In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

中文翻译：

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使用两种基于同伦方法的可变粘度耦合应力流体流动分析

在本文中，研究了不可压缩的，非等温的，耦合应力流体在两个平行壁之间稳定流动的Vogel模型的广义平面Couette流。控制方程简化为常微分方程。为了研究微分方程的非线性耦合系统，使用了具有DJ多项式的最优同伦渐近方法和渐近同伦摄动方法。介绍并讨论了重要的流动特性。我们获得了速度，平均速度，剪切应力，体积通量和温度的表达式。使用这些技术获得的结果是无限级数的形式。因此，可以很容易地计算出结果。通过建议的方法获得的各种结果进行了比较，并获得了很好的一致性。