Inertia effects on vortex instability of a horizontal natural convection flow in a saturated porous medium

Abstract

Inertia effects on the flow and vortex instability of a horizontal natural convection boundary flow in a saturated porous medium are examined by using the Forchheimer-extended Darcy equation of motion. In the base flow, similarity solutions are obtained for the case of the constant heat flux boundary condition. The stability analysis is based on the linear theory. The resulting eigenvalue problem, which retains the x-dependent perturbation terms, solt6p' ∂x and sol u ̄ (∂T' ∂x) , is solved by the local similarity method. Effects of flow inertia are measured and examined in terms of the Forchheimer number, Fr. It is found that as Fr increases, the heat transfer rate decreases, and the susceptibility of the flow to the vortex mode of instability increases. The effect of x-dependent temperature and pressure perturbations is shown to stabilize the flow as compared with x-independent temperature and pressure perturbations.