Multilayer topology optimization of microfluidic heat sinks using non-Newtonian fluid for electronics cooling

This study investigates the topology optimization of microfluidic heat sinks employing non-Newtonian fluids through a computationally efficient multilayer modeling framework to enhance thermal management for advanced electronics cooling applications. A novel three-layer thermal-fluid model is proposed for power-law fluids that achieves significant dimension reduction while preserving critical physical interactions. The model formulates conjugate heat transfer in fluid channels and heat conduction in top/bottom plates in a two-dimensional manner, incorporating out-of-plane flow boundaries, thermal conduction, and convective effects. Notably, this work introduces a Poiseuille flow approximation for the power-law fluid, enabling analytical derivation of out-of-plane velocity and viscosity profiles that explicitly capture shear-dependent behavior. A reduced fluid dynamics equation is then derived using a variational dimension reduction method, demonstrating enhanced stability and compatibility compared to existing approaches by fundamentally avoiding the division-by-zero issue. For heat transfer modeling, an adaptive temperature profile assumption along the channel height enables the derivation of simplified planar heat equations through the variational dimension reduction method, simultaneously integrating both out-of-plane conduction and convection effects. Validation against full three-dimensional models shows that the proposed three-layer model maintains good numerical consistency across various power-law indexes while significantly enhancing computational efficiency. Based on this model, a topology optimization methodology is developed by characterizing channel layouts as porous media fields. The effects of power-law index, pressure drop, and solid thermal conductivity on optimized channel configurations are systematically analyzed. Results demonstrate that optimized structures with streamlined fins achieve efficient heat transfer, verifying the effectiveness and reliability of the developed topology optimization methodology. This study establishes a computationally efficient topological optimization methodology of microchannel heat sink structures utilizing non-Newtonian fluids, providing technical support for the research of high-performance cooling devices in electronic equipment.