Three-dimensional natural convection around an inner circular cylinder located in a cubic enclosure with sinusoidal thermal boundary condition

Three-dimensional numerical simulations were conducted for the natural convection phenomena around an inner circular cylinder positioned in a cold cubic enclosure in the relatively high Rayleigh numbers of Ra=105 and Ra=106 at the Prandtl number of Pr=0.7. In this study, we observed the flow and heat transfer characteristics in the enclosure according to the variation of thermal boundary conditions on the bottom wall of the enclosure as well as the inner cylinder surface in the convection-dominant region. The Immersed Boundary Method (IBM) was used to capture the virtual wall boundary of the inner cylinder, based on the Finite Volume Method (FVM). Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of streamlines, iso-surfaces of three-dimensional isotherms and two dimensional views of isotherms. They depended on the number, size, strength and rotational directions of ascending plumes from the bottom wall as well as the hot inner cylinder as a function of the Rayleigh number and thermal boundary conditions. In addition, the distribution of Nusselt number on the walls of enclosure as well as the cylinder surface was presented as a function of the sinusoidal temperature variation on the bottom wall of the enclosure for different Rayleigh numbers of 105 and 106.