Hotspot Thermal Management via Thin-Film Evaporation—Part II: Modeling

Abstract

We developed a unified semianalytical thermal–fluidic model for hotspot (HS) thermal management via thin-film evaporation from well-defined silicon micropillar wicks. The capillary pressure generated at a receding liquid meniscus is matched with the flow resistance of the micropillar wick to estimate the dryout heat flux. In addition to modeling the fluidic transport within the porous wick structure, the thermal transport was modeled by solving the 3-D heat diffusion equation. The model prediction for the capillary-limited dryout heat flux agrees within ±20% accuracy with our experiments for the range of heat fluxes reported in this paper. Our comprehensive thermal–fluidic model shows that ultrahigh heat fluxes in excess of 10 kW/cm2 can be dissipated from a $640 \times 620~\mu \text{m}^{2}$ HS area via thin-film evaporation from microstructured surfaces by carefully selecting the thickness and thermal conductivity of the substrate. Furthermore, our results show that there is a global optimum pillar diameter-to-spacing ratio for a given micropillar wick thickness and spreading radius that maximizes the capillary-limited dryout heat flux. The physical insights gained from this paper can be used to improve and optimize the design of wicking structures for extreme heat flux thermal management.