A Multi-Fidelity Global Search Framework for Hotspot Prevention in 3D Thermal Design Space

TL;DR

This work introduces a Bézier-based multi-fidelity framework for global optimization of 3D heat sinks, coupling a pseudo-3D two-layer thermo-fluid model with a boundary-representation geometry to efficiently explore complex fin shapes. A CMA-ES optimizer drives a constrained, dual-objective search that minimizes pressure drop while meeting a surface-average base-plate temperature limit, using calibrated heat-transfer coefficients derived from high-fidelity simulations. The pseudo-3D model, validated against full 3D analyses, captures key thermal-hydraulic behavior with significantly reduced computational cost, enabling rapid design-space exploration. Results show up to ~50% reductions in pressure loss compared with straight fins, revealing clear trade-offs between thermal performance and hydraulic efficiency and demonstrating a scalable approach for fast, geometry-flexible heat sink optimization.

Abstract

We present a Bézier-based Multi-Fidelity Thermal Optimization Framework, which is a computationally efficient methodology for the global optimization of 3D heat sinks. The flexible Bézier-parameterized fin geometries and the adopted multi-fidelity pseudo-3D thermal modeling strategy meet at a balance between accuracy and computational cost. In this method, the smooth and compact Bézier representation of fins defines the design space from which diverse topologies can be generated with minimal design variables. A global optimizer, the Covariance Matrix Adaptation Evolution Strategy, minimizes the pressure drop with respect to a given surface-average temperature constraint to achieve improvement in the pressure loss. In the framework, the pseudo-3D model couples two thermally interacting 2D layers: a thermofluid layer representing the fluid domain passing through the fins, and a conductive base plate representing the surface where excessive average temperature is to be avoided. Both layers are coupled with calibrated heat transfer coefficients obtained from high-fidelity 3D simulations. For several fin geometries, the proposed framework has been validated by comparing the pseudo-3D results with those of full 3D simulations, which yielded good agreement in terms of temperature distribution and pressure drops when the computational cost was reduced by several orders of magnitude. Optimization results show that it attains up to 50\% pressure loss reduction compared to conventional straight-fin configurations, and it reveals a clear trade-off between thermal performance and hydraulic efficiency. Thus, the proposed method forms a new basis for fast, geometry-flexible, and optimized heat sink design, enabling efficient exploration of complex geometries.

Figures (9)

• Figure 1: (a) 3D schematic view of the problem with boundary conditions. (b) Simplified pseudo-3D model, showing the conversion from the full 3D model to two 2D models, with boundary conditions indicated.
• Figure 2: Workflow of the CMA-ES algorithm implemented to our problem. The design variables $X_k^{(g)}$ are turned into geometric representations by mapping them into Bézier-curves variations.
• Figure 3: Adaptation of the ellipsoid-shaped search distribution based on the covariance matrix and step size.
• Figure 4: Velocity magnitude ($|u|$) and base plate temperature ($T_{bp}$) distributions for (a) rectangular, (b) air-foil, and (c) arbitrary shape fins. (a) base plate average temperature, $\overline{T}_{\Omega_{bp}}$, and pressure drop value, $\Delta\overline{p}$, for pseudo 3D approach are 508.62(K) and -1.096(Pa), respectively, and for 3D full scale simulation are 517.75(K) and -1.348(Pa) (b) $\overline{T}_{\Omega_{bp}}$, and $\Delta\overline{p}$ for pseudo 3D approach are 549.86(K) and -0.71(Pa), respectively, and for 3D full scale simulation are 558.06(K) and -0.917(Pa) (c) $\overline{T}_{\Omega_{bp}}$, and $\Delta\overline{p}$ for pseudo 3D approach are 490.49(K) and -0.931(Pa), respectively, and for 3D full scale simulation are 497.12(K) and -1.148(Pa).
• Figure 5: Temperature and velocity magnitude error distribution for the different cases shown in figure \ref{['fig:validation_combined']}. The temperature error distributions shown in panels (a), (c), and (e) are computed using the relative error formula, $Error= (T_{bp}-T_{3D})/T_{3D}$. For the velocity field error distributions in panels (b), (d), and (f), the normalized mean-square error is employed, $Error= (|{\mathbf{u}}|_{\text{pseudo-3D}} - |\mathbf{u}|_{\text{3D}})^{2} / |\mathbf{u}|^2_{\text{ave,3D}}$.