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Research Papers: Natural and Mixed Convection

Experimental Effectiveness of Sierpinski Carpet Fractal Fins in a Natural Convection Environment

[+] Author and Article Information
David M. Calamas

Mem. ASME
Department of Mechanical Engineering,
Georgia Southern University,
P.O. Box 8046,
Statesboro, GA 30460
e-mail: dcalamas@georgiasouthern.edu

Daniel G. Dannelley

Mem. ASME
Department of Mechanical Engineering,
Embry Riddle Aeronautical University,
3700 Willow Creek Road,
Prescott, AZ 86301
e-mail: dannelld@erau.edu

Gyunay H. Keten

Department of Mechanical Engineering,
Georgia Southern University,
P.O. Box 8046,
Statesboro, GA 30460
e-mail: gk00703@georgiasouthern.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 31, 2015; final manuscript received April 11, 2017; published online May 16, 2017. Assoc. Editor: Gennady Ziskind.

J. Heat Transfer 139(9), 092501 (May 16, 2017) (12 pages) Paper No: HT-15-1824; doi: 10.1115/1.4036595 History: Received December 31, 2015; Revised April 11, 2017

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. 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. The thermal performance of the fractal fins was investigated in a natural convection environment with thermal radiation accounted for. Fin performance was analyzed under power inputs of 2.5, 5, 10, and 20 W. While fin efficiency was found to decrease with fractal iteration, fin effectiveness per unit mass increased with fractal iteration. In addition, a fractal fin inspired by the fourth iteration of the Sierpinski carpet fractal pattern was found to be more effective than a traditional straight rectangular fin of equal width, height, and thickness. When compared to a traditional straight 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 3.63% more effective, 16.19% less efficient, and 65.99% more effective per unit mass. The amount of the total heat transfer attributed to thermal radiation was also dependent on fractal iteration. Thermal radiation accounted for, on average, 57.00% of the total heat transfer for the baseline case, or zeroth fractal iteration. Thermal radiation accounted for 53.67%, 50.33%, 48.84%, and 45.84% of the total heat transfer for the first, second, third, and fourth fractal iterations, respectively.

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References

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Figures

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Fig. 1

Nomenclature and coordinate system

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Fig. 2

Sierpinski carpet fractal iterations 1–4

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Fig. 3

Sierpinski carpet fin mass as a function of iteration

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Fig. 4

Sierpinski carpet fin surface area as a function of iteration

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Fig. 5

Natural convection experimental layout

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Fig. 6

Front view of experiment with heater and thermocouple locations

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Fig. 7

Side (left) and top (right) view of experiment with thermocouple locations

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Fig. 8

Sierpinski carpet fractal fins

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Fig. 9

Fin effectiveness as a function of iteration for power inputs of 2.5, 5, 10, and 20 W

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Fig. 10

Fin effectiveness per unit mass as a function of iteration for power inputs of 2.5, 5, 10, and 20 W

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Fig. 11

Fin efficiency as a function of iteration for power inputs of 2.5, 5, 10, and 20 W

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Fig. 12

Nusselt number as a function of iteration for power inputs of 2.5, 5, 10, and 20 W

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Fig. 13

Convective and radiative effectiveness as a function of fractal iteration for a power input of 20 W

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Fig. 14

Convective, radiative, and total effectiveness per unit mass as a function of fractal iteration for a power input of 2.5 W

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