Research Papers

Constructal Law: Optimization as Design Evolution

[+] Author and Article Information
Adrian Bejan

Department of Mechanical Engineering and Materials Science,
Duke University,
Durham, NC 27708-0300
e-mail: abejan@duke.edu

Manuscript received March 18, 2014; final manuscript received April 9, 2014; published online March 17, 2015. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 137(6), 061003 (Jun 01, 2015) (8 pages) Paper No: HT-14-1137; doi: 10.1115/1.4029850 History: Received March 18, 2014; Revised April 09, 2014; Online March 17, 2015

Here, I review the physics meaning of optimization, knowledge and design evolution, and why these concepts and human activities are profoundly useful for human life. A law of physics is a concise statement that summarizes a phenomenon that occurs in nature. A phenomenon is a fact, circumstance, or experience that is apparent to the human senses and can be described. The design in nature phenomenon facilitates access for everything that flows, evolves, spreads, and is collected: river basins, atmospheric and ocean currents, animal life and migration, and technology (the evolution of the “human-and-machine species,” wealth, life). This phenomenon is summarized by the constructal law: the occurrence and evolution of designs in nature, its time direction. Based on its record, the constructal law accounts for the design phenomenon and also for all the phenomena that have been described individually (ad-hoc) with end-design (destiny) statements of “optimality” (min, max). Most notably, the constructal law accounts for contradictory end-design statements such as minimum entropy production and maximum entropy production, and minimum flow resistance and maximum flow resistance.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Bejan, A., 1997, AdvancedEngineering Thermodynamics, 2nd ed., Wiley, New York.
Bejan, A., 1982, Entropy Generation Through Heat and Fluid Flow, Wiley, New York.
Bejan, A., 1996, Entropy Generation Minimization, CRC Press, Boca Raton, FL.
Bejan, A., 1997, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, 40(4), pp. 799–816. [CrossRef]
Bejan, A., 1996, “Street Network Theory of Organization in Nature,” J. Adv. Transp., 30(2), pp. 85–107. [CrossRef]
Reis, A. H., 2006, “Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and Structure,” ASME Appl. Mech. Rev., 59(5), pp. 269–282. [CrossRef]
Bejan, A., and Lorente, S., 2011, “The Constructal Law and the Evolution of Design in Nature,” Phys. Life Rev., 8(3), pp. 209–240. [CrossRef] [PubMed]
Chen, L., 2012, “Progress in the Study on Constructal Theory and Its Applications,” Sci. China, Tech. Sci., 55(3), pp. 802–820. [CrossRef]
Bejan, A., and Lorente, S., 2013, “The Constructal Law of Design and Evolution: Physics, Biology, Technology, and Society,” J. Appl. Phys., 113, p. 151301. [CrossRef]
Kremer-Marietti, A., and Dhombres, J., 2006, L’Épistemologie, Ellipses, Paris.
Bejan, A., and Merkx, G. W., 2007, Constructal Theory of Social Dynamics, Springer, New York.
Kalason, P., 2007, Le Grimoire des Rois: Théorie Constructale du Changement, L'Harmattan, Paris.
Kalason, P., 2007, Épistémologie Constructale du Lien Cultuel, L'Harmattan, Paris.
Bejan, A., and Lorente, S., 2008, Design With Constructal Theory, Wiley, New York.
Queiros-Conde, D., and Feidt, M., 2009, Constructal Theory and Multi-Scale Geometries: Theory and Applications in Energetics, Chemical Engineering and Materials, Les Presses de L'ENSTA, Paris.
Rocha, L., 2009, Convection in Channels and Porous Media. Analysis, Optimization, and Constructal Design, VDM Verlag, Saarbrücken, Germany.
Bejan, A., Lorente, S., Miguel, A. F., and Reis, A. H., 2009, Constructal Human Dynamics, Security and Sustainability, IOS Press, Amsterdam.
Lorenzini, G., Moretti, S., and Conti, A., 2011, Fin Shape Optimization Using Bejan's Constructal Theory, Morgan & Claypool Publishers, San Francisco.
Bachta, A., Dhombres, J., and Kremer-Marietti, A., 2008, Trois Ètudes sur la Loi Constructale d'Adrian Bejan, L'Harmattan, Paris.
Bejan, A., and Zane, J. P., 2012, Design in Nature. How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, Doubleday, New York.
Acuña, N., 2012, Mindshare. Igniting Creativity and Innovation Through Design Intelligence, Motion, Henderson, NV.
Rocha, L. A. O., Lorente, S., and Bejan, A., 2012, Constructal Law and the Unifying Principle of Design, Springer, New York. [CrossRef]
Bejan, A., 2012, “Why the Bigger Live Longer and Travel Farther: Animals, Vehicles, Rivers and the Wind,” Nature Scientific Reports, p. 594, Report No. 2.
Bejan, A., 2000, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, UK.
Bejan, A., and Marden, J. H., 2006, “Unifying Constructal Theory for Scale Effects in Running, Swimming and Flying,” J. Exp. Biol., 209, pp. 238–248. [CrossRef] [PubMed]
Charles, J. D., and Bejan, A., 2009, “The Evolution of Speed, Size and Shape in Modern Athletics,” J. Exp. Biol., 212, pp. 2419–2425. [CrossRef] [PubMed]
Bejan, A., 2010, “The Constructal-Law Origin of the Wheel, Size, and Skeleton in Animal Design,” Am. J. Phys., 78, pp. 692–699. [CrossRef]
Bejan, A., 2006, Advanced Engineering Thermodynamics, 3rd ed., Wiley, New York.
Bejan, A., and Lorente, S., 2001, “Thermodynamic Optimization of Flow Geometry in Mechanical and Civil Engineering,” J. Non-Equilib. Thermodyn., 26(4), pp. 305–354. [CrossRef]
Lui, C. H., Fong, N. K., Lorente, S., Bejan, A., and Chow, W. K., 2012, “Constructal Design for Pedestrian Movement in Living Spaces: Evacuation Configurations,” J. Appl. Phys., 111, p. 054903. [CrossRef]
Lui, C. H., Fong, N. K., Lorente, S., Bejan, A., and Chow, W. K., 2013, “Constructal Design of Pedestrian Evacuation From an Area,” J. Appl. Phys., 113, p. 034904. [CrossRef]
Lorente, S., and Bejan, A., 2010, “Few Large and Many Small: Hierarchy in Movement on Earth,” Int. J. Des. Nat. Ecodyn., 5(3), pp. 254–267. [CrossRef]
Bejan, A., 2009, “The Golden Ratio Predicted: Vision, Cognition and Locomotion as a Single Design in Nature,” Int. J. Des. Nat. Ecodyn., 4(2), pp. 97–104. [CrossRef]
Bejan, A., and Lorente, S., 2011, “The Constructal Law Origin of the Logistics S Curve,” J. Appl. Phys., 110, p. 024901. [CrossRef]
Bejan, A., and Lorente, S., 2012, “The Physics of Spreading Ideas,” Int. J. Heat Mass Transfer, 555(4), pp. 802–807. [CrossRef]
Cetkin, E., Lorente, S., and Bejan, A., 2012, “The Steepest S Curve of Spreading and Collecting: Discovering the Invading Tree, Not Assuming It,” J. Appl. Phys., 111, p. 114903. [CrossRef]
Bejan, A., Lorente, S., and Lee, J., 2008, “Unifying Constructal Theory of Tree Roots, Canopies and Forests,” J. Theor. Biol., 254(3), pp. 529–540. [CrossRef] [PubMed]
Lorente, S., Lee, J., and Bejan, A., 2010, “The “Flow of Stresses” Concept: The Analogy Between Mechanical Strength and Heat Convection,” Int. J Heat Mass Transfer, 53(15–16), pp. 2963–2968. [CrossRef]
Reis, A. H., and Bejan, A., 2006, “Constructal Theory of Global Circulation and Climate,” Int. J. Heat Mass Transfer, 49(11–12), pp. 1857–1875. [CrossRef]
Bejan, A., 2013, “Technology Evolution, From the Constructal Law,” Advances in Heat Transfer, Vol. 45, E. M.Sparrow, Y. I.Cho, J. P.Abraham, and J. M.Gorman, eds., Academic Press, Burlington, VT, Chap. 3. [CrossRef]
Bejan, A., Lorente, S., Yilbas, B. S., and Sahin, A. S., 2011, “The Effect of Size on Efficiency: Power Plants and Vascular Designs,” Int. J. Heat Mass Transfer, 54(7–8), pp. 1475–1481. [CrossRef]
Bejan, A., 1984, Convection Heat Transfer, Wiley, New York.
Bejan, A., 2013, Convection Heat Transfer, 4th ed., Wiley, New York. [CrossRef]
Ledezma, G. A., Bejan, A., and Errera, M., 1997, “Constructal Tree Networks for Heat Transfer,” J. Appl. Phys., 82, pp. 89–100. [CrossRef]
Errera, M. R., and Bejan, A., 1998, “Deterministic Tree Networks for River Drainage Basins,” Fractals, 6, pp. 245–261. [CrossRef]
Kobayashi, H., Lorente, S., Anderson, R., and Bejan, A., 2013, “Trees and Serpentines in a Conducting Body,” Int. J. Heat Mass Transfer, 56(1–2), pp. 488–494. [CrossRef]
Guo, Z.-Y., Zhu, H.-Y., and Liang, S.-G., 2007, “Entransy—A Physical Quantity Describing Heat Transfer Ability,” Int. J. Heat Mass Transfer, 50(13–14), pp. 2545–2556. [CrossRef]
Grazzini, G., Borchiellini, R., and Lucia, U., 2013, “Entropy Versus Entransy,” J. Non-Equilib. Thermodyn., 38, pp. 259–271. [CrossRef]
Herwig, H., 2014, “Do We Really Need “entransy”? A Critical Assessment of a New Quantity in Heat Transfer Analysis,” ASME J. Heat Transfer, 136(4), p. 045501. [CrossRef]
Bejan, A., 2014, “Entransy, and Its Lack of Content in Physics,” ASME J. Heat Transfer, 136(5), p. 055501. [CrossRef]
Awad, M. M., 2014, “Entransy Is Now Clear,” ASME J. Heat Transfer, 136(5), p. 095502. [CrossRef]
Manjunath, K., and Kaushik, S. C., 2014, “Second Law Thermodynamic Study of Heat Exchangers: A Review,” Renew. Sustain. Energy Rev., 40, pp. 348–374. [CrossRef]
Olaveira, S. R., and Milanez, L. F., 2014, “Equivalence Between the Application of Entransy and Entropy Generation,” Int. J. Heat Mass Transfer, 79, pp. 518–525. [CrossRef]
Sekulic, D. P., Scuibba, E., and Moran, M. J., 2015, “Entransy: A Misleading Concept for the Analysis and Optimization of Thermal Systems,” Energy, 80, pp. 251–253. [CrossRef]
Bejan, A., and Lorente, S., 2004, “The Constructal Law and the Thermodynamics of Flow Systems With Configuration,” Int. J. Heat Mass Transfer, 47(14–16), pp. 3203–3214. [CrossRef]
Bejan, A., 2009, “Science and Technology as Evolving Flow Architectures,” Int. J. Energy Res., 33(2), pp. 112–125. [CrossRef]


Grahic Jump Location
Fig. 1

The evolution and spreading of thermodynamics during the past two centuries (after Ref. 2, Diagram 1, p. 8)

Grahic Jump Location
Fig. 2

The larger are more efficient, faster, live longer and travel farther lifetime: vehicles, animals, rivers, and the winds

Grahic Jump Location
Fig. 4

Economic activity means movement, which comes from the burning of fuel for human needs. This is demonstrated by the annual GDP of countries all over the globe, which is proportional to the fuel burned in those countries (data from International Energy Agency. Key World Energy Statistics, 2006). In time, all the countries are moving up and to the right, on the bisector.

Grahic Jump Location
Fig. 3

Everything that moves on earth is driven by fuel and food. It moves because an engine dissipates its work output into a brake.

Grahic Jump Location
Fig. 5

Large organs belong on large vehicles and animals. Every flow component has a characteristic size, which emerges from two conflicting trends. The useful energy dissipated because of the imperfection of the component decreases as the component size increases. The useful energy spent by the greater system (vehicle, animal) increases with the component size. The sum of the two penalties is minimum when the component size is finite, at the intersection between the two penalties. In time, the component evolves toward smaller sizes, because it improves and its penalty (the descending curve) slides downward.

Grahic Jump Location
Fig. 6

Predicted evolution of heat transfer density toward higher values, showing two phenomena: evolution toward smaller sizes (miniaturization), and stepwise changes in cooling technology

Grahic Jump Location
Fig. 7

Darcy flow on a square domain with low permeability (K) and high permeability (Kp). In time, K grains are searched and replaced by Kp grains such that the overall area-to-point flow access is increased faster ([45], available also in Refs. [24,28]).

Grahic Jump Location
Fig. 8

Constructal invasion of a conducting tree into a conducting body [46]



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In