The onset of double-diffusive convection in a Brinkman porous layer with convective thermal boundary conditions

Abstract

The onset of double-diffusive convection in a highly permeable porous medium with a horizontal throughflow is investigated considering the convective thermal boundary conditions. The convection occurring inside the medium is mainly due to the basic temperature difference between the two boundaries and the heat supplied from external sources at these boundaries. However, the effect of viscous dissipation and the changing mass flux due to temperature gradient (Soret effect), on the convection, is also considered. Due to the consideration of the viscous dissipation inside the medium, a nonlinear basic flow profile is obtained. The disturbances in the base flow are assumed in the form of two-dimensional oblique structures, which are inclined to the base flow at an angle γ(0≤γ≤π2). The effect of the coefficients of external heating at the two boundaries (the associated non-dimensional parameters are the Biot numbers, B0 and B1, respectively) is discussed extensively. The cases with various combinations of the limiting values of B0 and B1 are also discussed. Viscous dissipation has a stabilizing effect on the flow, as long as the external heating at the bottom boundary is higher than that at the upper boundary. The system stabilizes with the increase in the coefficient of external heating at the lower boundary. The solute concentration gradient has a linearly destabilizing effect on the flow, for all Le( 1). The Soret parameter has a linearly destabilizing effect on the flow, when the direction of solute concentration gradient opposes the direction of thermal buoyancy.