Thermal Performance of Fractal Fins in a Natural Convection Environment

The thermal performance of fractal fins in a natural convection environment was experimentally investigated. A fractal is an infinite pattern that repeats itself at different scales. Fractals have the property of self-similarity across different scales. This research was conducted into the natural convection performance of fractal fins. Convection is heat transfer between a solid surface and an adjacent fluid that is in motion. This mode of heat transfer is the combined effects of conduction heat transfer within the solid and the fluid motion of the surrounding air. Natural convection occurs due to the buoyancy effects caused by differing densities of the warmer air near the heated surface and the cooler surrounding air. When certain fractal patterns, like the Seirpinski carpet pattern utilized in this study, are used in the design of fins, an increase in surface area coupled with a decrease in mass can be achieved. As the rate of heat transfer is directly proportional to the surface area, the increase in surface area is highly desirable. Decreasing the mass of heat sink fins or thermal radiators is desirable for weight savings, especially in aerospace applications used to cool electronics and provide thermal control of crewed spaces. With a cost of over $10,000 per kilogram to low Earth orbit (LEO) and over $20,000 per kilogram to geosynchronous transfer orbit (GTO), increased effectiveness coupled with weight savings is an important area of study. The thermal performance of fractal fins, inspired by the first four iterations of the Sierpinski carpet pattern, was compared to the performance of traditional straight, rectangular fins of uniform cross section on the basis of fin efficiency, fin effectiveness, and effectiveness per unit mass. When compared to the baseline fin, the first four fractal iterations resulted in a 1.1%, 4.4%, 6.5%, and 12.0% decrease in fin efficiency respectively. The first two iterations of the fractal pattern resulted in a 9.7%, 15.9% and 12.9% decrease in fin effectiveness respectively; however, the fourth fractal iteration resulted in an 8.6% increase in fin effectiveness when compared with the baseline fin. Fin effectiveness per unit mass was also found to increase with each fractal iteration when compared to the baseline case due to the large increase in surface area to volume ratio with each successive iteration