This study presents a hybrid method of inverse method and three-dimensional computational fluid dynamics (CFD) commercial software along with experimental data and various flow models to investigate the natural convection heat transfer and fluid flow characteristics of vertical annular finned tube heat exchangers in a small chimney for various fin diameters. First, the inverse method of the finite difference method along with experimental temperature data is used to estimate the heat transfer coefficient on the fins. Afterwards, the CFD along with various flow models and the inverse results of the heat transfer coefficient is used to determine the air temperature and velocity profiles, the fin surface temperature and the heat transfer coefficient on the fins. More accurate results are obtained when the resulting heat transfer coefficient and fin temperature are as close as possible to the inverse results and the experimental temperature measurements, respectively. The results show that the zero-equation turbulence model is more suitable for this problem than other flow models, especially for larger fin spacing. The more grid points are not necessarily able to obtain more accurate results. The choice of the appropriate flow model and the number of grid points may depend on experimental temperature data and reliable heat transfer coefficient. Finally, it is found that the heat transfer coefficient increases with decreasing fin diameter and increasing fin spacing. Fin efficiency decreases with increasing fin diameter and fin spacing. The optimum fin spacing can vary with the D/d(0) value. Also, the proposed correlation between the Nusselt number and the Rayleigh number matches the inverse and numerical results obtained. (C) 2018 Elsevier Ltd. All rights reserved.