Title: Tree-shaped flow structures: are both thermal-resistance and flow-resistance minimisations necessary?

Authors: W. Wechsatol, S. Lorente, A. Bejan

Addresses: Department of Mechanical Engineering and Materials Science, Box 90300, Duke University, Durham, NC 27708-0300, USA. ' Department of Civil Engineering, National Institute of Applied Sciences (INSA), 135 Avenue de Rangueil, Toulouse 31077, France. ' Department of Mechanical Engineering and Materials Science, Box 90300, Duke University, Durham, NC 27708-0300, USA

Abstract: Constructal theory is applied to the cooling of a disc where heat is uniformly generated. The disc size and the total volume occupied by the ducts (distributing the flow from the centre to the periphery) are constrained. It is shown that when the objective is to minimise the global thermal resistance, the best design is the one built with radial ducts. On the other hand, the minimisation of the pumping power leads to tree-shaped structures. The results show that the two optimisation approaches, thermal and fluid-mechanical, generate results with nearly the same global performance. Yet, when the scale of the problem becomes smaller and smaller and dendritic flows perform better, demonstrating the usefulness and robustness of tree-shaped structures.

Keywords: constructal theory; electronics cooling; dendritic; tree networks; flow structures; thermal optimisation; fluid-mechanical optimisation.

DOI: 10.1504/IJEX.2004.004731

International Journal of Exergy, 2004 Vol.1 No.1, pp.2 - 17

Published online: 14 Jun 2004 *

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