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This study investigates the characteristics of first and second laws of thermodynamics including the convective heat transfer coefficient, entropy generation rate, and Bejan number for the hybrid nanofluid having graphene–platinum nanoparticles through a cylindrical microchannel liquid block. The geometry contains thirty-six microchannels having hydraulic diameter of 564 μm. The maximum values of the convection heat transfer coefficient, thermal entropy generation, and frictional entropy generation are obtained as 7653 W/m2K, 9.7 × 10−5 W/K, and 6.2 × 10−6 W/K, respectively. With increase of the particle concentration, the heat transfer coefficient and frictional entropy generation increase whereas the thermal entropy generation reduces. Furthermore, by increment of the heat load, the entropy generation due to the heat transfer increases, whereas the entropy generation due to the friction reduces. The influence of Reynolds number on the entropy production rates is more noticeable than the effect of particle fraction. Also, the entropy generation due to the heat transfer diminishes by raising the Reynolds number, while the entropy generation due to the friction intensifies. Furthermore, the Bejan number reduces with increment of the particle fraction and Reynolds number. Eventually, the entropy generation is modeled in terms of the Reynolds number, particle fraction, and heat flux by a neural network. [ABSTRACT FROM AUTHOR]