Nonlinear convection regimes in superposed fluid and porous layers under vertical vibrations: Positive porosity gradients

Abstract

We investigate the onset of average convection and its nonlinear regimes in a single-component fluid layer overlying a fluid-saturated porous layer. A heated from below cavity with a superposed fluid and a porous medium undergoes high-frequency and small-amplitude vertical vibrations in the gravitational field. Porosity of the medium decreases linearly with depth at a positive porosity gradient. Thermal vibrational convection equations are obtained by the averaging method and solved numerically. The shooting method, Galerkin method and finite-difference method are applied. It is shown that for small vibration accelerations, a convective flow is generated as short-wave rolls in the fluid layer overlying a porous medium. The heat flux undergoes abrupt changes as the supercriticality increases. It is due to the fluid flow penetrating into pores. A magnitude of the jump grows with the growth of vibration intensity. For sufficiently large vibration accelerations, the average convection is excited in the form of long-wave rolls that penetrate both layers. Here, the Nusselt number is 2–3 times higher than its value in the static gravity field.