This paper attempts to investigate and optimize the energy efficiency of a specific liquid block working with the water-Al2O3 nanofluid for utilization in electronics cooling. The effects of Reynolds number, nanoparticle size and volume concentration are evaluated. The uniform flow distribution in the liquid block results in a rather uniform temperature distribution on the surface of the electronic processor. Moreover, the surface temperature reduces while the power consumption intensifies by increasing either Reynolds number or particle concentration. The processor temperature and pumping power are considered as two objective functions in the optimization problem. A multi-objective optimization method and a decision-making based approach are employed to find the optimum points with minimum processor temperature and minimum power consumption. The optimal cases are obtained considering different states for relative importance of the objective functions. It is found that even in the conditions that the pumping power is of high importance, the nanofluids with great concentration and small nanoparticle size can be utilized. The results show that the effect of the concentration and particle size on the surface temperature is greater than that on pumping power, while the Reynolds number has a rather similar effect on the two objective functions.