A subspace method for 3D multiscale heat sink modelling and optimization

Abstract The increasing computational demands of modern microprocessors require efficient thermal management solutions. To address this design challenge, a novel 3D multiscale heat sink modelling and optimization framework is presented. The approach combines a multiscale momentum model with an iterative temperature-flux projection scheme that accurately resolves heat transport across the entire macroscale domain without relying on traditional homogenization methods. Unlike conventional fixed-grid topology optimization approaches, the framework maintains solution accuracy near solid/fluid interfaces whilst achieving superior computational efficiency, reducing memory requirements and computation time relative to equivalent explicit single-scale simulations. Bayesian optimization is utilized to demonstrate the framework’s practical utility by designing multiscale heat sinks with hundreds of unit cells subject to homogeneous, and more accurate in-homogeneous surface heat flux, achieving significantly larger heat transfer in both cases, whilst maintaining pressure drop constraints. This framework enables the practical optimization of complex 3D heat sink designs at multiscale resolutions previously intractable with traditional explicit modelling approaches.