A solution methodology has been employed that enables the fully developed regime in a duct of periodically varying cross section to be determined without dealing with the entrance region. The periodic duct considered here is a tube consisting of a succession of alternately converging and diverging conical sections. The numerical work was carried out for laminar flow in the Reynolds number range from 100 to 1000, for various taper angles of the converging and diverging sections, for two length-diameter ratios of the periodic geometry, and for Prandtl numbers of 0.7, 2.5, and 5. Experiments were also performed to verify the numerical predictions for the Nusselt number, and excellent agreement was found to prevail. The predicted Nusselt numbers for the periodic tube were compared with those for the straight tube. For Pr = 0.7, the periodic tube results generally fell below those for the straight tube, while for Pr = 5, moderate enhancement occurred due to the periodic area change. The pressure drops for the periodic tube were substantially greater than those for the straight tube.