The onset of convective instability of horizontal throughflow in a porous layer with inclined thermal and solutal gradients

The double diffusive convective instability of a horizontal throughflowin a fluid-saturated porous layer confined between two infinitely long boundaries is investigated. Inclined thermal and solutal gradients are considered along these impermeable boundaries. The Darcy-Brinkman equation is used for the momentum balance in the porous medium in order to show the contrast in the results as we switch to the Darcy regime from the Brinkman regime through the transition flow regime. The heat generated because of viscous dissipation in the medium is considered to be significant. The basic flow profile is a nonlinear one. The resulting eigenvalue problem is solved numerically using bvp4c in Matlab. More emphasis has been laid on the transition regime and the Brinkman regime. The influence of the viscous dissipation (Ge), horizontal thermal and solutal gradients (Ra-H and Sa(H)), vertical solutal gradient (Sa), and diffusivity ratio (Le) on the instability of the flow is discussed. The results are validated by comparing them with the existing results in the literature. In the case of pure Hadley flow, the horizontal solutal gradient has a stabilizing effect in the absence of the horizontal thermal gradient, whereas it has a destabilizing effect in the presence of the horizontal thermal gradient. It has a dual effect on the Hadley-Prats flow in the presence of a significant viscous dissipation. The vertical solutal gradient has a linearly destabilizing effect on the flow in all the regimes. The flow is found to be most stable in the Brinkman regime in most of the physical situations. Published by AIP Publishing.