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Heat generation from electronics increases with the advent of high-density integrated circuit technology. To come up with the heat generation, microscale cooling has been thought as a promising technology. Prediction of heat transfer rate is crucial in design of microscale cooling device but is not clearly understood yet. This work proposes a new correlation between heat transfer rate and Brinkman number which is nondimensional number of viscosity, flow velocity and temperature. Our experimental results showed a good empirical equation that Nu/(Re0.62 Pr0.33) is inversely proportional to the Brinkman number in laminar flow regime. It is expected that the equation proposed by this work can be useful to design microchannel cooling device.