Natural Convection in a Square Enclosure with Differentially Heated Two Horizontal Cylinders

Abstract

The present study numerically investigates two-dimensional natural convection in a cooled square enclosure with two inner circular cylinders, which have different isothermal conditions for different Rayleigh numbers in the range of 10³ ≤ Ra ≤ 10⁵. The cooled and heated isothermal conditions are imposed on the upper and lower cylinders, respectively. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively, and the radius of inner cylinders varies. For all Rayleigh numbers, as the radius increases, the cold upper cylinder occupies a much wider area in the upper half of the cold enclosure, resulting in the formation of a wider dead zone of the heat transfer and fluid flow in the upper half of the enclosure. Regardless of the radius variation, the circulation of the flow shows two overall rotating symmetric eddies with the secondary vortices over the upper surface of the upper cylinder. The trajectories of the primary eddy and secondary vortices considerably depend on the radius, especially at a higher Rayleigh number. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) through GCRC-SOP (no. 2011-0030013) and (no. 2010-0025618).