# Constructal theory: Wikis

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# Encyclopedia

Constructal design of a cooling system

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

## History

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 to designate, in the constructal theory's point of view, the naturally optimized forms such as rivers, trees and branches, lungs and also the engineered forms coming from a constructal evolutionary process of maximization of flow access in time.

## Principles

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

Some domains of application
Application What flows Tree channels Interstitial spaces
Packages of electronics Heat High-conductivity inserts (blades, needles) Low conductivity substrate
Urban traffic People Low-resistance street car traffic Street walking in urban structure
River basins Water Low-resistance rivulet and rivers Darcy flow through porous media
Lungs Air Low-resistance airways, bronchial passages diffusion in alveoli tissues
Circulatory system Blood Low-resistance blood vessels, capillaries, arteries, veins diffusion in capillaries tissues

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, and this 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 the smallest scale of the system. The constructal law is the principle that generates the perfect form, which is the least 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 (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it."

### 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

## Allometric exponents

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

For example:

• Kleiber's law, the relationship between metabolic rate q0 and body size M
$q_{0} \sim M^{\frac 3 4}$
• the relationship between breathing and heart beating times t and body size M
$t \sim M^{\frac 1 4}$
• the relationship between the mass transfer contact area A and body mass M:
$A \sim M^{\frac 7 8}$

Bejan's constructal law also explains why we have a bronchial tree with 23 levels of bifurcation. The constructal 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.

## References

• A. Bejan, Advanced Engineering Thermodynamics, Wiley-Interscience, 2nd edition, 896 p. ISBN 0-471-14880-6 ; 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 0-521-79388-2
• Proceedings of the Symposium "Bejan’s Constructal Theory of Shape and Structure" Edited by Rui N. Rosa, A. Heitor Reis & A. F. Miguel, Centro de Geofísica de Évora, Évora Geophysics Center, Portugal, 2004, ISBN 972-9039-75-5
• A. Bejan, "Constructal theory of organization in nature: dendritic flows, allometric laws and flight", Design and Nature, CA Brebbia, L Sucharov & P Pascola (Editors). ISBN 1-85312-901-1
• A. 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.
• A. H. Reis, A. Bejan, "Constructal theory of global circulation and climate", International Journal of Heat and Mass Transfer.
• Adrian Bejan, Sylvie Lorente, La loi constructale; traduction [de l'anglais] et avant-propos d'Angèle Kremer-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 philosophie des 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 constructale d'Adrian Bejan, Paris, L'Harmattan, 2008.