The effect of streamwise conduction on the entropy generation of low-Peclet-number nanofluid flow in circular microchannel heat sinks under exponentially decaying wall heat flux with constant pumping power condition is analytically studied. Mathematical models with and without streamwise conduction term in the energy equation are developed and closed-form solutions are obtained. Due to the dramatic increase in the effective thermal conductivity of nanofluids, the streamwise conduction effect is justified to be more significant in the nanofluids compared to their base fluids. The significance of the streamwise conduction which is prevalent in low-Peclet-number flow regime is greatly amplified when the volume fraction of nanoparticle is increased. The thermal characteristics of nanofluids are prominently affected due to the presence of streamwise conduction which consequently alters the characteristics of entropy generation in the second-law analysis. Significant deviations are observed when comparing the cases with and without streamwise conduction. Minimal entropy generation is identified in certain range of the low-Peclet-number flow regime, providing an ideal operating condition from the second-law aspect for nanofluid flow in microchannels. The exergetic effectiveness is also investigated based on the variations on the volume fraction of nanoparticle suspension and the microchannel aspect ratio. (C) 2013 Elsevier Ltd. All rights reserved.