Analytico-numerical study of optimal separation of species in an inclined Darcy–Brinkman porous cavity saturated with a binary mixture

• We study Soret convection in an inclined porous layer subjected to a constant heat flux.
• An analytical solution, validated numerically, is developed for the Brinkman model.
• Optimum conditions leading to maximum of separation are determined.
• From some thresholds of RT, Sh variations versus θ may lead to infinite asymptotic values only at low Da.
• In some cases, the curves of ΔS exhibit strong variations with Le, but negligible variations with RT.

Soret convection induced in an inclined rectangular porous cavity filled with a binary mixture and subjected to a constant heat flux is studied analytically and numerically using the Darcy–Brinkman model with the Boussinesq approximation. The relevant parameters for the problem are the thermal Rayleigh number (RT=1−106), the Lewis number (Le=10−3−104), the inclination angle of the cavity (θ=0−180°), the separation ratio (φ=0.5), the Darcy number (Da=10−5−103)(Da=10−5−103), and the aspect ratio of the cavity (Ar=12)(Ar=12). The limiting cases (Darcy and pure fluid media) are covered in this study. Optimum conditions leading to maximum separation of species are determined while varying the governing parameters in their respective ranges. From some thresholds of RT, asymptotic behaviors leading to ±∞ are observed in the evolution of ShSh versus Da (at low Da values) for some inclination θ. For the fluid medium (large Da values), such a behavior is not existing.