Pairing factorial design with finite element analysis to model and optimize heat transfer in finned heatsinks

Abstract

Effective thermal management is critical to many engineering applications, yet identifying optimal heat-transfer designs remains challenging due to complex interactions among material, geometry, and structural parameters. Here, we use a full-factorial design combined with thermal physics finite element simulations to systematically evaluate the effects of five factors—material, fin configuration, geometry, spacing, and thickness—on the time to boil water (τb) in a heatsink-assisted system. Using data from just 32 treatment simulations and a statistically reduced categorical model, we resolve all main effects and interactions, revealing that sparse fin spacing, aluminum material, and thin fins significantly reduce τb. While radial configurations generally outperform linear ones, interaction effects demonstrate that optimum performance depends on specific factor combinations; for example, linear designs can outperform radial ones when paired with certain geometries and materials. Contrary to intuition, neither surface area nor surface-area-to-mass ratio reliably predicts performance due to confounding effects of mass. The best-performing design—an Al-linear-trapezoidal-sparse-thin heatsink—achieved τ^b=618±2s, while other optimal designs emerged under constraints such as reduced mass or manufacturing simplicity. This study underscores the value of factorial design in navigating complex design spaces and optimizing thermal performance, offering a powerful framework for the development of next-generation heat transfer systems.