Entropy generation for a fully developed laminar viscous flow in a duct subjected to constant wall temperature is investigated analytically. The temperature dependence on the viscosity is taken into consideration in the analysis. The ratio of the pumping power to the total heat flux decreases considerably and the entropy generation increases along the duct length for viscous fluids. The variation of total exergy loss due to both the entropy generation and the pumping process is studied along the duct length as well as varying the fluid inlet temperature for fixed duct length. For low heat transfer conditions the entropy generation due to viscous friction becomes dominant and the dependence of viscosity with the temperature becomes essentially important to be considered in order to determine the entropy generation accurately.