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In this paper, the exergy rate analysis at a pin–fin micro-heat sink (MH/S) is investigated numerically. The critical part of a MH/S contains several square-shaped pin–fins. A turbulent flow of water/boehmite alumina nanofluid (N-F) moves on the pin–fins and cools the MH/S. Constant heat flux is entered into the lower part of the pin–fin MH/S. The governing equations are solved based on the control volume method and simple algorithm. The K-epsilon model is applied to model the N-F flow over pin–fins. The first-law, second-law efficiencies, gains exergy rate, loss exergy rate, and output exergy rate are studied in analysis. Variables considered in the problem consist of the inlet flow rate of N-F, N-Ps shape, and volume fraction of N-Ps in water. The main purpose of this paper is to investigate the exergy rate of various N-P shapes in a MH/S. The results of this study showed that increasing the flow rate reduces the …