Internal natural convection around a sphere in a rectangular chamber

In this study, a three-dimensional internal natural convection heat transfer between a cuboidal enclosure and a spherical surface placed in the enclosure, is investigated numerically. The effects of enclosure shape and Rayleigh number on the flow and heat transfer characteristics are analyzed for concentric and eccentric positions of sphere, respectively. The numerical results show that there exists a critical Rayleigh number beyond which the Nusselt number decreases as the temperature difference increases. This is attributable to the fact that the thermal diffusivity and kinematic viscosity of air both increases as the temperature increases, resulting in reduction of Rayleigh number with the temperature increases. Based on the numerical results, a correlation for predicting Nusselt number is proposed as a function of Rayleigh number and the enclosure shape for concentric and eccentric cases, respectively.