Stability of shear flow in a vertical heated channel filled with a porous medium

In the area of wall-bounded heated shear flows in a porous medium, most research works have been limited to laminar conditions. In this study, the Galerkin method is used to evaluate the linear stability characteristics of shear flows in a heated vertical channel filled with a high-porosity medium. The Brinkman-Forchheimer-extended Darcy model is employed to simulate the momentum and energy transport mechanisms. The key finding is that the fully developed heated shear flow in a porous channel can become unstable under only mild heating conditions. The most significant discovery is that the critical Rayleigh number encounters a large drop when the Reynolds number reaches a threshold value. This threshold value is found to be a function of the Darcy and Forchheimer numbers. It is also found that the way through which the critical wave number varies with the Reynolds number is strongly dependent on the Darcy number. The effects df the different Darcy and Forchheimer numbers on other stability characteristics are also presented and discussed.