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Irreversibility factors for the TiO2–water nanofluid flow are evaluated through entropy generation rates caused by friction and heat transfer by taking into account nanoparticle migration. Effects of three factors of viscosity gradient, non-uniform shear rate and Brownian diffusion are considered. The investigations are performed in both conventional channels and minichannels since the channel size has the considerable effects of on entropy generation. Influence of particle migration on the irreversibility factors is more noticeable in smaller channels such that with considering particle migration, the maximum thermal entropy generation rate increases about 51% for 0.2 mm channel, while this increment is almost 16% for 1 mm channel. Unlike results are obtained for conventional channels and minichannels, such that total entropy generation intensifies in minichannels and reduces in conventional channels by particle concentration increment. Friction is main factor in entropy generation for minichannels, while heat transfer demonstrates a higher contribution in conventional channels. The optimal channel size where minimum entropy generation occurs is obtained which is dependent on Reynolds number. Therefore, for lower Reynolds number, optimal case occurs at smaller channel size. Furthermore, diagrams of total entropy generation show minimum (optimal) point for 3 mm channel, while they demonstrate the constant trends for other channels. [ABSTRACT FROM AUTHOR]