Topology optimization for microchannel heat sinks with nanofluids using an Eulerian-Eulerian approach

TL;DR

The paper addresses the challenge of maximizing heat transfer in microchannel heat sinks cooled by nanofluids. It develops a density-based topology optimization framework using a two-phase Eulerian-Eulerian model, with automatic differentiation for sensitivities and a Globally Convergent Method of Moving Asymptotes (GCMMA) for optimization, under a fixed pressure drop. Two numerical experiments—one on a square design domain and one on a manifold microchannel heat sink unit cell—demonstrate how pressure drop and particle volume fraction influence optimized flow fields and cooling performance, achieving up to 11.6% improvement over conventional parallel-channel designs under identical nanofluid conditions. The results highlight the potential of topology-optimized nanofluid flow fields for compact thermal management and point to extensions to three-dimensional designs to capture full device physics.

Abstract

The demand for high-performance heat sinks has significantly increased with advancements in computing power and the miniaturization of electronic devices. Among the promising solutions, nanofluids have attracted considerable attention due to their superior thermal conductivity. However, designing a flow field that effectively utilizes nanofluids remains a significant challenge due to the complex interactions between fluid and nanoparticles. In this study, we propose a density-based topology optimization method for microchannel heat sink design using nanofluids. An Eulerian-Eulerian framework is utilized to simulate the behavior of nanofluids, and the optimization problem aims to maximize heat transfer performance under a fixed pressure drop. In numerical examples, we investigate the dependence of the optimized configuration on various parameters and apply the method to the design of a manifold microchannel heat sink. The parametric study reveals that the number of flow branches increases with the increased pressure drop but decreases as the particle volume fraction increases. In the heat sink design, the topology-optimized flow field achieves an 11.6% improvement in heat transfer performance compared to a conventional parallel flow field under identical nanofluid conditions.

Figures (14)

• Figure 1: Schematic diagram of a manifold microchannel heat sink: (a) The flow direction and key components in the MMCHS (b) Top view of a unit cell in the MMCHS.
• Figure 2: Schematic representation of the fluid domain $\Omega$ and the solid domain $D \backslash \Omega$ in the fixed design domain $D$, including the corresponding boundary expressions for the inlet $\mathit{\Gamma}^{\rm in}$, outlet $\mathit{\Gamma}^{\rm out}$, and wall $\mathit{\Gamma}^{\rm w}$.
• Figure 3: Flowchart of the topology optimization process.
• Figure 4: Analysis domain for the numerical scheme validation.
• Figure 5: Average Nusselt number is evaluated with the Reynolds number at different particle volume fractions in the analysis domain shown in Fig. \ref{['Fig.3']}.