The thermal effectiveness and entropy generation of parallel and counter-flow heat exchangers handling high-viscosity fluids have been numerically investigated. Both the viscous friction and the viscosity variations with temperature were considered in the analysis. The results show that the thermal effectivencss-NTU curves deviate gradually from the curves obtained using the assumption that the effect of viscosity is negligible. Moreover, the consideration of the viscous frictional heating effect results in a considerable increase in the heat exchanger entropy. An optimum heat exchanger size could be determined from both first law and second law of thermodynamics points of view. The results show also that the effect of viscous friction with variable viscosity becomes more significant for lower inlet temperatures of high-viscosity fluid. Copyright (C) 2002 John Wiley Sons, Ltd.