Probing the Accuracy of Experimental Data on Nusselt Numbers Within Miniature Heat Sinks

Abstract

Achieving accurate experimental data in conjugate heat transfer studies to calculate Nusselt number can be challenging due to its complex three-dimensional thermal hydraulics nature. This study is devoted to evaluating the accuracy and reliability of experimental approaches used to calculate the Nusselt number in miniature heat sinks. It is observed that three major parameters including (1) axial heat conduction within the solid substrate of heat sinks, (2) thermal contact resistance, and (3) assumed uniform wall temperature, as well as wall heat flux distributions, influence the reported experimental data in the literature. The results obtained from the developed analytical and computational models in this study revealed that the assumptions of local uniform wall temperature and heat flux distributions for small-scale heat sinks result in underestimated Nusselt numbers calculated from experiments. At lower Reynolds number (<200) flows in miniature heat sinks with a high solid to fluid thermal conductivity ratio (>> 1), it is shown that the fluid bulk temperature should be measured away from the heat sink inlet and outlet to minimize the effect of axial heat conduction within the solid substrate of the microscale heat sinks on calculated Nusselt numbers. As the third important parameter, the influence of thermal contact resistance on the Nusselt number calculation in a miniature heat sink is studied where thermal slip length is considered. Finally, the concurrent effects of thermal contact resistance and thermal developing region are considered to explicate the obtained trends in the experimental Nusselt numbers dataset.