Thermal Performance of Sierpinski Carpet Fractal Fins in a Natural Convection Environment

When certain fractal geometries are used in the design of fins or heat sinks the surface area available for heat transfer can be increased while system mass can be simultaneously decreased. In order to assess the thermal performance of fractal fins for application in the thermal management of electronic devices an experimental investigation was performed. The experimental investigation assessed the efficiency, effectiveness, and effectiveness per unit mass of straight rectangular fins inspired by the first four iterations of the Sierpinski carpet fractal pattern. The thermal performance of the fractal fins was investigated in a natural convection environment. While fin efficiency was found to decrease with fractal iteration fin effectiveness per unit mass increased with fractal iteration. In addition, a fractal fin inspired by the fourth iteration of the Sierpinski carpet fractal pattern was found to be more effective than a traditional straight rectangular fin of equal width, height, and thickness. When compared to a traditional straight rectangular fin, or the zeroth fractal iteration, a fin inspired by the fourth fractal iteration of the Sierpinski carpet fractal pattern was found to be 4.87% more effective, 15.19% less efficient, and 67.98% more effective per unit mass. The amount of the total heat transfer attributed to thermal radiation was also dependent on fractal iteration. Thermal radiation accounted for 45.52% of the total heat transfer for the baseline case, or zeroth fractal iteration. Thermal radiation accounted for 51.94%, 50.17%, 52.77%, and 66.62% of the total heat transfer for the first, second, third, and fourth fractal iteration respectively.