The finite difference method in conjunction with the least-squares scheme and experimental temperature data is used to predict the average heat transfer coefficient and fin efficiency on the fin of annular-finned tube heat exchangers in natural convection for various fin spacings. The radiation and convection heat transfer coefficients are simultaneously taken into consideration in the present study. The heat transfer coefficient on this annular circular fin is assumed to be non-uniform. Thus the whole annular circular fin is divided into several sub-fin regions in order to predict the average heat transfer coefficient W and fin efficiency from the knowledge of the ambient temperature, tube temperature and fin temperature recordings at several selected measurement locations. The results show that the W value increases with increasing the fin spacing S, and the fin efficiency decreases with increasing the fin spacing S. However, these two values respectively approach their corresponding asymptotical values obtained from a single fin as S -> infinity. The fin temperature departs from the ideal isothermal situation and decreases more rapidly away from the circular center with increasing the fin spacing. In order to validate the accuracy of the present inverse scheme, a comparison of the average heat transfer coefficient on the fin between the present estimates and those obtained from the correlation recommended by current textbooks is made. (c) 2006 Elsevier Ltd. All rights reserved.