通过数值模拟和用 Mathcad 软件包准备的图形说明进行了研究。