The finite difference method in conjunction with the least-squares scheme and experimental temperature data is proposed to predict the average heat transfer coefficient (h) over bar and fin efficiency eta(f) on a vertical square fin of one-circular tube plate finned-tube heat exchangers for various air speeds and fin spacings. The distribution of the heat transfer coefficient on the fin can be very non-uniform, thus the whole square fin is divided into several sub-fin regions in order to predict the (h) over bar and eta(f) values. These two predicted values can be obtained using the present inverse scheme in conjunction with the knowledge of the temperatures recordings at several selected measurement locations. The results show that the heat transfer coefficient on the upstream fin region can be markedly higher than that on the downstream fin region. The (h) over bar value increases with increasing the fin spacing S and air speed V-air, and the eta(f) value decreases with increasing the S and V-air, values. The (h) over bar and eta(f) values respectively approach their corresponding asymptotical values obtained from a single fin as S -> infinity. The distributions of the fin temperature depart from the ideal isothermal situation and the fin temperature, decreases more rapidly away from the circular center with increasing the fin spacing and air speed. (c) 2006 Elsevier Ltd. All rights reserved.