Non-Darcy flow stability of mixed convection in a vertical channel filled with a porous medium

The linear stability analysis of mixed convection in a heated vertical channel filled with a porous medium was investigated. The Galerkin method was employed in this calculation. The results indicated that the fully developed laminar flow could become unstable under a mild heating condition for higher modified Darcy numbers of Da∗=1 and 10−2, but the critical Rayleigh number increases substantially for Da∗=10−4. The disturbance kinetic energy budget analysis showed that, for Da∗=1 and 10−2, there are generally three instability types, the thermal-buoyant, mixed, and thermal-shear instabilities for low, intermediate, and high Reynolds numbers, respectively, while for Da∗=10−4, the thermal-buoyant instability is the only driving mechanisms of flow instability regardless of the value of Reynolds number.