In this study, the heat transfer, pressure drop and entropy generation in shell and helically coiled tube heat exchangers, are numerically investigated. The heat transfer rate is intensified by installing the annular fins on the outer surface of the coiled tube. The fluid of coil side is the hot water which flows through the coiled tube at temperature of 70 degrees C and velocity of 1 m/s. While, on the shell side, the cooling dry air flows through the shell side at temperature of 10 degrees C and velocity of 1-4m/s. The height and number of the fins change, as well as the velocity of the shell side fluid. The main results of this study are some correlations which are suggested for the estimation of the Nusselt number and friction factor of the shell side. Furthermore, the relationship between the NTU, the entropy generation rate and the thermal effectiveness are obtained. The model is validated by comparing the numerical values of the Nusselt numbers of both side and the friction factor of the coil side, with the predicted values based on the previous empirical correlations. In the last section of this study; as a guide for the designer of these types of heat exchangers; a sample problem is defined and solved. Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.