This paper extends to the field of convective heat transfer the constructal theory of optimizing the access of a current that flows between one point and a finite-size volume, when the volume size is constrained. The volume is bathed by a uniform stream. A small amount of high-conductivity fin material is distributed optimally through the volume, and makes the connection between the volume and one point (fin root) on its boundary. The optimization proceeds in a series of volume subsystems of increasing sizes (elemental volume, first construct, second construct). The shape of the volume and the relative thicknesses of the fins are optimized at each level of assembly. The optimized structure emerges as a tree of fins in which every geometric detail is a result of minimizing the thermal resistance between the finite-size volume and the root point (source, sink). Convection occurs in the interstitial spaces of the tree. The paper shows that several of the geometric details of the optimized structure are robust, i.e., relatively insensitive to changes in other design parameters. The paper concludes with a discussion of constructal theory and the relevance of the optimized tree structures to predicting natural self-organization and self-optimization.
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Research Papers
Constructal Trees of Convective Fins
A. Bejan,
A. Bejan
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300
e-mail: abejan@aduke.edu
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N. Dan
N. Dan
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300
Search for other works by this author on:
A. Bejan
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300
e-mail: abejan@aduke.edu
N. Dan
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300
J. Heat Transfer. Aug 1999, 121(3): 675-682 (8 pages)
Published Online: August 1, 1999
Article history
Received:
October 1, 1998
Revised:
April 5, 1999
Online:
December 5, 2007
Citation
Bejan, A., and Dan, N. (August 1, 1999). "Constructal Trees of Convective Fins." ASME. J. Heat Transfer. August 1999; 121(3): 675–682. https://doi.org/10.1115/1.2826032
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