Boiling heat transfer and bubble distribution on inhomogeneous wetting surface patterned with Sierpinski carpet

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.

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

Journal of Heat Transfer ◽

10.1115/1.4036595 ◽

2017 ◽

Vol 139 (9) ◽

Cited By ~ 2

Author(s):

David M. Calamas ◽

Daniel G. Dannelley ◽

Gyunay H. Keten

Keyword(s):

Heat Transfer ◽

Experimental Investigation ◽

Natural Convection ◽

Thermal Radiation ◽

Total Heat ◽

Unit Mass ◽

Sierpinski Carpet ◽

Total Heat Transfer ◽

Fractal Pattern ◽

Sierpiński Carpet

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

Volume 8B: Heat Transfer and Thermal Engineering ◽

10.1115/imece2015-51985 ◽

2015 ◽

Author(s):

David Calamas ◽

Daniel Dannelley ◽

Gyunay Keten ◽

Philip Hines

Keyword(s):

Heat Transfer ◽

Experimental Investigation ◽

Thermal Radiation ◽

Thermal Performance ◽

Total Heat ◽

Unit Mass ◽

Sierpinski Carpet ◽

Total Heat Transfer ◽

Fractal Pattern ◽

Sierpiński Carpet

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. 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 4.87% more effective, 15.19% less efficient, and 67.98% 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 45.52% of the total heat transfer for the baseline case, or zeroth fractal iteration. Thermal radiation accounted for 51.94%, 50.17%, 52.77%, and 66.62% of the total heat transfer for the first, second, third, and fourth fractal iteration respectively.

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

Volume 8: Heat Transfer and Thermal Engineering ◽

10.1115/imece2017-71697 ◽

2017 ◽

Author(s):

David Calamas ◽

Daniel Dannelley ◽

Jennifer Shaffer ◽

Valentin Soloiu

Keyword(s):

Heat Transfer ◽

Free Convection ◽

Thermal Radiation ◽

Thermal Performance ◽

Unit Mass ◽

Sierpinski Carpet ◽

Fractal Pattern ◽

Sierpiński Carpet ◽

The Impact ◽

Equal Height

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.

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Molecular Dynamics Investigation on Thermal Conductivity and Photon Behaviors of Graphene With Sierpinski Carpet Fractal Defects

Frontiers in Energy Research ◽

10.3389/fenrg.2021.819395 ◽

2022 ◽

Vol 9 ◽

Author(s):

Wei Yu ◽

Yongjing Wu ◽

Xiangxiang Shao ◽

Xiwen Wang

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Molecular Dynamics ◽

Numerical Results ◽

Sierpinski Carpet ◽

Defective Graphene ◽

Underlying Mechanisms ◽

Non Equilibrium Molecular Dynamics ◽

Sierpiński Carpet ◽

Blockage Effect

The thermal conductivity (TC) of graphene with Sierpinski carpet fractal (SCF) and regular carpet (RC) defects is numerically studied by the non-equilibrium molecular dynamics (NEMD) method. The influences of porosity, fractal levels, and types of defects on the TC of graphene are clarified, and the underlying mechanisms of phonon behaviors are uncovered. The numerical results indicate that the defects in graphene induce the atoms that have the heat transfer blockage effect, and thus, the TC of defective graphene decreases with increasing porosity. With the increase in fractal levels, more atoms have the heat transfer blockage effect, which induces the TC of graphene with SCF defects to sharply decrease. Moreover, compared with the graphene with RC defects, more atoms participate in the heat transfer blockage under the graphene with SCF defects, which leads to the lower TC of graphene with SCF defects.

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