The main purpose of this study is to use the three-dimensional commercial package along with experimental data and the inverse result of the heat transfer coefficient to investigate the effect of the computational domain boundary set on the natural convection heat transfer and fluid flow characteristics of single-tube vertical annular fin and tube heat exchanger in a box with an upward opening. Various flow models are introduced. The air temperature and velocity profiles, fin temperature and heat transfer coefficient on the fins are determined by the commercial package. More accurate numerical results and an appropriate flow model can be obtained if the resulting heat transfer coefficient and the fin temperature are close to the inverse result and experimental fin temperature data, respectively. However, differences in boundary condition set at the side walls of the box can affect air velocity and temperature profiles. The choice of the appropriate flow model can also be related to the boundary set of the computational domain. Thus, the suitability of the boundary condition set must be checked at the side walls of the box. (C) 2017 Elsevier Ltd. All rights reserved.