A second law analysis is carried out on convective heat transfer in fully developed region with constant wall temperature through circular, trianglar and rectangular ducts. Besides, the entropy generation rate expression is obtained and the loss rate of available energy in convective heat transfer processes is defined as well. At the same time, the influence of initial temperature difference between fluid and wall as well as the influence of fluid friction on the loss rate of available energy is discussed. Then, the thermodynamic performances of several typical ducts are compared. Finally , the optimum initial temperature difference with the minimum loss rate of available energy is also obtained.