Researchers at Imperial College London, working with engineers from ToffeeX in London, have published a new modelling framework in Springer Nature that enables the optimization of three-dimensional heat sinks at scales previously considered impractical. The approach abandons homogenization and grid-based methods in favor of an explicit multiscale representation, allowing accurate modelling of fluid and thermal interactions across hundreds of microstructures while significantly reducing computational requirements.
The study demonstrates that the framework can cut memory use by up to 90 percent and reduce computation time by 70 percent compared with explicit single-scale simulations. Validation against high-fidelity numerical models confirmed errors below 10 percent in both fluid momentum and heat transport. By handling domains with as many as 400 unit cells, the method extends optimization into regimes that existing approaches struggle to reach. These improvements are particularly relevant for cooling microprocessors, where non-uniform heat distributions and tight pressure constraints dictate design performance.
Imperial’s modelling strategy combines a multiscale momentum solver with an iterative temperature-flux projection scheme. This coupling avoids homogenized approximations and preserves accuracy at solid–fluid interfaces, where density-based topology optimization often fails. Validation included heterogeneous unit-cell arrangements, showing that the solver could replicate single-scale accuracy while running 2.5 times faster. Unlike conventional single-scale models, which scale poorly as problem size grows, the multiscale solver distributed calculations across unit cells, enabling efficient parallel processing. In one demonstration, a 1600-cell pin-fin array with 50 million degrees of freedom was solved in just over 90 minutes using 127 processors, capturing complex flow and temperature patterns at a fraction of the cost of traditional methods.
Bayesian optimization was integrated to design pin-fin microstructures under varying heat flux profiles. Each optimization used over one hundred processors but completed in less than 80 hours, a timescale not feasible for single-scale simulations of equivalent size. For benchmarks, homogeneous pin-fin layouts were compared against optimized configurations. Under uniform heat flux, optimization improved heat transfer by 75 percent while maintaining pressure-drop limits. Under localized flux, representative of chip hotspots, performance gains reached 558 percent. These results indicate that designs tuned for realistic, inhomogeneous thermal loads can extract far more heat than conventional uniform arrangements.
Heat sink design has long been constrained by trade-offs between accuracy and computational feasibility. Explicit computational fluid dynamics methods offer precision but are limited to small or simplified geometries. Level-set methods provide cleaner definitions of interfaces but remain sensitive to starting conditions and convergence issues. Density-based topology optimization allows broader searches, yet struggles with blurred boundaries and requires additional processing to produce manufacturable designs. By keeping explicit representations while distributing computation across scales, the new framework removes these limitations and enables detailed, manufacturable solutions.
Performance testing highlighted scalability as a key strength. While single-scale solvers became less efficient with domain size due to meshing overhead and solver bottlenecks, the multiscale approach maintained speed by decomposing domains into smaller problems that could be solved concurrently. This capability is essential for optimization, where larger numbers of unit cells provide finer control over local thermal and fluid flows. The framework’s validation campaign confirmed that both flow and thermal solvers achieved accuracy within 10 percent of single-scale results, making it reliable for design applications.
Some limitations remain. In the homogeneous flux case, the optimized design left unused margin in the pressure-drop constraint because Gaussian process regression within the Bayesian framework underestimated solutions close to feasibility boundaries. This conservatism limited performance near the constraint. The authors suggest that improved constraint-handling techniques or constrained acquisition functions could address this. They also note that coarse interpolation of design variables may have reduced the optimizer’s ability to fine-tune local flows in the inhomogeneous flux scenario, leaving pockets of unexploited cooling capacity at the outlet.
Heat sinks play a critical role in computing and power electronics, ensuring device reliability and lowering energy consumption through efficient thermal management. The new framework shows that explicit multiscale modelling, once too computationally expensive, can now be applied to designs with hundreds of unit cells. By coupling microscale detail with macroscale behavior, it makes it possible to optimize layouts for realistic operating conditions, including localized hotspots common in modern processors.
Future directions identified in the study include alternative optimization strategies to expand the number of design variables, refined discretization strategies to better match non-uniform heat flux distributions, and expanded microstructure parameterization beyond simple pin-fin radii. The framework’s scalability suggests potential for use in advanced cooling systems across CPUs, GPUs, and other high-power devices where efficient heat removal is critical.
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Featured image shows heat sink side view. Image via Springer Nature.
