Abstract: In this study, a second law comparison of irreversibility is used to determine the optimum duct geometry which minimizes losses for a range of laminar flows with constant wall heat flux condition. Water as a working fluid is considered. The duct geometries used are rhombic with various angle of bevel and circular. Hydraulic diameters are used for the different geometries. The rhombic geometry with the angle of 90°, when the frictional contributions of entropy generation become important is the best. Also power required to overcome fluid friction in the mentioned duct is smallest.