Effects of inclination angle and fluid parameters on binary fluid convection in a tilted rectangular cavity

Abstract

Thermal convection of binary fluid mixtures with negative separation ratios in a tilted rectangular cavity heated from below is numerically investigated using a high-accuracy finite-difference method. The fluids under consideration are Newtonian fluids with the Prandtl number (Pr) and Lewis number (Le) in the ranges of 0.01≤Pr≤10 and 0.001≤Le≤1, respectively. Extensive direct numerical simulations are conducted to explore the dynamics of the system by varying the control parameters, namely, the relative Rayleigh number (r) and the inclination angle of the cavity (β) together with the separation ratio (ψ) in the ranges of 1.0≤r≤2.0, 0°≤β≤90°, and −0.6≤ψ≤0. It is found that the inclination angle leads to a distinct trend for heat and mass transfer: the Nusselt number first decreases for small β, then gradually increases for moderate β, and finally decreases again for large β when r varies from 1.4 to 2.0. The optimal inclination angle lies in the range of 54°≤β∗≤64°, where the heat transport peaks. The Sherwood number initially decreases for small β, then increases with increasing β, and finally remains constant for large β. We present the bifurcation diagram of the solutions for different separation ratios, focusing on the distinct variation trends of the inclination angle. The corresponding heat- and mass-transfer properties of the flow on different branches of the bifurcation diagram are investigated. Furthermore, we explore the effect of the relative Rayleigh number, Prandtl number and Lewis number as well as the separation ratio on heat and mass transfer for various inclination angles, and obtain the Nusselt number as a function of the separation ratio and inclination angle.