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Analytico–Numerical Study of Soret–Driven Thermosolutal Convection within an Inclined, Fluid–Saturated Porous Cavity
Ahmed Rtibi, Abdelkhalek Amahmid, Mohammed Hasnaoui, Abderrazzak Khadiri and Antonio Campo

Thermo-solutal natural convection in an inclined porous cavity induced by combined external heat flux and Soret effect is studied analytically and numerically in this work. In the porous cavity, the long side walls are subject to constant heat flux, while the short side walls are insulated. In addition, all cavity walls are impermeable to mass transfer. It is assumed that the binary fluid saturating the porous medium is governed by the Darcy model. The analyses will revolve around large aspect ratios, and a selected collection of thermal Darcy-Rayleigh number, RT, Lewis number, Le, cavity inclination, θ, and separation parameter, ϕ, in the respective ranges 1 ≤ RT  ≤ 103, 10-3Le ≤ 103, 0° ≤ θ ≤ 180° and -0.5 ≤ ϕ ≤ 1. Invoking the parallel flow approximation in the core region of the porous cavity, an analytical solution is obtained and later validated numerically by means of a finite difference technique. It is found that for negative values of the separation parameter ϕ, the Sherwood number Sh exhibits a pronounced decline within a certain sub-interval of the thermal Darcy-Rayleigh number RT for intermediate values of the inclination angle θ. At relatively large cavity inclinations θ, the heat transfer is found to deteriorate when the separation ratios ϕ are positive for some Le values. Further, the evolution of Nu in terms of Le validates the existence of a threshold value for the latter. Moreover, Nu stabilizes and stays almost independent of the separation parameter, ϕ.

Keywords: Heat and mass transfer, inclined porous cavity, thermo-solutal natural convection, Soret effect, analytico-numerical study.

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