Numerical predictions of natural convection with liquid fluids contained in an inclined arc-shaped enclosure

In the present paper a numerical study has been performed of the flow behavior and natural convection heat transfer characteristics of liquid fluids contained in an inclined arc-shaped enclosure. The governing equations are discretized using the finite-volume method and curvilinear coordinates. The Prandtl number (Pr) of the liquid fluids is assigned to be 4.0 and the Grashof number (Gr) is ranged within the regime 1 × 105 ≦ ≦ 4 × 106. On the other hand, the inclination angle (θ) of the enclosure is varied within 0° ≦ θ ≦ 360°. Of major concern are the effects of the inclination and the buoyancy force on the flow and the thermal fields, and based on the numerical data of the thermal field the local and overall Nusselt numbers are calculated. Results show that the arc-shaped enclosure for Pr = 4.0 at Gr = 4 × 106 and θ = 90° exhibits the best heat transfer performance. The poor heat transfer performance for Pr = 4.0 fixed at Gr = 1 × 105 and θ = 180° exhibits the arc-shaped enclosure, respectively. As the value of Grashof number is elevated from 105 to 4 × 106, at θ = 90°, the magnitude of Nu is elevated from 13.946 to 25.3 (81.4% increase); however, at θ = 180°, the magnitude is elevated from 11.655 to 13.475 (15.6% increase) only.