RESEARCH PAPERS: Conduction Heat Transfer

Constructal Three-Dimensional Trees for Conduction Between a Volume and One Point

[+] Author and Article Information
G. A. Ledezma

Harvard University, Shriners Hospital Research Center, Massachusetts General Hospital, One Kendall Square, Building 1400W, Cambridge, MA 02139

A. Bejan

Department of Mechanical Engineering and Materials Science, Duke University, Box 90300, Durham, NC 27708-0300

J. Heat Transfer 120(4), 977-984 (Nov 01, 1998) (8 pages) doi:10.1115/1.2825918 History: Received December 30, 1997; Revised June 24, 1998; Online December 05, 2007


This paper extends to three-dimensional heat conduction the geometric “constructal” method of minimizing the overall thermal resistance between a finite-size volume and a small heat sink. The volume contains (i) low-conductivity material that generates heat at every point, and (ii) a small amount of high-conductivity material that must be distributed optimally in space. The given volume is covered in a sequence of building blocks (volume sizes) that starts with the smallest volume element, and continues toward larger assemblies. It is shown that the overall shape of each building block can be optimized for minimal volume-to-point resistance. The relative thicknesses of the high-conductivity paths can also be optimized. These optima are developed analytically and numerically for the smallest elemental volume and the first assembly. The high-conductivity paths form a tree network that is completely deterministic.

Copyright © 1998 by The American Society of Mechanical Engineers
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