Topology Optimization of Coral-Like Heat Sinks under Pool Boiling for Two-Phase Immersion Cooling

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Abstract

Heat sinks having extended surface area can substantially increase the heat dissipation limit of two-phase immersion cooling compared to the critical heat flux limit of flat surfaces. However, the highly nonlinear and boiling-regime-dependent surface boundary condition makes designing an optimal two-phase immersion heat sink a challenge, and no systematic design approach currently exists. In this work, we propose a density-based topology optimization method for designing heat sinks under pool boiling conditions. Boiling on a heat sink is modeled as a conduction problem with convective boundary condition, where the heat transfer coefficient is defined as a function of superheat and spans all boiling regimes (natural convection, nucleate boiling, transition boiling, and film boiling). 

The heat sink is represented as voxelized density distribution within the design domain, with the thermal conductivity modeled as a function of local density. The boiling boundary conditions are implicitly incorporated at the heat sink interface using an interpolation function of density and superheat. Penalizations are applied to both the thermal conductivity and the boiling boundary conditions to enforce a binary final design, while density filtering and Heaviside projection are applied to control the feature length scale. Optimized heat sink designs are generated iteratively using a multi-objective cost function, with the adjoint method applied to compute sensitivity at each optimization iteration. The resulting coral-like heat sink designs are predicted to effectively dissipate heat at a footprint-area-based power density significantly exceeding the critical heat flux of a flat surface, and are further shown to outperform conventional pin-fin and plate-fin arrays as benchmarks.

 A detailed analysis of heat sink superheat and heat transfer distributions further reveals that the optimized designs effectively spread the heat load and reduce the conduction resistance by maintaining the surface area with high heat transfer coefficients in the nucleate boiling regime close to the heat input region. The superheat-dependent boundary condition captures the drastic reduction in heat transfer coefficient with transition to film boiling and naturally penalizes operations in such unfavorable regimes, facilitating the generation of heat sinks that avoid thermal runaway. This study demonstrates the effectiveness of proposed topology optimization method in balancing the heat spreading and conduction resistances under a boiling boundary condition to achieve optimal two-phase immersion heat sink performance.

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