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

Abstract

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. The Sierpinski carpet fractal pattern, when utilized in the design of an extended surface, can provide more effective heat dissipation while simultaneously reducing mass. 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 first four fractal iterations of the Sierpinski carpet pattern, used in the design of extended surfaces, were examined in a forced convection environment. The thermal performance of the Sierpinski carpet fractal fins was quantified by the following performance metrics: efficiency, effectiveness, and effectiveness per unit mass. The fractal fins were experimentally examined in a thermal testing tunnel for a range of Reynolds numbers. As the Reynolds number increased, the fin efficiency, effectiveness and effectiveness per unit mass were found to decrease. However, as the Reynolds number increased the Nusselt number was found to similarly increase due to higher average heat transfer coefficients. The fourth iteration of the fractal pattern resulted in a 6.73% and 70.97% increase in fin effectiveness and fin effectiveness per unit mass when compared with the zeroth iteration for a Reynolds number of 6.5E3. However, the fourth iteration of the fractal pattern resulted in a 1.93% decrease in fin effectiveness and 57.09% increase in fin effectiveness per unit mass when compared with the zeroth iteration for a Reynolds number of 1.3E4. The contribution of thermal radiation to the rate of heat transfer was as high as 62.90% and 33.69% for Reynolds numbers of 6.5E3 and 1.3E4 respectively.