Science and technology as evolving ﬂow architectures · 2010-06-07 · nonequilibrium systems (constructal theory). Geophysical and biological ﬂow systems evolve in one direction,

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2009; 33:112–125Published online 9 July 2008 in Wiley InterScience(www.interscience.wiley.com). DOI: 10.1002/er.1427

Science and technology as evolving flow architectures

Adrian Bejan�,y

Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, U.S.A.

SUMMARY

This essay traces the evolution of thermodynamics from its origins to ad hoc applications of thermodynamicoptimization (entropy generation minimization) and the principle-based generation of flow configuration innonequilibrium systems (constructal theory). Geophysical and biological flow systems evolve in one direction, towardconfigurations that flow more easily. This evolutionary process is like an animated movie in which existing flow designsare replaced by designs that offer greater flow access. This paradigm fuels a new attitude toward globalization andsustainability: the natural way to bring the less advanced areas into the flow of things is to allow the vascular systems ofgoods, people and ideas to bathe the whole earth more and more freely. Constructal theory shows that freedom is goodfor design, and that the future belongs to vascularized architectures with increased svelteness and optimal distributionof imperfection. Copyright r 2008 John Wiley & Sons, Ltd.

KEY WORDS: constructal; evolution; science; technology; history; sustainability; globalization; civilization; energyfuture

1. A NEW ATTITUDE TOWARDGLOBALIZATION AND SUSTAINABILITY

‘People in advanced countries consume too muchenergy’. We hear such statements daily. In thedebate on how to build a better and ‘moresustainable’ energy future for the developed anddeveloping world, the implications are intended tobe obvious. One is that advanced countries byconsuming less energy, will and should leave morefuel to the less advanced countries to burn. Anotheris that burning fuel, in any case, is inherently bad,like smoking or gluttony. Fuel abstinence or at thevery least a ‘low calorie’ diet is the solution.

Is the world really foolhardy to have arrived atthis level of civilization by consuming ‘too much’energy? By taking a look at basic physics and thehistory of societal organization and globaldevelopment, we can examine this questionwithout bias.

‘Energy production’ means the shaft workproduced by a heat engine or a power plant.Throughout most of our history, work wasproduced by people and animals, with minormedieval contributions from windmills and waterwheels. The big change in the evolution of humanswas the development of heat engines in the 1700s,followed by the rapid industrialization of the

*Correspondence to: Adrian Bejan, Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC27708-0300, U.S.A.yE-mail: [email protected]

Received 15 August 2007

Accepted 26 September 2007Copyright r 2008 John Wiley & Sons, Ltd.

western world in the 1800s and theelectrification of the globe in the 1900s. Thisglobal flow of technology continues, and it definesus today.

In its simplest description, the workthat a power plant delivers per unit time (thepower) is proportional to the rate of heating thatthe plant receives from the burning fuel.The delivered power output can be mechanical,as through a turning shaft, or electrical throughcables. The delivered power is proportionalto the rate at which fuel is consumed timesthe efficiency of the power plant. For power, weneed fuel use and efficiency. Both have beenincreasing in time (Figure 1). This evolutioncontinues.

This is completely analogous to what occurson a much greater and diverse scale in animaldesign. The mechanical power delivered bymuscles is proportional to the rate of foodconsumption (the metabolic rate). This analogycasts humans in a different light on the stage ofevolution: we are ‘human and machinespecies’, evolving in visible terms (right now)because our minds and engineered extensions(machines, technologies) are evolving. We are alot bigger, a lot more complicated, and alot more powerful than the naked bodies shownin anatomy books.

Why do humans need power? For thesame reason that animals need muscle power: tomove mass on the earth’s surface. Recent

theoretical work on the origins of animallocomotion [4,5] has shown that for all types oflocomotion (running, flying, swimming), animalforce is roughly equal to the body weight, and theminimum work that the body performs isproportional to the body weight times thedistance traveled. The consumed food or fuel is‘converted’ into mass moved.

Our cars, construction sites, and everything elsewe do (our legacy) are the product of this. All theanimals and all of us consume food and fuel andthe result is the shaping and reshaping (the mixing)of the earth’s surface.

Now we can address the question posed at thestart. People in advanced countries burn more fuelper capita than people in less advanced countries.Why? Because the flow of mass on theearth’s surface is distributed nonuniformly.‘Advanced’ means just that, more mass movedover longer distances, along certain channels. Theflow map has history and memory. In time, newchannels appear and the old ones become thicker(Figures 2 and 3).

To argue for a more uniform distribution offuel consumption is to recommend a more uniformdistribution of mass movement (goods, people,information) on the globe. This soundsprogressive, but even a global government wouldbe hard pressed to achieve it.

Our movement and animal locomotion is massthat flows on the earth with the same tendency asthat of water in a river basin. The tendency is togenerate in time configurations that make it easierto flow. This natural evolutionary phenomenon iswhat the constructal law covers. The configuringof the flow structure means the optimal distributionof imperfection: flow resistances, obstacles,bottlenecks, and choke points, all in the rightamounts and in the right places on the map. Thewinning blueprint—the flow pattern that survivesin time—is the communal allocation of flowresistances (channels) to areas without channels.

The striking feature of winning designs innature is their nonuniform distribution of channelsizes and flow rates. The river basin is a tree, a flowdesign with very few big channels and very manysmall channels. The urge of the smallest is thesame as the urge of the biggest: the urge is to flow

Figure 1. Time evolution of the second law efficiency ofpower plants, and the growth of power generation worldwide ([1]; efficiency data from [2]; power generation data

from [3]).

SCIENCE AND TECHNOLOGY AS EVOLVING FLOW ARCHITECTURES 113

Copyright r 2008 John Wiley & Sons, Ltd. Int. J. Energy Res. 2009; 33:112–125

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more easily. This is why all sizes come togetherinto a tree-shaped vascularized tissue. This is whyEuropean integration and globalization are naturaloccurrences.

How should we proceed? Clearly, not byfighting nature. The nonuniform distribution ofpower generation and use will continue to happen.Needed is a new attitude toward globalization and

Figure 2. Where aircraft flew in 1992 and the persistent contrail coverage (in % area cover) for the 1992 aviation fleet(from [6]). See also [7].

Figure 3. Where aircraft will fly in 2050 and the persistent contrail coverage (in % area cover) based on meteorologicalanalysis data and on fuel emission database for 2050 (from [6]). See also [7].

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sustainability. For this, the river basin and therail and highway networks are excellentmetaphors.

The natural way to bring the less advancedareas into the flow of things is to allow the riverbasins of goods, people, and information to bathethe whole earth more and more freely. Constructaltheory has shown that freedom is good for design.These freely changing flow configurations are whatwill attach the overlooked areas to the bigbranches. This natural phenomenon should berecognized, so that policy makers may make theright decisions faster.

2. THE EVOLUTION OF TECHNOLOGY

Times change, generations replace generations, butthe principles remain. Contrivances, gadgets, andfads are just the opposite. They parade in front ofour eyes, but their impact on the ‘thin book’ offundamentals is nil.

I was reminded of this last semester because of awonderful coincidence called ‘serendipity’—theroad to important but unintended discoverieswhen the traveler has his eyes open. For science,serendipity is the kitchen, the storeroom, and thecook. I was at The National Conservatory of Artsand Professions (CNAM), in Paris. CNAM has a300-year old edifice with towers, inner court,statues, clocks, and history chiseled in stone. Inthe front court, there is the statue of Denis Papinand the first piston and cylinder machine thatexpanded steam to produce work (1690). This wasbefore the engine builders of Britain and 80 yearsbefore James Watt.

Around the buildings, and around the ceilingsof the oldest and most decorated classrooms, arethe names of those who left their mark. One is SadiCarnot. Without it there would be no thermo-dynamics, power engineering, and standard ofliving as we know them today. Sadi Carnot cameto CNAM to contemplate, to think in quiet aboutthe army of contrivances that was invadingFrance: the steam engines. The industrialrevolution was on the march. Britain hadindustrialized itself in the 1700s. A century later,it was the turn of the continent to do the same.

Why were the steam engines invading? Becausetheir effect on people’s lives was good. It wasdramatic. Engines were empowering people. Theywere liberating slaves, serfs, and animals. Theywere facilitating the movement of humanity allover the globe.

The principle that Sadi Carnot saw in thatparade of machines is that every thing flows oneway, from high to low. This is the one-waydirection—the time arrow—of irreversibility.Water flows through a pipe from high pressureto low pressure. Heat flows from high temperatureto low temperature. Water falls from high to lowthrough a water wheel. This principle is knowntoday as the second law of thermodynamics,irreversibility, dissipation, inefficiency, one way,‘water under the bridge’, etc. Today, this isthermodynamics, the science of everything thatkicks and moves.

The new principle that the CNAM storyillustrates for us today is the principle ofevolution of design (e.g. Figure 1). Theflow configurations (the engine designs) compete,and the designs that flow ‘more easily’ are the onesthat survive. The human and machinespecies evolves, and its evolution shows ‘live’how all other flow systems have evolved,from geophysics to biology and socialorganization on the globe. In this constructaldirection of time the flow configurations becomemore efficient, more compact (svelte), and coverlarger spaces [8–10]. This principle is theconstructal law:

For a finite-size flow system to persist in time(to survive) its configuration must evolvesuch that it provides greater and greateraccess to the currents that flow through it[11,12].

Both principles are in action, the second lawand the constructal law. Their footprints persist,like the river beds and the beaten tracks. The riverand the caravan that do not follow their beds andbeaten tracks do not get far. The engineer whodoes not recognize the two principles lives in theprethermodynamics era (in mechanics) and doesnot get far either.



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3. FROM ENTROPY GENERATIONMINIMIZATION TO CONSTRUCTAL

THEORY

The improvements summarized in Figure 1 hap-pened because 10 generations of designers andbuilders have done their best to minimize ‘losses’.Sadi Carnot wrote about the importance ofavoiding friction and heat transfer across finitetemperature differences, however, common sense(the urge to live better) lead the human andmachine species in the direction of Figure 1anyway.

Carnot identified the principle that onegeneration later became the second law, and inthis way he kick-started thermodynamics as ascience distinct from mechanics. The history ofthermodynamics is not the subject of this section.The subject is the observation that after beingeducated in the use of the first law and the secondlaw, engineers have always sought to improve theglobal performance of the power plant orrefrigeration plant. They used thermodynamics,and they accomplished great things with it. Yet,there was nothing in the laws of thermodynamicsto indicate that the global performance of flowsystems must increase in time.

This observation surprises many and with goodreason. The observation has been around us,everywhere and forever. That design exists andimproves in time has been taken for granted. Thehardest things for us to question are the mostcommon and the most obvious.

We thermodynamicists have expanded thelanguage and techniques of our discipline inorder to make it easier for engineers to improvetheir machines. The losses that Carnot warnedagainst became ‘irreversibility’, ‘entropygeneration’ ð _SgenÞ and ‘exergy destruction’. Thatthese thermodynamics-sounding names represent‘losses’ was formalized in the Gouy–Stodolatheorem,

_Wrev � _W ¼ T0_Sgen ð1Þ

The name ‘theorem’ is correct, because Equation(1) is derived by combining the first law with thesecond law. To calculate the loss ð _Wrev � _W ; or_SgenÞ is to perform ‘second law analysis’, ‘exergy

analysis’, ‘entropy generation analysis’, etc. Theconfiguration of the thermodynamic system isassumed given. As shown in Figure 4 at thevolumetric level, and in Figure 5 at themacroscopic level, this ‘combined-laws’ analysisindicates where losses occur and how large they are.

To minimize losses is a different concept. Thereis nothing in the laws of thermodynamicsto require that ð _Wrev � _WÞ or _Sgen must bedecreased by us, nature or anybody else. In spiteof this theoretical vacuum, our discipline marchedforward and developed methods and strategies forminimizing losses. It marched in time because thisis the direction of better science (Section 5).Science rushes forward even when the necessary‘new’ concepts, words, and laws are not available.To make real progress in these early stages,scientists misuse the existing language [14].

My way of identifying and minimizing losses isthe method of entropy generation minimization(EGM), which has its origins in my doctoral thesis

Figure 4. Volumetric s000gen distribution of entropy gen-eration rate in a laminar boundary layer flow on a planewall with heat transfer. The wall is at y5 0. Theboundary layer is sketched in the bottom plane [13].

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at MIT—in a series of papers that began with [15]and led to my first Wiley book [16]. Note here thatthe decision to minimize Sgen was arbitrary.Thermodynamics did not give me that right.

Constructal theory is a mental viewing that Ihad about 10 years ago. I saw that by optimizingglobally a flow system, I was minimizing thermaland fluid-flow resistances together. I was balancingthem so that their sum is minimum. I was notminimizing them individually, and I was certainlynot eliminating them. I was not aiming for theCarnot limit. The flow system was destined toremain imperfect. I was like an artist, attemptingto paint the least imperfect fresco possible.

In the mid-1990s I came to the realization thatall this effort meant that I was generating flowgeometry. I was discovering the drawing (thedesign), that is, the configuration for a flowsystem (nonequilibrium system, in thermo-dynamics) that did not have configuration. Thegeneration of configuration is a universally presentphenomenon, which did not have a universalunderlying principle in physics. The generation offlow configuration is the phenomenon responsiblefor the morphology and evolution of natural flow

systems (animate and inanimate) and engineeredsystems.

It became clear that one does not need the wordentropy to state the principle of evolution of theflow configuration in time. That principle is a newlaw of physics—the constructal law stated inSection 2. Configuration is the footprint—thefossil, the evidence of a tendency in time: flowsystems seek and find configurations that provideprogressively greater access to their currents.Existing flow configurations are replaced bybetter flowing configurations, smoothly orstepwise, in animal design, river basin design,automobile design, and geopolitical design.

The time arrow of the constructal law is not tobe confused with the time arrow of the second law.The second law is the law of entropy generation,whereas the constructal law is the law ofconfiguration generation. The concept defined bythe second law is entropy. The concept defined bythe constructal law is evolution of configuration(design, pattern, layout, drawing).

4. THE ANIMATED MOVIE OFCONFIGURATION GENERATION

To see why the constructal law is a law of physics,ask why the constructal law is different than (i.e.distinct from or complementary to) the other lawsof thermodynamics, think of an isolated thermo-dynamic system that is initially in a state ofinternal nonuniformity (e.g. regions of higher andlower pressures or temperature, separated byinternal partitions that suddenly break). The firstand second laws account for numerous observa-tions that describe a tendency in time, a timearrow: if enough time passes, the isolated systemsettles into a state of equilibrium (no internalflows, maximum entropy at constant energy, etc.).The first and second laws speak of a black box.They say nothing about the configurations (thedrawings) of the things that flow. Classicalthermodynamics was not concerned with theconfigurations of nonequilibrium (flow) systems.

This tendency, this time sequence of drawingsthat the flow system exhibits as it evolves, is thephenomenon covered by the constructal law: not

Figure 5. Exergy wheel diagram for a power plant withsimple Rankine cycle [12].



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the drawings per se, but the time direction in whichthey morph if given freedom. No drawing innature is ‘predetermined’ or ‘destined’ to be or tobecome a particular image. The actual evolutionor lack of evolution (rigidity) of the drawingdepends on many factors, which are mostlyrandom (Figure 6). One cannot count on havingthe freedom to morph in peace (undisturbed).

Once again, a comparison with the second law isrevealing. No isolated system in nature ispredetermined or destined to end up in a state ofuniform intensive properties so that all future flowsare ruled out. One cannot count on the removal ofall the internal constraints. One can count even lesson anything being left in peace, in isolation.

The second law does proclaim the existence of a‘final’ state: the concept of equilibrium in an

isolated system, at sufficiently long times.Similarly, the constructal law proclaims theexistence of a final nonequilibrium (flow) state:the concept of the equilibrium flow architecture[8,9], when all possibilities of increasing morphingfreedom and flow performance have beenexhausted.

Constructal theory is now a fast-growing fieldwith contributions from many sources, which havebeen reviewed on several occasions [7,10,19–25].This new body of literature is not reviewed here. Inthis section I sketch a balance between the originaldisclosure of the theory and the newerdevelopments. Striking a balance is a welcomeopportunity to reflect, because during the 10 yearsthat passed, we questioned the earliest work andimproved the results, drawings, and language. The

Figure 6. Top: Development of an artificial river basin over a 15.2� 9.1m2 rainfall erosion area [17]; Bottom:Simulations based on an erosion model with uniform erosion resistance, and random erosion resistance [18].

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bottom line, however, is that constructal theory isthe 1996 law cited in Section 2 of this article. Theconstructal law statement is general; it does notuse words such as tree, complex versus simple, ornatural versus engineered.

In retrospect, I find that it is important forreaders not to confuse the constructal law withpredictive applications of the idea in variousdomains. How to deduce a class of flowconfigurations by invoking the constructal law isan entirely different (separate, subsequent) thought,which in my teaching effort is called the researcher’sfreedom to choose the problem and solutionmethod [26]. There are several classes of flowconfigurations, and each class can be derived fromthe constructal law in several ways: analytically(pencil and paper) or numerically, approximately ormore accurately, blindly (random search) or usingintelligence (strategy, shortcuts), and so on. Classesthat our group treated in detail, and by severalmethods, are the cross-sectional shapes of ducts, thecross-sectional shapes of rivers, internal spacings,and tree-shaped architectures.

For example, to discover ‘trees’ our grouptreated them not as models (many have publishedand continue to publish models) but as fundamentalaccess-maximization problems: volume to point,area to point, line to point, and the respectivereverse flow directions. Important is the elementarygeometry notion that the ‘volume’, the ‘area’, andthe ‘line’ represent infinities of point. Ourtheoretical discovery of trees stems from thedecision to connect one point (source, or sink)with an infinity of points (volume, area, line). It isthe reality of the continuum (the infinity of points)that is routinely discarded by modelers whoapproximate the space as a finite number ofdiscrete points and then cover the space withdrawings made out of ‘sticks’, which (of course)cover the space incompletely (and from this fractalgeometry). Recognition of the continuum requires astudy of the interstitial spaces between the treelinks. The interstices can only be bathed by high-resistivity diffusion (an invisible, disorganized flow),whereas the tree links serve as conduits for low-resistivity organized flow (visible streams, ducts).

The two modes of flowing with thermodynamicimperfection, the interstices and the links, must be

balanced so that together they contributeminimum imperfection to the global flowarchitecture. The flow architecture is thegraphical expression of the balance between linksand their interstices. The deduced architecture(tree, duct shape, spacing, etc) is the optimaldistribution of imperfection. Those who modelnatural tree-shaped flows and do not optimizethe layout of every black line on its allocated whitepatch, miss the drawing. The white is as importantas the black.

For tree-shaped flow architectures we usedthree approaches. In 1996, I started with ananalytical pencil and paper method based onseveral simplifying assumptions: rectangularelements, 901 angles between stem andtributaries, a construction sequence in whichsmaller optimized constructs are retained,constant-thickness branches, and so on[11,27,28], Figure 7a. Months later, we publishedthe same problem [29] but we did it numerically byabandoning most of the simplifying assumptions(e.g. the construction sequence) used in the firstpapers, e.g. Figure 7b. In 1998 we revisited theproblem numerically [18] in an area-point flowdomain with random low-resistivity blocksembedded in a high-resistivity background byusing the language of Darcy flow (permeabilityinstead of conductivity and resistivity), Figure 6.

In summary, the three methods tried during thefirst 2 years of constructal theory taught us thattrees with ‘better performance’, asymmetry, and‘more natural looks’ are born as we progressin time, that is, as we endow the flow structurewith more freedom to morph, Figures 8 and 9.

Figure 7. Elemental volume with high-conductivitychannel (black) on a low-conductivity background: (a)uniform thickness and (b) optimal thickness for volume-

to-point flow with minimal global resistance [29].



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Freedom is good for the performance and survivalof a flow structure, be that natural or engineered,animate or inanimate, human or animal society,and so on. Design improvement without freedomto change the structure is nonsense. Rigid flowstructures are brittle: dictatorial schemes andstraight river channels are short lived.

The main idea that remains is the constructallaw. Here is the ‘click’ that I felt as I ended mysecond paper on constructal trees ([11]; pp.813–815; published on 1 November, 1996because in 1996 the International Journal of Heatand Mass Transfer was experiencing an overflow ofpapers and was assigning 1997 numbers to issuesthat it was publishing in 1996):

The commonality of these phenomena is muchtoo obvious to be overlooked. It was noted inthe past and most recently (empirically) infractal geometry, where it was simulated basedon repeated fracturing that had to be assumedand truncated. The origin of such algorithmswas left to the explanation that the brokenpieces (or building blocks, from the point ofview of this paper) are the fruits of a process ofself-optimization and self-organization.The present paper places a purely deterministicapproach behind the word ‘self’: the searchfor the easiest path (least resistance) whenglobal constraints (current, flow rate, size) areimposed.

If we limit the discussion to examples of livingflow systems (lungs, circulatory systems nervoussystems, trees, roots, leaves), it is quite acceptableto end with the conclusion that such phenomenaare common because they are the end result of along running process of ‘natural selection’. A lothas been written about natural selection and theimpact that efficiency has on survival. In fact, torefer to living systems as complex power plantshas become routine. The tendency of livingsystems to become optimized in every buildingbloc and to develop optimal associations of suchbuilding blocks has not been explained: it hasbeen abandoned to the notion that it is imprintedin the genetic code of the organism.If this is so, then what genetic code might beresponsible for the development of equivalentstructures in such nonliving systems as riversand lightning? What genetic code is responsiblefor man-made networks (such as the trees inthis paper)? Certainly not mine, becausealthough highly educated, neither of my parentsknew heat transfer (by the way, thermody-namics was not needed in this paper). Indeed,whose genetic code is responsible for thesocietal trees that connect us, for all theelectronic circuits, telephone lines, air lines,assembly lines, alleys, streets highways andelevator shafts in multistory buildings?There is no difference between the living andthe nonliving when it comes to the opportunityto find a more direct route subject to globalconstraints, for example, the opportunity ofgetting from here to there in an easier (faster)manner. If living systems can be viewed as

Figure 8. Performance versus freedom domain of lami-nar-duct flows that connect the center of a disc with 192

equidistant points on the perimeter [30].

Figure 9. Emergence of asymmetry in the constructallayout of trees consisting of triangular and hexagonal

area elements [31].

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engines in competition for better thermody-namic performance, then physical systems toocan be viewed as living entities (animals!) incompetition for survival. This analogy is purelyempirical: we have an immense body of case-by-case observations indicating that flow config-urations (living and nonliving) evolve andpersist in time, while others do not. Now weknow the particular feature (maximum flowaccess, minimum global flow) that sets eachsurviving design apart, but we have no theore-tical basis on which to expect that the designthat persists in time is the one that has thisparticular feature. This body of empiricalevidence forms the basis for a new law ofnature that can be summarized as (the con-structal law, cited at the end of Section 2). This‘fourth law’ brings life and time explicitly intothermodynamics and creates a bridge betweenphysics and biology.

To the story of constructal trees I must add thatI first worked on deducing trees for fluid flow (e.g.[28]); but when I saw how old, voluminous, andestablished the empirical (modeling) literature ofthis field is (from physiology to river morphology),I remembered hard lessons learned early in mycareer. It is risky for an amateur to submitsomething entirely new to an established group[‘risk’ means rejection and worse: loss of credit forthe idea, because (in accordance with theconstructal law) good ideas travel fast!]. Thesurer approach was to translate the idea into thesafer language of minimum travel time [27] andminimal thermal-diffusion global resistance [11] infreely morphing area-point flows, and to submitthe idea to peers who do not have an ax to grind. Itworked, despite the 1-year delay that this doubletranslation caused in the dissemination of theconstructal law.

5. SCIENCE AS CONSTRUCTAL FLOWARCHITECTURE

The evolution of thermodynamics from Carnot toEGM and now constructal theory is an illustrationof a more general constructal phenomenon of

evolution of flow configuration in time. Science,ideas, news, and education flow and cover theglobe like the streams of river basins. They cover amultidimensional territory better known as his-tory, geography, and civilization. The flow archi-tecture of science continues to change, to improve,and to grow.

Physics is our knowledge of how nature works.Physics (or nature) is everything, includingengineering: the biology and medicine of human1

machine species. Our knowledge is condensed insimple statements (thoughts, connections), whichevolve in time by being replaced by simplerstatements. We ‘know more’ because of thisevolution in time, not because brains becomebigger and neurons smaller and more numerous.Our finite-size brains keep up with the steady inflowof new information through a process ofsimplification by replacement: in time, andstepwise, bulky catalogs of empirical information(e.g. measurements, data, complex empirical models)are replaced by much simpler summarizingstatements (e.g. concepts, formulas, constitutiverelations, principles, laws). A hierarchy ofstatements emerges along the way: it emergesnaturally because it is better (cf. the constructal law).

The simplest and most universal are the laws.The bulky and the laborious are being replaced bythe compact and the fast. In time, scienceoptimizes and organizes itself in the same waythat a river basin evolves: toward configurations(links, connections) that provide faster access oreasier flowing. The bulky measurements ofpressure drop versus flow rate through roundpipes and saturated porous media were renderedunnecessary by the formulas of Poiseuille andDarcy. The measurements of how things fall(faster and faster and always from high to low)were rendered unnecessary by Galilei’s principleand the second law of thermodynamics.

The hierarchy (specialization) that scienceexhibited at every stage in the history of itsdevelopment is an expression of its never-endingstruggle to optimize and redesign itself. Hierarchymeans that measurements, ad hoc assumptions,and empirical models come in huge numbers, a‘continuum’ above which the compact statements(the laws) rise as needle-shaped peaks. Both are



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needed, the numerous and the singular. One classof flows (information links) sustains the other. Themany and unrelated heat engine builders of Britainfed the imagination of one Sadi Carnot. In turn,Sadi Carnot’s mental viewing (thermodynamicstoday) feeds the minds of contemporary and futurebuilders of all sorts of machines throughout theworld.

Civilization with all its constructs (science,religion, language, writing, etc.) is this never-ending physics of generation of newconfigurations, from the flow of mass, energy,and knowledge to the world migration of thespecial persons to whom ideas occur (the creative).Good ideas travel. Better flowing configurationsreplace existing configurations (the constructallaw). Empirical facts (observations) are extremelynumerous, like the hill slopes of a river basin. Thelaws are the extremely few big rivers, the Seine andthe Danube.

6. THERMODYNAMICS OF FLOW SYSTEMSWITH CONFIGURATION

Thermodynamics has reached an impasse similarto the development of the heat engine twocenturies ago [7,32]. The need is great, the valueof research and education is obvious, and valuableimprovements are occurring every day. What ismissing is a scientific base, a fundamental frame-work that ties together what is being achieved andguides us into the future. We all know theheadlines: chaos versus order, Darwinism versusdesign in nature, globalization, diminishing energyresources, environmental impact, and sustainabledevelopment.

An impasse is a historic opportunity for science.It is the moment to spring into a new direction andto march loudly against the crowd. Fuels are notgiven, environments are not infinite, and energytransformations do not occur in isolation. Flowsystems are not black boxes with inflows andoutflows and no structure internally. The realworld (nature, physics) has structure, organizationand pattern. Until now, thermodynamics was notconcerned with the architecture (the drawings) ofthe systems that inhabit its black boxes.

The route to historic impact is paved withfundamentals. In the thermodynamics thatemerges, the readjustments of fossil andrenewable fuel streams (i.e. new equilibria of howto flow) are being predicted and optimized basedon principles. In this new science, the shrinking ofthe environment (i.e. new equilibria between ourflows and the external ones) is predicted andoptimized based on principles. Thermodynamicsystems have new properties such as configuration,objective, svelteness, and freedom to morph.The new science is by its very naturetransdisciplinary—a science of systems of systems.

No flow system is an island. No river existswithout its wet plain. No city thrives without itsfarmland and open spaces. Everything that flowedand lived to this day to ‘survive’ is in an optimalbalance with the flows that surround it and sustainit. The air flow to the alveolus is optimallymatched to the blood that permeates through thevascularized tissue and vice versa.

Yes, vascularized is a good way to describe thesystems that the new science of thermodynamicswill cover. The tissues of energy flows, like thefabric of society and all the tissues of biology, areoptimized architectures. Not just ‘any’architectures, as in the black boxes of classicalthermodynamics, but the equilibrium, or the near-equilibrium flow architectures. The climbing tothis high podium of performance is thetransdisciplinary effort—the balance betweenseemingly unrelated flows, territories, anddisciplines. This balancing act—the optimaldistribution of imperfection—generates the verydesign of the process, power plant, city,geography, and economics.

The need for considering the whole—themacroscopic system—is great and universal. Nomatter how successful we are in discovering andunderstanding small-scale phenomena andprocesses, we are forced to face the challenge toassemble the invisible elements into palpabledevices. The invisible grains must be kept alivewith flows, which connect them, and serve them.The challenge is to construct, that is, to connect,and optimize while assembling.

This challenge is becoming increasinglydifficult. While the smallest scales are becoming

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smaller, the number of components and thecomplexity of the useful device (alwaysmacroscopic) become greater. A good example isthe rush to nanotechnology. Technology meansmore than the new physical phenomena that mayappear on the frontiers of progressively smallerscales. A technology is truly new when it is madeuseful in the form of macroscopic devices thatimprove our lives. Usefulness means that we mustdiscover principles of constructing, connecting,and packing multiscale flow systems intomacroscopic spaces.

The new gadgets are like the engines in theinvasion contemplated by Carnot (Section 2).Certain is that they will all be forgotten, unlessthere is a Sadi Carnot watching, to see a patternand immortalize it with a short page in the thinbook of principles. This happens only rarely andwhen it does it illustrates again the constructalprinciple of ‘one sustains the crowd’ (Section 5).

And so, I arrive at the essence of constructaltheory or the thermodynamics of nonequilibriumsystems with configuration—the union that itforges between physics, engineering science, andlife sciences. We see this union in Figure 10. Earth,with its solar heat input, heat rejection, and wheels

of atmospheric and oceanic circulation, is a heatengine without shaft: its maximized (but not ideal)mechanical power output cannot be delivered toan extraterrestrial system. Instead, the earthengine is destined to dissipate through air andwater friction and other irreversibilities (e.g. heatleaks) all the mechanical power that it produces. Itdoes so by ‘spinning in its brake’ the fastest that itcan (hence the winds and the ocean currents,which proceed along easiest routes). Because theflowing earth is a constructal heat engine, its flowconfiguration has evolved in such a way that it isthe least imperfect that it can be. It producesmaximum power, which it then dissipates atmaximum rate. A principle of maximumdissipation is now being invoked ad hoc ingeophysics: all such writings refer only to whatgoes on in the brake and are already covered bythe constructal law.

The heat engines of engineering and biology(power plants, animal motors) have shafts, rods,legs, and wings that deliver the mechanical powerto external entities that use the power (e.g. vehiclesand animal bodies needing propulsion). Becausethe engines of engineering and biology areconstructal, they morph in time toward flow

Figure 10. Every nonequilibrium (flow) component of the earth functions as an engine that drives a brake [33].The constructal law governs ‘how’ the system functions: by generating a flow architecture that distributes imper-fections through the flow space and endows it with configuration. The ‘engine’ part evolves in time toward generatingmaximum power (or minimum dissipation), and as a consequence, the ‘brake’ part exhibits maximum dissipation.Evolution means that each flow system assures its persistence in time by freely morphing into easier and easierflow structures under finiteness constraints. The arrows proceed from left to right because this is the generaldrawing for a flow (nonequilibrium) system, in steady or unsteady state. When equilibrium is reached, all the flows

cease, and the arrows disappear.



DOI: 10.1002/er

configurations that make them the least imperfectthat they can be. Therefore, they evolve towardproducing maximum mechanical power (underfiniteness constraints), which, for them, means atime evolution toward minimum dissipation(minimum entropy generation rate).

If we look outside an engineering or biologyengine, we see that all the mechanical power thatthe engine delivers is destroyed through frictionand other irreversibility mechanisms (e.g.transportation and manufacturing for man,animal locomotion, and body heat loss toambient). The engine and its immediateenvironment (the brake), as one thermodynamicsystem, are analogous to the whole earth (Figure10). After everything is said and done, the flowingearth (with all its engine1brake components,rivers, fish, turbulent eddies, etc.) accomplishesas much as any other flow architecture, animate,or inanimate: it mixes the earth’s crust mosteffectively—more effectively than in the absenceof constructal phenomena of generation of flowconfiguration.

Irrefutable evidence of this accomplishment ishow all the large eddies of biological matter havemorphed and spread over larger areas andaltitudes, in this sequence in time: fish in water,walking fish and other animals on land, flyinganimals in the atmosphere, flying man1machinespecies, and man1machine species in the outerspace. The balanced and intertwined flows thatgenerate our engineering, economics, and socialorganization are no different than the natural flowarchitectures of biology (animal design) andgeophysics (river basins, global circulation).

NOMENCLATURE

Symbols

A0 5 elemental area (m2)A3 5 third construct (m2)D 5 blade thickness (m)ex 5 specific flow exergy (J kg�1)_E 5 exergy rate (W)f 5 dimensionless flow resistanceL 5 disc radius (m)

_m 5mass flow rate (kg s�1)n0 5 number of ducts that reach the

disc centerp 5 number of pairing levels_Sgen 5 entropy generation rate (WK�1)

_S00

gen 5 volumetric entropy generationrate (Wm�3K�1)

T0 5 environment temperature (K)V 5 total flow volume (m3)Vx;N;Vy;N 5 velocity components (m s�1)_W 5 power output (W)_Wrev 5 power output in the reversible

limit (WK�1)x, y 5 cartesian componentsZII 5 second-law efficiency of power

plants, Figure 1DP 5 pressure difference (Pa)n 5 kinematic viscosity (m2 s�1)

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Science and technology as evolving ﬂow architectures · 2010-06-07 · nonequilibrium systems (constructal theory). Geophysical and biological ﬂow systems evolve in one direction,