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.

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Fig. 1

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

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Fig. 2

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

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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.

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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.

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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.

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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

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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]).

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Fig. 8

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




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