The linear and nonlinear stability analyses of micropolar fluid flow in a horizontal porous layer heated from below in the presence of throughflow is numerically investigated. The Brinkman model is considered to govern the micropolar fluid flow within the porous region. The main purpose of the present study is to investigate the behavior of the subcritical region for micropolar fluid parameters in the presence of throughflow. The energy approach is used to analyze nonlinear stability, whereas the normal mode scheme is used to investigate linear stability. The obtained eigenvalue problems related to linear and nonlinear stability analyses are solved numerically using the bvp4c routine in MATLAB. Finally, the critical thermal Rayleigh number is determined for the given values of the governing parameters. It is observed that the subcritical area decreases as the Darcy number (Da), micropolar parameter (m), and absolute value of throughflow parameter (|Pe|) decrease. Furthermore, there is no subcritical gap in the absence of the throughflow effect for micropolar fluid flow, which is a good agreement for the linear and nonlinear thresholds.

中文翻译：

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水平多孔层中微极性流体流动的线性和非线性稳定性分析

对存在通流的情况下从下方加热的水平多孔层中微极性流体流动的线性和非线性稳定性分析进行了数值研究。 Brinkman 模型被认为控制多孔区域内的微极性流体流动。本研究的主要目的是研究存在通流情况下微极性流体参数的亚临界区域的行为。能量法用于分析非线性稳定性，而简正模方案用于研究线性稳定性。使用 MATLAB 中的 bvp4c 例程对所获得的与线性和非线性稳定性分析相关的特征值问题进行数值求解。最后，针对给定的控制参数值确定临界热瑞利数。观察到亚临界面积随着达西数（Da）、微极性参数（m）和通流参数绝对值（|Pe|）的减小而减小。此外，在没有微极性流体流动的通流效应的情况下，不存在亚临界间隙，这与线性和非线性阈值有很好的一致性。