Research Papers: Heat Transfer Enhancement

Radiant Fin Performance Using Fractal-like Geometries

[+] Author and Article Information
Daniel Dannelley

Department of Mechanical Engineering,
The University of Alabama,
Box 870276,
Tuscaloosa, AL 35487-0276
e-mail: danne001@crimson.ua.edu

John Baker

Department of Aerospace Engineering
and Mechanics,
The University of Alabama,
Box 870280,
Tuscaloosa, AL 35487-0280
e-mail: john.baker@eng.ua.edu

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 20, 2012; final manuscript received February 26, 2013; published online July 18, 2013. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 135(8), 081902 (Jul 18, 2013) (8 pages) Paper No: HT-12-1384; doi: 10.1115/1.4023883 History: Received July 20, 2012; Revised February 26, 2013

The results of a computational study into the thermal performance of thermally radiating fractal-like fins are presented. Previous experimental studies have shown that fractal patterns increase the heat transfer surface area while simultaneously reducing mass. Two fractal patterns were used for comparison, the modified Koch snowflake and the Sierpinski carpet. For an isothermal base fin radiating to free space, the fin effectiveness and fin efficiency are presented for the zeroth and first four fractal iterations in order to quantify the performance. Emissivity, width/thickness ratio, base temperature, and fin material were varied to better understand their impact on the performance of fractal-like fins. Based upon the observed results, fractal-like fins greatly improve the fin effectiveness per unit mass. In certain cases, fin effectiveness per unit mass was found to increase by up to 46%. As the cost of access to space is significant, this reduction in mass could lead to savings for spacecraft thermal management applications.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Gilmore, D. G., ed., 2002, Spacecraft Thermal Control Handbook, Vol. 1, 2nd ed., Aerospace Press, El Segundo, CA, pp. 207–222.
Krikkis, R. N., and Razelos, P., 2002, “Optimum Design of Spacecraft Radiators With Longitudinal Rectangular and Triangular Fins,” ASME J. Heat Transfer, 124(5), pp. 805–810. [CrossRef]
Kumar, S. S., Nayak, V., and Venkateshan, S. P., 1993, “Optimum Finned Space Radiators,” Intl. J. Heat Fluid Flow, 14(2), pp. 191–200. [CrossRef]
Sparrow, E. M., and Ecker, E. R. G., 1962, “Radiant Interaction Between Fin and Base Surfaces.” Transactions ASME: Proc. Aviation Conference, Los Angeles, CA, pp. 12–18.
Sparrow, E. M., Eckert, E. R. G., and Irvine, T. F., 1961, “The Effectiveness of Radiating Fins with Mutual Irradiation,” J. Aerosp. Sci., 28, pp. 763–778. [CrossRef]
Sparrow, E. M., Miller, G. B., and Jonsson, V. K., 1962, “Radiating Effectiveness of Annular-Finned Space Radiators, Including Mutual Irradiation Between Radiator Elements,” J. Aerosp. Sci., 29, pp. 1291–1299. [CrossRef]
Krishnaprakas, C. K., 1996, “Optimum Design of Radiating Rectangular Plate Fin Array Extending From a Plane Wall,” ASME J. Heat Transfer, 118(2), pp. 490–492. [CrossRef]
Krishnaprakas, C. K., 1997, “Optimum Design of Radiating Longitudinal Fin Array Extending From a Cylindrical Source,” ASME J. Heat Transfer, 119(4), pp. 857–860. [CrossRef]
Ellison, G., 1979, “Generalized Computations of the Gray Body Shape Factor for Thermal Radiation from a Rectangular U-Channel,” IEEE T. Compon. Hybr., 2(4), pp. 517–522. [CrossRef]
Razelos, P., and Krikkis, R. N., 2001, “Optimum Design of Longitudinal Rectangular Fins With Base-to-Fin Radiant Interaction,” Heat Transfer Eng., 22, pp. 3–17.
Karlekar, B. V., and Chao, B. T., 1963, “Mass Minimization of Radiating Trapezoidal Fins with Negligible Base Cylinder Interaction,” Intl. J. Heat Mass Tran., 6, pp. 33–48. [CrossRef]
Kumar, S. S., and Venkateshan, S. P., 1994, “Optimized Tubular Radiator With Annular Fins on a Nonisothermal Base,” Intl. J. Heat Fluid Flow, 15, pp. 399–410. [CrossRef]
Arslanturk, C., 2006, “Optimum Design of Space Radiators With Temperature-Dependent Thermal Conductivity,” Appl. Therm. Eng., 26, pp. 1149–1157. [CrossRef]
Keller, H. H., and Holdredge, E. S., 1970, “Radiation Heat Transfer for Annular Fins of Trapezoidal Profile,” ASME J. Heat Transfer, 92, pp. 113–116. [CrossRef]
Naumann, R. J., 2004, “Optimizing the Design of Space Radiators,” Intl. J. Thermophys., 25, pp. 1929–1941. [CrossRef]
Schnurr, N. M., Shapiro, A. B., and Townsend, M. A., 1976, “Optimization of Radiating Fin Arrays With Respect to Weight,” ASME J. Heat Transfer, 98, pp. 643–648. [CrossRef]
Chung, B. T. F., and Zhang, B. X., 1991, “Minimum Mass Longitudinal Fins With Radiation Interaction at the Base,” J. Franklin Institute, 328, pp. 143–161. [CrossRef]
Chung, B. T. F., and Zhang, B. X., 1991, “Optimization of Radiating Fin Array Including Mutual Irradiations Between Radiator Elements,” ASME J. Heat Transfer, 113, pp. 814–822. [CrossRef]
Krishnaprakas, C. K., and Narayana, K. B., 2003, “Heat Transfer Analysis of Mutually Irradiating Fins,” Intl. J. Heat Mass Tran., 46(5), pp. 761–769. [CrossRef]
Wilkins, J. E., 1960, “Minimum-Mass Thin Fins Which Transfer Heat Only by Radiation to Surroundings at Absolute Zero,” J. SIAM, 8, pp. 630–639.
Murali, J. G., and Katte, S. S., 2008, “Experimental Investigation of Heat Transfer Enhancement in Radiating Pin Fin,” Jordan J. Mech. Indust. Eng., 2, pp. 163–167.
Rea, S. N., and West, S. E., 1976, “Thermal Radiation from Finned Heat Sinks,” IEEE T. Part Hyb. Pac., 12, pp. 115–117. [CrossRef]
Khor, Y. K., Hung, Y. M., and Lim, B. K., 2010, “On the Role of Radiation View Factor in Thermal Performance of Straight-fin Heat Sinks,” Intl. Commun. Heat Mass Tran., 37, pp. 1087–1095. [CrossRef]
Abramzon, B., 1997, “A Simple Closed-form Solution for Evaluation of Radiative Heat Transfer from a Rectangular Fin Array,” IEEE T. Compon. Pack., 20, pp. 225–229.
Yu, S. H., Jang, D., and Lee, K. S., 2012, “Effect of Radiation in a Radial Heat Sink Under Natural Convection,” Intl. J. Heat Mass Tran., 55, pp. 505–509. [CrossRef]
Shabany, Y., 2008, “Radiation Heat Transfer From Plate-Fin Heat Sinks,” Proc. of 24th IEEE SEMI-THERM Symposium, San Jose, CA, pp. 132–136.
Dannelley, D., and Baker, J., 2012, “Natural Convection Fin Performance Using Fractal-Like Geometries,” J. Thermophys. Heat Trans., 26(4), pp. 657–664. [CrossRef]
Kraus, A. D., Aziz, A., and Welty, J. R., 2001, Extended Surface Heat Transfer, Wiley, New York, pp. 577–583.
Devaney, R. L., 1990, “Geometric Iterations: Fractals,” Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, Addison-Wesley Pub, Menlo Park, CA.
Fox, R. W., and McDonald, A. T., 1992, “Dimensional Analysis and Similitude,” Introduction to Fluid Mechanics, John Wiley & Sons, New York.


Grahic Jump Location
Fig. 1

Computational model validation

Grahic Jump Location
Fig. 2

Sierpinski carpet (top) and modified Koch snowflake (bottom)

Grahic Jump Location
Fig. 3

Isometric views, zeroth iteration, w = 10.16 cm and t = 0.3175 cm

Grahic Jump Location
Fig. 4

Area/initial area versus iteration

Grahic Jump Location
Fig. 5

Fin effectiveness/mass, variable fractal pattern

Grahic Jump Location
Fig. 6

Fin effectiveness, variable emissivity

Grahic Jump Location
Fig. 7

Fin effectiveness/mass, variable emissivity

Grahic Jump Location
Fig. 8

Fin efficiency, variable emissivity

Grahic Jump Location
Fig. 9

Fin effectiveness, variable width/thickness ratio

Grahic Jump Location
Fig. 10

Fin effectiveness/mass, variable width/thickness ratio

Grahic Jump Location
Fig. 11

Fin efficiency, variable width/thickness ratio

Grahic Jump Location
Fig. 12

Fin effectiveness/mass, variable Tb

Grahic Jump Location
Fig. 13

Fin effectiveness/mass, variable material

Grahic Jump Location
Fig. 14

Fin effectiveness correlation




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In