Natural Convection Fin Performance Using Fractal-Like Geometries

Abstract

Fractal geometries are shown to increase surface area significantly with patterns such as the Sierpinski carpet providing the potential for mass reduction. Two fractal geometries were used in this study, the modified Koch snowflakeandtheSierpinskicarpet.Thisstudyexamines finperformanceforthebaselinecases(atriangular finand a square fin) relative to the first three fractal iterations for both geometries. Constant heat rate conditions were applied to the base of the fins, and the temperature distribution across the fins was observed using an infrared camera. Fin effectiveness and fi ne f ficiency were calculated for each fin geometry to quantify the effects of using fractal geometries to improve fin performance. Based on the observed results, fractal geometries can be used to improve fin performance, particularly when the decrease in fin mass is a performance criteria. As fins are used for passive thermal management in many industrial and electronic devices, the use of fractal-like geometries has wide reaching potential. Nomenclature A = area, m 2 C = constant d = constant h = heat transfer coefficient, W=m 2 -K k = thermal conductivity, W=m-K m = mass, kg Nu = Nusselt number, hw=k n = iteration index Q = heat rate, W T = temperature, K t = fin thickness, m w = fin base length, m � = width/thickness ratio � T = average fin to ambient temperature difference, K � = fin effectiveness = emissivity � = fi ne fficiency