Three dimensional (3D) stacking of semiconductor chips is an emerging technology which promises improved electrical performance including improved bandwidth, reduced wire interconnection lengths, and reduced signal delay. However, due to the higher power density per unit volume of the stacking, it poses great challenge for thermal management. Inter-tier microfluidic cooling with microgaps with surface area enhancements such as pin fins can potentially achieve superior thermal performance. As such, the hydraulic and thermal characteristics of this configuration over parametric ranges of practical interest are important. Conventional correlations developed in the literature for macropin fins show large errors for dense arrays of micropins.
In this work, the hydraulic and thermal characteristics of a microgap with pin fin were investigated for a large range of Reynolds number (Re) based on pin fin diameter (Dp) by numerical modeling. The effects of the pin fin dimensions including diameter, transversal spacing, longitudinal spacing, height and Re on the friction factor (f) and colburn j factor were studied. Correlations of the f and j for dense arrays of micro pins are developed based on parametric runs over 22< Re <357, pin fin diameter of 100 μm, pitch/ diameter ratios of 1.5 ∼ 2.25, and height/ diameter ratios of 1.5 ∼ 2.25. The validity of the correlations is confirmed by experiments. Lastly, a parametric optimization was done and the thermal resistance of the microgap with 150 W heat generation is reduced by 28.5% with the optimized dimensions for a given pumping power compared to an un-optimized pin fin configuration.