We study the hydrodynamics of the boundary layer flow of Carreau fluid over a moving wedge embedded in a porous medium in the presence of the applied magnetic field. The velocity of the wedge and mainstream is approximated by the power of distance from the leading boundary layer edge. Governing equations that model a non-Newtonian fluid in the boundary layer are reduced to an ordinary differential equation using the appropriate similarity transformations. The Chebyshev collocation and shooting algorithms based results show that there are non-unique solutions in the boundary-layer for the same system parameters. When the velocity ratio parameter is reduced the wall shear stress on the surface starts to increase till a critical value beyond which no solution exists. Thus, linear stability based on eigenvalue analysis helps to determine which of these non-unique solutions is physically realizable. When the magnetic field and permeability effects on the boundary-layer flow are increased the system shows unique solutions which are always stable. A detailed mechanism behind these results is discussed.

中文翻译：

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多孔介质中 Carreau 流体磁流体动力边界层流动的数值研究：切比雪夫搭配法

我们研究了 Carreau 流体在存在外加磁场的情况下在嵌入多孔介质中的移动楔块上边界层流动的流体动力学。楔形和主流的速度近似于距前沿边界层边缘的距离的幂。使用适当的相似变换将边界层中模拟非牛顿流体的控制方程简化为常微分方程。基于切比雪夫搭配和射击算法的结果表明，对于相同的系统参数，边界层存在非唯一解。当速度比参数减小时，表面上的壁面剪应力开始增加，直到达到临界值，超过该值就无解。因此，基于特征值分析的线性稳定性有助于确定这些非唯一解中的哪些是物理上可实现的。当磁场和磁导率对边界层流动的影响增加时，系统显示出始终稳定的独特解。讨论了这些结果背后的详细机制。