This paper considers the oscillatory flow of the Oldroyd-B fluid in a tube with a right triangular cross-section. The partial differential equation for describing the unidirectional flow of Oldroyd-B fluid is derived. For treating the triangular region, the unstructured mesh finite element method is applied. For verifying the accuracy of the finite element method, the source term is introduced and the exact solution is constructed. We obtain an analytical solution for the isosceles triangular cross-section tube and analyze the effects of different parameters on the velocity amplitude and phase difference of the Oldroyd-B fluid flow. In addition, the dynamic characteristics for the unsteady-state Oldroyd-B fluid flow are discussed and the influence of the involved parameters, such as the pressure gradient, the relaxation and retardation time parameters on the velocity distribution are also investigated and the flow mechanism is analyzed graphically. At the same condition, we find that only the tube with an isosceles right triangle cross-section can produce the oscillatory flow. Finally, the fluid mechanism between the Newtonian fluid and the Oldroyd-B fluid for special cases is analyzed and discussed in detail.

中文翻译：

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Oldroyd-B 流体在直三角截面管中振荡流动的机理分析


本文考虑了 Oldroyd-B 流体在直三角形横截面的管中的振荡流动。推导了描述 Oldroyd-B 流体单向流动的偏微分方程。为了处理三角形区域，应用了非结构化网格有限元方法。为了验证有限元方法的准确性，引入了源项并构造了精确的解。我们获得了等腰三角形截面管的解析解，并分析了不同参数对 Oldroyd-B 流体流动速度幅值和相位差的影响。此外，讨论了非稳态 Oldroyd-B 流体流动的动力学特性，研究了压力梯度、弛豫和延迟时间参数等相关参数对速度分布的影响，并以图形方式分析了流动机制。在相同条件下，我们发现只有具有等腰直角三角形横截面的管子才能产生振荡流。最后，详细分析和讨论了特殊情况下牛顿流体和 Oldroyd-B 流体之间的流体机制。