Effects of thermal boundary conditions on natural convection in a square enclosure with an inner circular cylinder differdentially heated from bottom wall

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

Two-dimensional numerical simulations are carried out for natural convection in an enclosure with a hot inner cylinder located at the center for four different Rayleigh numbers of 103, 104, 105 and 106. The immersed boundary method (IBM) was used to handle the virtual surface of the inner circular cylinder with a no-slip boundary condition. The Prandtl number Pr was taken to be 0.7 corresponding to that of air. This study focuses on the effect of the temperature variation of bottom wall of the enclosure on thermal and flow structures of natural convection. The results indicate negligible changes in thermal and flow structures based on variations in the size of the local heating zone on the bottom wall at Ra =103 and 104, although there is a small variation in the convection velocity in the enclosure. At Ra = 105, small inner vortices formed in the lower part of the cylinder show significant changes in their size with increases due to increasing the bottom wall temperature. At Ra = 106, the magnitude of convection velocity becomes much larger than that when Ra = 105. As a result, much stronger rising plumes than those for Ra = 105 were formed on the top of the cylinder. And the secondary vortices form and separate above the bottom surface of the cylinder. The generation and dissolution of vortices are dependent mainly on the temperature of bottom wall in the enclosure.