Multiple microchannel heat transfer systems have been developed for the urge of rapid and effective cooling of the electronic devices, which have become smaller and more powerful but also produced more heat. Two different types of single-phase liquid cooling, including the straight and U-shaped microchannel heat sinks, have been utilized to reduce the temperature of the electronic chips. The cooling performances however depend on the preferences of different factors such as the thermal resistances, the pressure drops, and the heat flows at the solid-fluid interfaces. Lower thermal resistance represents higher temperature reduction; lower pressure drop means lower usage of the pumping power; and higher heat flows indicates more effective cooling between the heat spreader and the liquid. In this paper, an optimization strategy based on the prioritized performances has been developed to find the optimal design variables for multiple objectives: minimal thermal resistances, minimal pressure drops and maximal heat flows. The fuzzy and correlated preferences are modeled by the Gaussian membership functions with respect to different levels of the objective function values. The overall performances are formulated based on the prioritized preferences and maximized on the Pareto-optimal solution set to find the solutions for various preference conditions. Two case studies have been discussed. The first case considered the prioritized preferences based on uni-objective function values while the second one focused on the preferences of the thermal resistances and the efficiency measures, correlatively evaluated by the flow rates, pressure drops, and heat flows.

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