The concepts of fully developed flow and heat transfer have been generalized to accommodate ducts whose cross-sectional area varies periodically in the streamwise direction. The identification of the periodicity characteristics of the velocity components and of a reduced pressure function enables the flow field analysis to be confined to a single isolated module, without involvement with the entrance region problem. A similar modular analysis can be made for the temperature field, but the periodicity conditions are of a different nature depending on the thermal boundary conditions. For uniform wall temperature, profiles of similar shape recur periodically. On the other hand, for prescribed wall heat flux which is the same for all modules, the temperature field itself is periodic provided that a linear term related to the bulk temperature change is subtracted. The concepts and solution procedure for the periodic fully developed regime were applied to a heat exchanger configuration consisting of successive ranks of isothermal plate segments placed transverse to the mainflow direction. The computed laminar flow field was found to be characterized by strong blockage effects and massive recirculation zones. The fully developed Nusselt numbers are much higher than those for conventional laminar duct flows and show a marked dependence on the Reynolds number.