Double-Diffusive Mixed Convection Inside a Rectangular Cavity Driven by Opposing Buoyancy and Shear Effects

This paper studies mixed double-diffusive convection both numerically and analytically within a double lid-driven rectangular cavity with imposed constant thermal and solutal fluxes on the vertical boundaries while the horizontal walls are considered insulated and impermeable. The opposing flow case is considered where the applied fluxes and moving walls work in opposing directions. To numerically solve the problem governing equations, the finite volume method is adopted, while the parallel flow approximation is used to derive the analytical solution. It is found that the convection main governing parameters are: thermal Rayleigh number \(Ra_{T}\) , buoyancy ratio \(N\) , Lewis number \(Le\) , and Peclet number \(Pe\) . The two established solutions display perfect agreement for the considered wide ranges of controlling parameters. For a mixed convection regime, increasing \(Ra_{T}\) reduces flow strength and the rates of heat and mass transfer due to the opposing nature of applied boundary conditions, while for a dominant natural regime, increasing \(Ra_{T}\) does the opposite resulting in a more pronounced convective regime. As for the effect of the buoyancy ratio, it promotes the contribution of natural regime in the overall convection as it increases.