In this work, the laminar decaying inlet swirl flow in a straight micro-pipe with wall slip is solved analytically and the solution verified numerically. Based on a fully developed parabolic axial velocity profiles, the swirl velocity equation is solved by the separation of variable technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within the micro-pipe from the inlet, the wall slip and the inlet swirl velocity profile. The effects of the parameters on the swirl velocity distribution and the swirl decay are analyzed along the flow. Addition of a swirling velocity to the flow of a fluid in a pipe is of great importance in enhancement transport characteristics. The current results offer analytical equations to estimate the swirl velocity distribution with slip at the walls for the design of swirl flow devices. Furthermore, to quantify mixing, the change in the average distance traveled by fluid particles from inlet in a swirl flow is compared with the average distance traveled by the fluid particles in case of no swirl. A clear enhancement of the average distance traveled is obtained. In our opinion the present work is useful to researchers looking for enhancement of transport characteristics in micro-pipes.

中文翻译：

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带壁滑移的层流微管流中的入口涡流衰减和混合

在这项工作中，对具有壁滑移的直微管中的层流衰减入口涡流进行了解析求解，并对该解进行了数值验证。基于完全发展的抛物线轴向速度分布，旋流速度方程通过变量分离技术求解。该解表示为流动雷诺数、微管内距入口的轴向距离、壁滑移和入口涡流速度分布的函数。沿流动分析了参数对旋流速度分布和旋流衰减的影响。向管道中的流体流动添加涡流速度对于增强传输特性非常重要。目前的结果提供了分析方程来估计涡流速度分布与壁上的滑移，用于设计涡流装置。此外，为了量化混合，将旋流中流体颗粒从入口移动的平均距离的变化与没有旋流时流体颗粒移动的平均距离的变化进行比较。获得了平均行驶距离的明显增强。在我们看来，目前的工作对于寻求增强微管传输特性的研究人员很有用。