The effects of viscous dissipation on the entropy generation of water–alumina nanofluid convection in circular microchannels subjected to exponential wall heat flux are investigated. Closed-form solutions of the temperature distributions in the streamwise direction are obtained for the models with and without viscous dissipation term in the energy equation. The two models are compared by analyzing their relative deviations in entropy generation for different Reynolds numbers and nanoparticle volume fractions. The incorporation of viscous dissipation prominently affects the temperature distribution and consequently the entropy generation. When the viscous dissipation effect is neglected, the total entropy generation and the fluid friction irreversibility are nearly twofold overrated while the heat transfer irreversibility is underestimated significantly. By considering the viscous dissipation effect, the exergetic effectiveness for forced convection of nanofluid in microchannels attenuates with the increasing nanoparticle volume fraction and nanoparticle diameter. The increase in the entropy generation of nanofluid is mainly attributed to the intensification of fluid friction irreversibility. From the aspect of the second-law of thermodynamics, the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness is invalidated.