This paper considers the fundamental question of whether the optimal geometry of dendritic tree networks is symmetric or asymmetric. Asymmetry of dendritic networks is a result of the relation between flow resistance and flow fraction at each bifurcation node. Asymmetry of bifurcation (asymmetry of -shaped assemblies) appears when the flow fraction at each bifurcation node is not equal to one-half. Asymmetric bifurcation provides lower flow resistance than symmetric bifurcation. Murray’s law of bifurcation is valid only when the flow fraction at every bifurcation node in dendritic networks is one-half and the networks are symmetric. General rules to construct asymmetric trees are developed and reported in this paper. It is shown that even through pressure drops across round and square cross-sectional shape channels are different; their flow resistances can be expressed by similar relations.
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1 December 2006
Research Article|
December 06 2006
Constructal dendritic geometry and the existence of asymmetric bifurcation
W. Wechsatol;
W. Wechsatol
a)
Department of Mechanical Engineering,
King Mongkut’s University of Technology Thonburi
, Rasburana, Bangkok 10140, Thailand
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J. C. Ordonez;
J. C. Ordonez
Department of Mechanical Engineering,
Florida State University
, Tallahassee, Florida 32310-6046 and Center for Advanced Power Systems, Florida State University
, Tallahassee, Florida 32310-6046
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S. Kosaraju
S. Kosaraju
Department of Mechanical Engineering,
Florida State University
, Tallahassee, Florida 32310-6046 and Center for Advanced Power Systems, Florida State University
, Tallahassee, Florida 32310-6046
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a)
Electronic mail: [email protected]
J. Appl. Phys. 100, 113514 (2006)
Article history
Received:
June 22 2006
Accepted:
September 18 2006
Citation
W. Wechsatol, J. C. Ordonez, S. Kosaraju; Constructal dendritic geometry and the existence of asymmetric bifurcation. J. Appl. Phys. 1 December 2006; 100 (11): 113514. https://doi.org/10.1063/1.2388732
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