This work presents analytical and numerical studies for pure Couette and combined Poiseuille‐Couette flows under slip. The fluid behaviour is described by the recently proposed viscoelastic model, known as the generalised simplified Phan‐Thien‐Tanner constitutive equation, that considers the Mittag‐Leffler function instead of the classical linear and exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The solutions derived in this work allow a better understanding of the model and its influence on the slippery behaviour of some complex fluids, contributing in this way to improve the modeling of complex fluids.

中文翻译：

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广义Phan-Thien-Tanner流体滑流的分析和数值研究

这项工作提出了对纯Couette以及滑移下的Poiseuille-Couette混合流的分析和数值研究。流体行为由最近提出的粘弹性模型描述，称为广义简化的Phan-Thien-Tanner本构方程，该模型考虑了Mittag-Leffler函数，而不是应力张量迹线的经典线性和指数函数，并提供了一个或两个新的拟合常数，以实现更高的拟合灵活性。通过这项工作得出的解决方案可以更好地理解模型及其对某些复杂流体的滑移行为的影响，从而有助于改进复杂流体的建模。