Effect of circular cylinder location on three-dimensional natural convection in a cubical enclosure

This paper presents the results of immersed boundary method-based three-dimension numerical simulations of natural convection in a cubical enclosure with an inner circular cylinder at a Prandtl number of 0.7. This simulation spans three decades of Rayleigh number, Ra, from 10³ to 10⁶. The location of the inner circular cylinder is changed vertically along the centerline of the cubical enclosure. This study primarily focuses on the effects of both buoyancy-induced convection and the location of the inner circular cylinder on heat transfer and fluid flow in the cubical enclosure. In the range of Rayleigh numbers considered in this study, the thermal and flow fields eventually reach steady state, regardless of the location of the inner cylinder. When Ra is 10³, the end wall of the cubical enclosure has a negligible effect on the thermal and flow fields in the enclosure. However, in the range of 10⁴ ≤ Ra ≤ 10⁶, the effect of the end wall on heat transfer and fluid flow in the enclosure depends on both the location of the inner cylinder and the Rayleigh number. Detailed analysis results for the distribution of streamlines, isotherms, and Nusselt numbers are presented in this paper.