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Constructal tree networks for heat transfer

Publication ,  Journal Article
Ledezma, GA; Bejan, A; Errera, MR
Published in: Journal of Applied Physics
1997

This paper addresses the fundamental problem of how to connect a heat generating volume to a point heat sink by using a finite amount of high-conductivity material that can be distributed through the volume. The problem is one of optimizing the access (or minimizing the thermal resistance) between a finite-size volume and one point. The solution is constructed by covering the volume with a sequence of building blocks, which proceeds toward larger sizes (assemblies), hence, the "constructal" name for this approach. Optimized numerically at each stage are geometric features such as the overall shape of the building block, its number of constituents, and the internal distribution of high-conductivity inserts. It is shown that in the optimal design, the high-conductivity material has a distribution with the shape of a tree. Every aspect of the tree architecture is deterministic: the shapes of the largest assembly and all its constituents, the number of branches at each level of assembly, the relative position of building blocks in each assembly, and the relative thicknesses of successive branches. The finer, innermost details of the tree architecture (e.g., the branching angle) have a negligible effect on the overall thermal resistance. The main conclusion is that the structure, working mechanism, and minimal resistance of the tree network can be obtained deterministically, and that the constrained optimization of access routes accounts for the macroscopic structure in nature. © 1997 American Institute of Physics.

Duke Scholars

Published In

Journal of Applied Physics

Publication Date

1997

Volume

82

Issue

1

Start / End Page

89 / 100

Related Subject Headings

  • Applied Physics
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Ledezma, G. A., Bejan, A., & Errera, M. R. (1997). Constructal tree networks for heat transfer. Journal of Applied Physics, 82(1), 89–100.
Ledezma, G. A., A. Bejan, and M. R. Errera. “Constructal tree networks for heat transfer.” Journal of Applied Physics 82, no. 1 (1997): 89–100.
Ledezma GA, Bejan A, Errera MR. Constructal tree networks for heat transfer. Journal of Applied Physics. 1997;82(1):89–100.
Ledezma, G. A., et al. “Constructal tree networks for heat transfer.” Journal of Applied Physics, vol. 82, no. 1, 1997, pp. 89–100.
Ledezma GA, Bejan A, Errera MR. Constructal tree networks for heat transfer. Journal of Applied Physics. 1997;82(1):89–100.

Published In

Journal of Applied Physics

Publication Date

1997

Volume

82

Issue

1

Start / End Page

89 / 100

Related Subject Headings

  • Applied Physics
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences