Effect of viscous dissipation on the convective instability induced by inclined temperature gradients in a non-Darcy porous medium with horizontal throughflow

Abstract

The linear stability of the convective flow induced by an inclined temperature gradient in a horizontal porous layer with horizontal mass flow is studied. The momentum equation is modelled using the Brinkman model. The contribution of viscous dissipation to the medium is taken into account. The governing parameters are the Gebhart number (Ge), horizontal Rayleigh number (RaH), Darcy number (Da), and Péclet number (Pe). Da→0 represents the Darcy regime and Da→∞ represents the clear fluid regime. The basic flow is considered to be a superposition of the flow induced by the inclined temperature gradient and the horizontal mass flow. This flow is termed as the Hadley-Prats flow. The stability of this base flow in the Brinkman regime is investigated. The longitudinal and transverse rolls are discussed. A comparison has been made between the effect of viscous dissipation on the Hadley-Prats flow in the Darcy model and the present results with Da→0. With the increase in the Darcy number, the longitudinal rolls come out as the favorable mode of instability except for some special cases. Viscous dissipation has a dual role on the convective stability depending on the direction of the horizontal throughflow in both the Darcy and the Brinkman regimes.