An analysis of heat transfer in hydrodynamically developed laminar pipe flow with a general thermal boundary condition has been performed. This general boundary condition follows from the temperature distribution in pure cross-flow heat exchangers under the assumption of constant overall heat transfer coefficient. It includes as a special case exponential wall heat flux distribution which occurs in most other heat exchanger flow arrangements. Analytical results were compared to numerical calculations to investigate the coupling of thermal boundary condition with variable local overall heat transfer coefficient depending on the length of flow path. Finally, the implications of these results on heat exchanger design have been discussed.