Laminar forced convection inside tubes with externally fitted circular fins is considered, by modelling the presence of the fins as a harmonically varying effective Biot number along the duct’s length, and solving the related Graetz-type problem. The ideas in the generalized integral transform technique are utilized to provide a complete solution to this a priori non-transformable problem, allowing for the establishment of thermal entry region results over a wide range of the dimensionless axial coordinate.