constructal_theory

Constructal design of a coolingsystem

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The constructal theory puts forth the idea that the generation of design(configuration, pattern, geometry) in nature is a physics phenomenonthat unites all animate and inanimate systems, and that this phenomenonis covered by the Constructal Law stated by Adrian Bejan in 1996: "Fora finite-size (flow) system to persist in time (to live), its configurationmust evolve such that it provides easier access to the imposed currentsthat flow through it."

1 History2 Principles

2.1 Constructal law2.2 Thermodynamical analogy

3 Allometric exponents4 External links5 References

5.1 Popular literature

The constructal theory was developed by Adrian Bejan in 1996.

"Constructal" is a word coined by Bejan, coming from the Latin verb construere, to construct, in order todesignate, in the constructal theory's point of view, the naturally optimized forms such as rivers, trees andbranches, lungs and also the engineered forms coming from a constructal evolutionary process ofmaximization of flow access in time.

For example, in point-area and point-volume flows, constructal theory predicts tree architectures, such flowsdisplaying at least two regimes: one highly resistive and a less resistive one. Constructal theory can beapplied at any scale: from macroscopic to microscopic systems.

Some domains of application

ApplicationWhatflows

Tree channels Interstitial spaces

Packages ofelectronics

Heat High-conductivity inserts (blades, needles) Low conductivity substrate

Urban traffic People Low-resistance street car trafficStreet walking in urbanstructure

Constructal theory - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Constructal_law

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River basins Water Low-resistance rivulet and riversDarcy flow through porousmedia

Lungs Air Low-resistance airways, bronchial passages diffusion in alveoli tissues

Circulatory system BloodLow-resistance blood vessels, capillaries,arteries, veins

diffusion in capillariestissues

The main principle of the constructal theory is that every system is destined to remain imperfect.

According to this, the best that can be done is to optimally distribute the imperfections of the system, andthis optimal distribution of imperfection will generate the geometry or shape of the studied system.

The constructal way of distributing the system's imperfection is to put the more resistive regime at thesmallest scale of the system. The constructal law is the principle that generates the perfect form, which is theleast imperfect form possible.

Constructal law

The constructal law was stated by Bejan in 1996 as follows: "For a finite-size system to persist in time (tolive), it must evolve in such a way that it provides easier access to the imposed currents that flow throughit."

Thermodynamical analogy

Analogies between thermodynamics and constructal theory

Thermodynamics Constructal theory

State Flow architecture (geometry, structure)

Process Change of structure

Properties Global objective and global constraints

Equilibrium state Equilibrium flow architecture

Fundamental relation Fundamental relation

Constrained equilibrium states Nonequilibrium architectures

Removal of constraints Increased freedom to morph

Energy minimum principle Maximization of flow access

In contrast to fractal models of phenomena, the constructal law is predictive and thus can be testedexperimentally. One illustration of this is its application to a variety of allometric laws for which extensivedata over several orders of magnitude of the variables exist.

For example:

Kleiber's law, the relationship between metabolic rate q0 and body size M

the relationship between breathing and heart beating times t and body size M


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the relationship between the mass transfer contact area A and body mass M:

Bejan's constructal law also explains why we have a bronchial tree with 23 levels of bifurcation. Theconstructal theory of the flow architecture of the lung predicts and offers an explanation for:

the dimensions of the alveolar sac,the total length of the airways,the total alveolar surface area,the total resistance to oxygen transport in the respiratory tree.

Constructal Theory web portal (http://www.constructal.org/en/theory/presentation.html) :publications, events, links, etc.Unified Physics Theory Explains Animals' Running, Flying And Swimming(http://www.dukenews.duke.edu/2005/12/locomotiontheory.html) : Duke University article.

A. Bejan, Advanced Engineering Thermodynamics, Wiley-Interscience, 2nd edition, 896 p. ISBN0-471-14880-6 ; 3rd edition, 2006, ISBN 0-471-67763-9.A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge,UK, 2000, 324 p. ISBN 0-521-79388-2Proceedings of the Symposium "Bejan’s Constructal Theory of Shape and Structure" (http://cge-1.uevora.pt/~bejansymposium/) Edited by Rui N. Rosa, A. Heitor Reis & A. F. Miguel, Centro deGeofísica de Évora, Évora Geophysics Center, Portugal, 2004, ISBN 972-9039-75-5A. Bejan, "Constructal theory of organization in nature: dendritic flows, allometric laws and flight",Design and Nature, CA Brebbia, L Sucharov & P Pascola (Editors). ISBN 1-85312-901-1A. H. Reis, A. F. Miguel, M. Aydin (May 2004). "Constructal theory of flow architecture of the lungs".Med Phys. 31 (5): 1135–40. PMID 15191302 (http://www.ncbi.nlm.nih.gov/pubmed/15191302) .A. H. Reis, A. Bejan, "Constructal theory of global circulation and climate"(http://www.sciencedirect.com/science?_ob=ArticleURL&_aset=V-WA-A-W-A-MsSWYWW-UUA-U-AAVUZBZYVY-AABYWADZVY-ZUDBDCYCD-A-U&_rdoc=1&_fmt=summary&_udi=B6V3H-4J2W0N2-4&_coverDate=01%2F19%2F2006&_cdi=5731&_orig=search&_st=13&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=89441fb0b28e21ddd42397b12bbd20de) , International Journal of Heat and Mass TransferVolume 49, Issues 11-12, Pages 1857-1875, June 2006.Adrian Bejan, Sylvie Lorente, La loi constructale; traduction [de l'anglais] et avant-propos d'AngèleKremer-Marietti. - Paris ; Budapest ; Torino : l'Harmattan, DL 2005 (14-Condé-sur-Noireau : Impr.Corlet numérique). - 1 vol. (109 p.) : ill., couv. ill. ; 24 cm. - (Collection Épistémologie et philosophiedes sciences). Bejan, Adrian (1948-....) Bibliogr. p. 99-109. - DLE-20050511-22456. - 530.4 (21) . -ISBN 2-7475-8417-8 (br.) : 11,50 EUR.Abdelkader Bachta, Jean Dhombres, Angèle Kremer-Marietti, Trois Etudes sur la loi constructaled'Adrian Bejan, Paris, L'Harmattan, 2008.

Popular literature

Maggie Wittlin, "A Finger on the Pulse of the World" (http://www.seedmagazine.com/news/2006/01/a_finger_on_the_pulse_of_the_w.php) , January 13, 2006.

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