Free Convection Heat Transfer From Sierpinski Carpet Fractal Fins of Varying Size

Abstract

This works experimentally investigates the thermal performance of extended surfaces inspired by the first four fractal iterations of the Sierpinski carpet fractal pattern in a free convection environment. Fractal fins inspired by the Sierpinski carpet fractal pattern can result in an increase in surface area for convective heat transfer coupled with a simultaneous decrease in mass and are thus desirable in aerospace applications. The thermal performance of the Sierpinski carpet fractal fins was quantified based on fin efficiency, fin effectiveness, and perforated fin effectiveness. When compared with a solid rectangular fin, without perforations, and of an equal base area and package volume a fin inspired by the fourth iteration of the Sierpinski carpet fractal pattern was found to be more effective at dissipating heat by convection. The impact of fin size on the thermal performance of the fractal fins was investigated for a range of power inputs applied at the base (2.5 W, 5 W, and 10 W). A 5.08 cm × 5.08 cm (2 in × 2 in × 1/16 in) fractal fin inspired by the fourth iteration of the Sierpinski carpet fractal was found to have a convective effectiveness, convective efficiency, and convective effectiveness per unit mass, 10.91% more, 10.31% less, and 77.65% more, than a traditional solid (non-perforated) rectangular fin of equal height, width, and thickness. Similarly, a 10.16 cm × 10.16 cm (4 in × 4 in × 1/8 in) fin inspired by the fourth fractal iteration was found to have a convective effectiveness, convective efficiency, and convective effectiveness per unit mass, 3.97% more, 15.91% less, and 66.54% more, than a traditional solid (non-perforated) rectangular fin of equal height, width, and thickness. Thus, the thermal performance of the fractal fins increased as the size of the fins decreased. Regardless of size, the contribution of thermal radiation was significant (often greater than 50%) and should not be neglected. In general, for a fin with a uniform cross-section, intersurface thermal radiation accounts for a significant percentage of thermal radiation heat transfer, particularly as the size of the perforations decreases.