This paper investigates the linear stability of the flow in the two-dimensional boundary-layer flow of the Carreau fluid over a wedge. The corresponding rheology is analysed using the non-Newtonian Carreau fluid. Both mainstream and wedge velocities are approximated in terms of the power of distance from the leading edge of the boundary layer. These forms exhibit a class of similarity flows for the Carreau fluid. The governing equations are derived from the theory of a non-Newtonian fluid which are converted into an ordinary differential equation. We use the Chebyshev collocation and shooting techniques for the solution of governing equations. Numerical results show that the viscosity modification due to Carreau fluid makes the boundary layer thickness thinner. Numerical results predict an additional solution for the same set of parameters. Thus, a further aim was to assess the stability of dual solutions as to which of the solutions can be realized. This leads to an eigenvalue problem in which the positive eigenvalues are important and intriguing. The results from eigenvalues form tongue-like structures which are rather new. The presence of the tongue means that flow becomes unstable beyond the critical value when the velocity ratio is increased from the first solution.

中文翻译：

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移动楔上Carreau流体剪切稀化和剪切增稠边界层流动的数值解

本文研究了 Carreau 流体在楔上的二维边界层流动中流动的线性稳定性。使用非牛顿 Carreau 流体分析相应的流变学。主流速度和楔形速度都是根据距边界层前缘距离的幂来近似的。这些形式展示了 Carreau 流体的一类相似流。控制方程是从非牛顿流体的理论推导出来的，它们被转换为常微分方程。我们使用切比雪夫搭配和射击技术来求解控制方程。数值结果表明，由于 Carreau 流体引起的粘度改变使边界层厚度变薄。数值结果预测了同一组参数的附加解。因此，另一个目的是评估双重解决方案的稳定性，以确定哪些解决方案可以实现。这导致了一个特征值问题，其中正特征值很重要并且很有趣。特征值的结果形成了相当新的舌状结构。舌头的存在意味着当速度比从第一个解决方案增加时，流动变得不稳定超过临界值。