Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel

In this paper, we report the influence of different terms appearing in the momentum equation on the stability of buoyancy-assisted mixed convection in a vertical channel filled with a porous medium. Four different models: (i) Darcy-Brinkman (DB), (ii) Darcy-Brinkman-Forchheimer (DBF), (iii) Darcy-Brinkman-Wooding (DBW), and (iv) Darcy-Brinkman-Forchheimer-Wooding (DBFW) are considered and a comparative study is made based on a linear stability analysis. We consider a Prandtl number range of Pr = 0.1-10, which corresponds to water and gases. Judged from the instability boundary curves, it is found that with reduction of Darcy number there exists an equivalence of DB with DBF model from one side, and an equivalence of DBW with DBFW model from the other side. When the medium is a gas, a significant difference between DB and DBW (or DBF and DBFW) is visible, which is not the case for water. Furthermore, it is found that in case of a gas, inertia force destabilizes the flow, whereas, form drag stabilizes it. In contrast to a fluid-filled channel (where inertia term always destabilizes the buoyancy-assisted flow), here this destabilizing property might turn into a stabilizing one when fluid viscosity and permeability of the medium are changed. In the case of water, for Da = 10−2, the inertia term stabilizes the flow beyond Re = 25. When Da is reduced by one order of magnitude, the destabilizing effect continued up to Re = 220. The combined effect of form drag (Forchheimer term) and inertia (Wooding term) on the stability of the flow is more intensive than their individual effects provided the medium is highly permeable. In most cases studied here, the disturbance flow patterns are similar for DB and DBF from one side, and DBW and DBFW from the other side.