An analysis has been carried out for laminar heat transfer in a circular tube subjected to an axially periodic variation of the external heat transfer coefficient (or of its dimensionless counterpart, the Biot number). This thermal boundary condition serves to model flow in a tube fitted with a regularly spaced array of annular fins. It was found from numerical solutions that external finning yields substantial heat transfer enhancement compared with an unfinned tube, especially when the Biot number of the unfinned tube is low. The degree of enhancement is quite insensitive to the period of the Biot number variation provided that the overall proportions of the unfinned and finned surface are maintained and the Biot number level is also maintained. An increase in the interfin spacing tends to diminish the enhancement. A constant-Biot-number model intended to approximate the heat transfer results for the periodic-Biot-number case was devised and tested. The predictions of this simplified model are especially accurate at low Biot numbers. The results of the laminar flow analysis have suggested ways of modeling turbulent heat transfer in externally finned tubes.