Optimization of natural convection heat sinks with inverted trapezoidal fins and elliptical perforations

This study presents an optimal design for a three-dimensional natural convection heat sink featuring an inverted trapezoidal geometry with elliptical perforations. The design was validated through numerical simulations and experiments. Key parameters such as the top width L₁, bottom width L₂, fin height H₀, and the axes of the elliptical perforations R₁ and R₂ were optimized based on minimum base temperature condition while keeping the fin volume constant. This optimization process utilized the Levenberg–Marquardt Method (LMM) and CFD-ACE + software. In Design A, the replacement of rectangular fins with inverted trapezoidal fins resulted in a significant reduction in the average base temperature, decreasing from 87.4 °C to 73.4 °C. The thermal resistance also decreased from 6.2 °C/W to 4.8 °C/W, primarily due to a 47 % decrease in fin height and an increase in the top width. Design B introduced optimized elliptical perforations, further lowering the temperature to 66.4 °C and thermal resistance to 4.1 °C/W. This improvement was attributed to enhanced airflow penetration and the creation of a bifurcated thermal plume. In order to verify the reliability of the numerical model, this study first fabricated physical prototypes of original design, Design A and Design B heat sinks, and conducted experimental measurements. Considering that heat loss inevitably occurs during the experiment due to imperfect insulation at the contact surface between the electric heating plate and the heat sink base plate, as well as from the surrounding environment, we gradually reduced the input power in the simulation and repeatedly compared the simulated and measured temperatures until the two sets of results nearly overlapped. The experimental data, adjusted for approximately 4.4 % heat loss (with an input of 9.56 W), matched the simulations with a margin of error within 5 %. Overall, Design B demonstrated the best performance, achieving a thermal resistance that was 33.9 % lower than the original design and 14.6 % lower than Design A, indicating significant potential for high-efficiency passive cooling.