In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity ...

中文翻译：

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瞬态挤压流的精确近似解

在本文中，我们报告了两种新的理论方法来检查薄流体间隙中快速发展的流动，这在工业应用和生物系统中被广泛观察到。该问题的特点是雷诺数和斯特劳哈尔数非常小，使得流体对流加速度可以忽略不计，而其局部加速度则不然。我们已经为这个问题开发了一个精确的解决方案，它表明当粘性效应来不及出现时，流动以无粘性极限开始，随后是随后的发展流动，其中粘性效应继续渗透到整个流体间隙. 还使用边界层积分方法开发了近似解。该解精确地捕捉了瞬态流体流动过程的一般行为，并且与精确解非常吻合。我们还使用 Ansys-CFX 进行了数值模拟。获得了解析解和数值解之间的极好一致性，表明了有效性......