This paper aims to determine the exact solutions of non-Newtonian fluid namely micropolar fluid with MHD in a porous medium by traveling wave method. The governing equations of incompressible micropolar fluid with MHD in a porous medium are non-linear PDEs reduced to ODEs through wave parameter ξ = m x + n y + U t . The set of new exact solutions are determined for five different cases. In special cases, the solution for micropolar fluid with and without MHD and porous effects can also be obtained from general solutions. Furthermore, these solution reduces to a Newtonian solution if we put vortex viscosity κ →0. Finally, the influence of the material and other parameters of interest on the fluid motion, as well as a comparison among micropolar and Newtonian fluids is also analyzed by 2D and 3D graphical illustrations.

中文翻译：

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MHD微极性流体在多孔介质中的新行波解

本文旨在通过行波法确定非牛顿流体，即具有 MHD 的微极流体在多孔介质中的精确解。多孔介质中具有 MHD 的不可压缩微极流体的控制方程是通过波参数 ξ = mx + ny + U t 将非线性偏微分方程简化为常微分方程。这组新的精确解是针对五种不同情况确定的。在特殊情况下，微极性流体有无MHD和多孔效应的解也可以从一般解中求得。此外，如果我们将涡流粘度 κ → 0，这些解决方案将简化为牛顿解决方案。最后，材料和其他感兴趣的参数对流体运动的影响，以及微极和牛顿流体之间的比较也通过 2D 和 3D 图形说明进行分析。