The main objective of this paper is to explore the existence of thermodynamic irreversibility due to laminar fluid flow with heat transfer under fully-developed conditions through a duct of circular cross-section. The evaluation of thermodynamic trade-offs caused by Simultaneous heat transfer under a finite temperature-difference and fluid friction has been examined in terms of dimensionless entropy generation as a performance criterion. The temperature dependence of viscosity is taken into consideration in the analysis. Expressions involving relevant variables for entropy generation and pumping power for constant viscosity and temperature-dependent viscosity have been derived. The dimensionless entropy-generation defined on the basis of total heat-transfer rate attains a minimum along the duct length and the ratio of pumping power to total heat-transfer rate increases considerably along the duct length when the fluid is heated. The dimensionless entropy-generation increases as the dimensionless ratio of inlet wall to fluid temperatures (a) increases, but the pumping power ratio decreases as alpha increases. The results correspond to the constant viscosity assumption and temperature-dependent viscosity cases are compared and it was found that the constant viscosity assumption may yield a significant amount of deviation in entropy-generation and pumping power from those for the temperature-dependent viscosity case, especially for more viscous fluids. (C) 2003 Elsevier Ltd. All rights reserved.