Effect of an internal thermal-conductive cylinder on the conjugate conduction-convection in an enclosure

Abstract

We numerically studied the conjugate conduction-convection in an enclosure with a circular cylinder placed at the center. The enclosure is differentially heated on its lateral sidewalls but keeps adiabatic for the top and bottom sidewalls. The internal cylinder is assumed thermally conductive which is determined by the ratio of thermal conductivity coefficient between solid and fluid medium. The influence of the cylinder is conducted through two mechanisms: the conduction in the cylinder which alters the temperature distribution in the enclosure and thus the buoyancy acting on the fluid, and the confinement on the fluid circulation especially in the region close to the walls of the enclosure. We aim to explore the effects of cylinder diameter and thermal conductivity ratio on the conjugate conduction-convection under two Rayleigh numbers, i.e., Ra = 10⁴ and 10⁶, to consider both weak convection and convection dominant conditions. The effects of the two parameters are analyzed by the thermal and flow distributions, wall heat transfer and the flow behaviors around the cylinder. Numerical results reveal smooth circulation of fluid within the enclosure at Ra = 10⁴ without the formation of local vortices. Since convection is relatively weak at this Rayleigh number, the thermal and flow distributions are roughly skew-symmetric about the center of the geometry, and the variation of thermal characteristics with the cylinder diameter and thermal conductivity ratio is significant for the top-left and bottom-right regions of the enclosure because of strong local heat transfer. However, two local circulating vortices are generated beside the cylinder and move upward with increasing thermal conductivity ratio and are deformed at Ra = 10⁶. The spatial variations of temperature and Nusselt number on the solid walls are relatively small in magnitude compared with the Ra = 10⁴ case, while the variation tendency with respect to the two governing parameters is generally monotonic.

Additional information

Funding

The work was supported by NSFC (51706205) and Science and Technology Plan Project of Zhejiang Province (LGG20E060001).