Development of Power Law Design Tool for Hotspot Mitigation Using Parallel Microchannel Heat Exchanger

Unconstrained temperatures and hotspots negatively impact the performance of integrated circuits, typically by inducing excessive leakage power or exceeding peak junction temperatures. This highlights two primary design considerations when developing a thermal management system for such devices: maximize heat evacuation from the system and maintain a homogeneous temperature distribution over the system. This work is focused on the latter. The objective of this study is to provide a design tool for engineers in the form of a refined power law for hotspot mitigation using parallel microchannel heat exchangers. The tool relates local power density to the hydraulic diameter of a local microchannel and would allow engineers to size each microchannel based on full-chip power density maps. A power law was developed previously using a combined analytical and computational approach, capable of balancing temperature standard deviation to within 5.0% over Reynolds numbers between 40 and 450. This study further refines the power law by considering a wider range of flow distributions and hotspot power densities in a multivariable regression analysis. A laminar flow regime was used with Reynolds numbers between 200 and 2200. The local hotspot heat flux was fixed at 19.8 W/cm
²
while surrounding heat flux was varied between three and eight times less than the hotspot. A computational analysis of several microchannel heat exchangers designed using this power law demonstrated that it could balance the temperature to a standard deviation 1.59% on average at low Reynolds number and 3.40 % on average at high Reynolds number, for hotspot power ratios up to 2.6. Compared to reference models with uniform channel size, the temperature standard deviation was reduced by an average of 83.2% at low Reynolds number and 61.1% at high Reynolds number. However, a simultaneous average temperature rise of 17.5% and 4.70% was observed, respectively. Furthermore, we demonstrate power law efficacy is impacted by channel density, indicating that the analytical development of the power law may require the inclusion of conduction effects between channels.