Coupled conduction-convection problem for a cylinder in an enclosure

The coupled heat conduction/convection problem for a solid cylinder in either a rectangular or a circular enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The temperature distribution in the cylinder and in the fluid is obtained showing that the usual practice of prescribing a uniform heat flux boundary condition at the interface may not lead to an accurate solution. From the profile of the local Nusselt number, which is strongly dependent on the Rayleigh number but weakly dependent on the thermal conductivity ratio, it is concluded that most of the heat transfer takes place in the lower half of the cylinder through a convective mode.