具有滑移条件和倾斜磁场的Prandtl流体蠕动流的数学建模

中文摘要 AI 辅助

本文对非牛顿Prandtl流体在倾斜非对称通道中的蠕动流进行了理论分析。我们探讨了倾斜磁场对蠕动流的影响。这对于涉及狭窄、倾斜（倾斜）管道（类似于血管或消化系统）中流体流动的应用具有相关性。该模型还包括热力学方面，如热扩散（Soret效应）以及由壁-流体滑移条件引起的粘性耗散，这可能有助于优化诸如芯片实验室系统和透析机等医疗设备。在本研究中，通过质量、热量和动量平衡分别考虑了通用化学物质的浓度、温度和流体速度。使用适用于长波长（低频）和低雷诺数的数值技术对解进行近似。研究还讨论了捕获现象，这在临床角度上至关重要。所获得的见解可以提高对胃肠道和血管中生理流动的理解。通过理解流体如何运动以及颗粒如何被捕获，这些见解可能有助于设计改进的医用泵和人工器官。提供了流体速度分布、温度分布和通用化学物质浓度的图形可视化。此外，数值结果通过与基准问题的闭式解进行比较而得到验证。

英文摘要

The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid subject to peristaltic flow through an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications involving fluid flow in narrow, inclined (tilted) tubes similar to blood vessels or the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation resulting from wall-fluid slip conditions, which may help optimize medical devices such as lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature, and fluid velocity are taken into account through mass, heat, and momentum balances, respectively. The solution is approximated using numerical techniques suitable for long wavelengths (low frequency) and low Reynolds numbers. The study also discusses trapping phenomena, which are crucial from a clinical point of view. The developed insights can improve the understanding of physiological flows in the gastrointestinal tract and blood vessels. By understanding how the fluid moves and how particles are trapped, these insights may contribute to the design of improved medical pumps and artificial organs. Graphical visualizations are provided for the fluid velocity profile, temperature distribution, and concentration of a generic chemical. Furthermore, the numerical results are validated through comparison with a closed-form solution from a benchmark problem.

发表机构

• University of Hasselt（哈瑟尔特大学）

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