Mechanical Engineering (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Dr. David Calamas


This experimental investigation studies the thermal performance of the first four iterations of the Sierpinski carpet pattern in a natural convection environment. This particular fractal geometry is promising in that it increases the available surface area for heat transfer while simultaneously decreasing the mass of the system. This makes it a potentially advantageous design for fins or heat sinks, especially in aerospace applications where minimizing mass of the system is essential. The thermal performance was evaluated by comparing the efficiency, effectiveness, and effectiveness per unit mass for each fractal iteration. The results indicate that efficiency decreases with each fractal iteration while effectiveness per unit mass increases with fractal iteration. The fourth iteration fractal fin was found to be approximately 10.7% more effective, 10.2% less efficient, and 77.3% more effective per unit mass when compared to a traditional straight rectangular fin of equal height, width, and thickness (the zeroth fractal iteration). Based on the results of a view factor analysis, thermal radiation was found to comprise an average of 42.3%, 39.7%, 39.1%, 38.5%, and 34.9% of the total heat transfer for the zeroth, first, second, third, and fourth fractal iteration fins, respectively. Therefore, the contribution of thermal radiation to the total heat transfer of the system cannot be neglected in future studies using this fractal pattern.