Based on the first and the second laws of thermodynamic, the entropy generation of heat transfer process from the inside to the outside through a duct is analyzed. A dimensionless entropy generation number based on the fluid of inside duct is introduced and an analytical expression for the dimensionless entropy generation number is obtained. The effect of some dimensionless parameters on the irreversibility performance of heat transfer process through a duct is discussed. The results show that an optimal Reynolds number of fluid inside duct is found to make dimensionless entropy generation number minimum , the dimensionless entropy generation number increases with the increment of the ratio of the Reynolds number of inside and outside duct fluids, dimensionless inlet temperature difference and dimensionless characteristic geometric dimension. The results from this paper provide a reference for the thermodynamic performance evaluation on the basic heat transfer process through a duct and enhancement in double sides of duct.