This study conducted three-dimensional numerical simulations of the natural convection in a long, cold, rectangular enclosure containing a hot, circular cylinder or an elliptical cylinder. The immersed boundary method (IBM) was used to capture the virtual wall boundary of the cylinder based on the finite volume method (FVM). Four radii of inner cylinders were considered in the Rayleigh number range of 10(4) <= Ra <= 10(6) as key simulation parameters to investigate the size effect of the circular and elliptical cylinders. The detailed effects were analyzed by visualization of the three-dimensional iso-surfaces of the temperature and vortical structures, as well as the three-dimensionality in the system. The heat transfer characteristics from the surfaces of a circular cylinder or elliptical cylinder and the walls of enclosure were addressed. The heat transfer characteristics were affected by the radius of the circular and elliptical cylinders. (C) 2019 Elsevier Ltd. All rights reserved.