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In this research, for the first time, the impact of wavy orientations on the entropy generation and exergy destruction of the wavy microchannel working with various types of aqueous nanofluid is addressed. To this end, two Left–Right and Up–Down wavy microchannels were developed, and the laminar flows of silver, aluminum oxide, and hybrid silver-aluminum oxide nanofluids, each with concentrations of 1%, 2%, and 3%, were numerically simulated using the multi-phase mixture model. The simulation was carried out at constant pumping powers of 0.05 W, 0.15 W, 0.25 W, and 0.35 W, and the inlet temperature of 300 K. The results demonstrated that the total exergy destruction for the Left–Right wavy microchannel is on average 20% lower than the Up-Down one. In both of the microchannels, using nanofluid decreases the destructed exergy, with the largest irreversibility reduction related to the silver nanofluid case. Also, utilizing nanofluids increases the effectiveness number, while raising the pumping power declines it. Moreover, the values of the effectiveness number are higher for the Up-Down wavy microchannel compared to those of the Left–Right one. Finally, for 3% silver nanofluid at pumping power of 0.05 W in the Left–Right wavy microchannel, the highest value of second law efficiency is obtained, while it is lowest for the water at pumping power of 0.35W in the Up–Down wavy microchannel.