Mixed and Forced Convection Heat Transfer Characteristics of Sierpinski Carpet Fractal Fins

When specific 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 in a mixed and forced convection environment. Fin performance was analyzed for power inputs of 10, 20, and 30 W while the fins were subject to uniform velocities of 1, 2, and 4 m/s. While fin efficiency was found to decrease with fractal iteration, fin effectiveness per unit mass increased with fractal iteration, regardless of power input and uniform velocity. When compared to a traditional solid 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 on average 6.76% more effective, 13.66% less efficient, and 71.01% more effective per unit mass when subject to a uniform velocity of 1 m/s. However, for higher velocities, a fourth iteration was found to be less effective than the zeroth iteration, regardless of power input. Thus, Sierpinski carpet fractal fins should be used in natural and mixed convection environments where they have been found to be more effective than traditional solid rectangular fins. However, when compared with traditional perforated fins, fins inspired by the Sierpinski carpet fractal pattern have been found to offer an increase in perforated fin effectiveness.