This study presents a hybrid method of three-dimensional computational fluid dynamics (CFD) commercial software and inverse method along with experimental data and various flow models to study the natural convection heat transfer and fluid flow characteristics of vertical annular elliptical finned tube heat exchangers for various fin spacings. The inverse method of the finite difference method along with the experimental temperature data is first applied to estimate the heat transfer coefficient on the fins. After that, CFD along with various flow models and estimated heat transfer coefficients are used to determine air temperature and air velocity profiles, fin surface temperature and heat transfer coefficient on the fins. More accurate numerical results, appropriate flow model and number of grid points, number of iterations and relative convergence criteria can be obtained when the resulting heat transfer coefficient and fin temperature are as close as possible to the inverse results and experimental temperature measurements, respectively. The results show that the zero-equation turbulence model is more suitable for this study than other flow models. The choice of relative convergence criteria, number of iterations and grid points are important for obtaining more accurate results. The commercial software version, the relative convergence criteria for momentum and energy equations, the number of iterations and the N-t value vary with the fin spacing. The effect of the round-off error on the numerical results obtained needs to be considered. The heat transfer coefficient increases with increasing fin spacing and approaches a constant. The best fin spacing is about 18 mm. The fin efficiency of the annular elliptical fins is higher than that of the annular circular fins. The proposed correlations between Nusselt number and Rayleigh number is in good agreement with the numerical and inverse results obtained. (C) 2018 Elsevier Ltd. All rights reserved.