Linear and nonlinear stability analyses of micropolar fluid flow in horizontal porous layers

Abstract

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.