On the significance of developing boundary layers in integrated water cooled 3D chip stacks

We present in this paper a fundamental hydrothermal investigation of the next generation interlayer integrated water cooled three-dimensional (3D) chip stacks, with high volumetric heat generation. Such investigation of flow through microcavities with embedded heat transfer structures such as micro pin-fin arrays and microchannels is crucial for the successful realization of 3D chip stacks. We focus mainly on the complex physics of the entrance region of the cooling microcavities in order to assess its importance. The flow and heat transfer in the entrance region is strongly influenced by developing boundary layers and, as we show herein, the development lengths can occupy a significant portion of the microcavity due to the size restrictions of the 3D chip stack. These effects make a fundamental understanding of conjugate heat transfer in microcavities with heat transfer structures a necessity. The flow field and heat transfer in the entrance region are characterized by means of correlations determining the effective coolant permeability as well as the heat transfer coefficient as a function of the streamwise coordinate x, the flow Reynolds number (Re) and the Prandtl number. Based on a thermal non-equilibrium porous medium model relying on these results, a substantially improved estimation of pressure drop and temperature distribution inside the chip stack is realized. The modeling results are validated against measurements on a 3D chip stack simulator. The range of flow rates and thermal loads in the hot spots of the chip stack, over which it is crucial to consider the developing hydrothermal effects, are analyzed and discussed in detail. Moreover, microchannel and micro pin-fin structures are compared, showing more than 20% increased performance of the latter for all operating conditions investigated.