Thermal interface resistance remains a bottleneck for thermal transport in electronic systems, comprising a significant portion of overall system thermal resistance. Performance of thermal interface materials (TIMs) is largely dependent on the bulk thermal conductivity of the TIM but also on the bond-line thickness (BLT) of the applied material as well as interfacial contact resistances. Recently, Hierarchically Nested Channels (HNCs), created by modifying the surface topology with hierarchical arrangements of microchannels in order to improve flow, were proposed to reduce both required squeezing force and final BLTs in interfaces. In this paper, a topological optimization framework that enables the design of channel arrangements is developed. The framework is based on a resistance network approximation to Newtonian squeeze flow. The approximation, validated against finite element method (FEM)-based solutions, allows efficient, design-oriented solutions for squeeze flow in complex geometries. A comprehensive design sensitivity analysis exploiting the resistance network approximation is also developed and implemented. The resistance approximation and the sensitivity analysis is used to build an automated optimal channel design framework. A Pareto optimal problem formulation for the design of channels is posed and the optimal solution is demonstrated using the framework.

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