Analytical and numerical studies on microscale heat sinks for electronic applications

Thermal models for cooling microscale electronic processor chips through forced and natural convection heat sinks are presented in this paper. This research is an extension of an earlier study where extensive analyses were done to develop necessary heat transfer equations for the heat sink of a Pentium III chip. Once the prediction of these model equations closely matched the performance of Pentium III heat sink, we applied them to a processor chip of micrometer scale. This led to the design of a miniaturized heat sink based upon a scaling procedure. In this heat sink, airflow was found to be in micron-size channels. Therefore, calculation of the Knudsen number was necessary to verify that the continuum theory still held for our designed microchannels. Analysis showed that heat dissipated from the heat sink, based upon forced convection over the fins, was 204 mW. We also considered radiation heat transfer from the sink, which gave a smaller value of 0.8 mW based upon an emissivity of 0.07. All analyses to this point were based upon analytical relations. Next we refined our analysis using the computational fluid dynamics code Fluent to obtain improved results. This yielded refined velocities, heat transfer coefficients and a total heat dissipation of 268 mW from microsize fins.