Characteristics of thermal convection in a rectangular channel with an inner cold circular cylinder

Based on three-dimensional numerical simulations, results are presented for natural convection in a rectangular channel with an inner cold circular cylinder. The Prandtl number is 0.7 and the Rayleigh number is changed in the range of 1 × 103 to 1 × 106. The rectangular channel is heated from the bottom wall of the channel and cooled from the top wall. The adiabatic thermal boundary condition is implemented at the vertical side walls of the rectangular channel. A low-temperature isothermal boundary condition is applied at the surface of the cylinder. The radius of the inner circular cylinder is changed in the range of 0.1-0.4L, where L is the height of the rectangular channel. By changing the radius of the cylinder, we investigate the effect of the inner cold circular cylinder on thermal convection and heat transfer in the space between the cylinder and the rectangular channel. With respect to the radius and Rayleigh number of the cylinder, the thermal and flow field is categorized into six regimes: steady symmetric two-dimensional convection, steady asymmetric two-dimensional convection, steady symmetric three-dimensional convection, steady asymmetric three-dimensional convection, time periodic convection, and aperiodic convection. The map of thermal and flow regimes is presented as a function of the radius and Rayleigh number of the cylinder. This paper presents detailed analysis results for the isotherms, vortical structure, boundary layer thicknesses, and Nusselt numbers and includes a comparison of the results for a rectangular channel without an inner cylinder.