Rui Namorado Rosa

(Évora, 20th November 2003)


A brief appraisal of Professor Adrian Bejan's work

(Proceedings of the Symposium “Bejan's Constructal Theory of Shape and Structure”, 2004, Rui N. Rosa, A. Heitor Reis et Antonio F. Miguel (Editeurs), Centro de Geofísica de Évora, Univ. d'Évora, Portugal.)


Adrian Bejan is a professor with the College of Engineering at Duke University (North Carolina, USA) and one of the one hundred most cited authors in the area of engineering. Born in 1948 in Galati (Romenia), he received his bachelor’s degree in Mechanical Engineering at the Massachusetts Institute of Technology in 1972 where, later in 1976, he also received his doctorate. Prof. Adrian Bejan’s research work spans a wide variety of thermal engineering topics: the minimization of entropy generation, exergetic analysis, natural convection, combined transfer of energy and mass, convection in porous media, turbulence, etc. More recently, he developed the Constructal Theory of Form and Structure in Nature.
Prof. Adrian Bejan is the author of 14 books on engineering, energy and environmental topics, and the author of more than 350 scientific articles. He is part of the editorial board or is editor for 21 international journals. He is member of several scientific societies, receiving numerous honours from many of them. He holds 12 honorary doctorates from prestigious universities outside of the United States.
Adrian Bejan is distinguished as much by the great originality and versatility of his scientific work, widely renowned and praised, as by his exceptional didactic aptitude, repeatedly illustrated in his academic textbooks, several of them serving as primary references texts for engineering studies throughout the world. Much of the contents of his textbooks resulting from his abundant and innovative research work, Adrian Bejan conveys in them the imaginative approach of a exceptional researcher. Conversely, we are led to suppose that he finds, in his engineering lectures at university, a good deal of motivation and inspiration that he later conveys into in his research work.
He has attracted the attention of the scientific community in recent years as the author of the Constructal Theory, in which the relationship between form and structure in engineering and form and structure in nature is depicted. The optimization of the overall functioning of systems subjected to constraints has been identified as the essential principle in the generation of form and structure in both natural and artificial systems with internal fluid circulation. The geometric structures that result from the application of this principle in engineering are called ‘constructs’. The recognition that the same principle is the basis for the generation of the shape of systems with internal fluid circulation, whether living or inanimate, led to the thesis of the Constructal Theory, whose most recent developments were systematized in his book, Shape and Structure, from Engineering to Nature (Cambridge University Press, 2000).
In addition to engineering, this theory has since revealed its inquisitive and explanatory potential in other areas, such as biology and medicine (allometric laws, structure of the respiratory and circulatory systems, bodily rhythms, organ and tissue structures) and earth sciences (circulation of planetary fluids, structures of river basins, etc.). It also reveals some promising developments in social sciences.

On science and engineering

The most important development in the art of the XV century was the introduction of linear perspective: a system of representing three-dimensional space based on the principles of Euclidean geometry. We should realize that the developments in art and technology were really two fronts of a single great advance. Isolate one part of it from another, and you lose the full meaning of that crucial moment in history.
Let’s examine the relationship between artistic activity and technical activity. We have a borderline concept – design - which lies between making a thing and giving it an appropriate shape. This tradition comes back from the Renaissance. Artist-engineers would draw a machine both to show how to construct it and to give it a harmonious shape. They searched inspiration in the shapes observed in Nature – as they considered natural laws as perfection rules. Today, with computer assisted and multimedia art concepts, people are combining their artistic vision with the latest advances of information and communication technology; and in doing so, artists sometimes make their own contributions to further technology advance. Nowadays, as in the XV century, knowledge is being combined between different domains.
In the beginning of Modern Science age, mathematically formulated theories were introduced as premises for the deduction of factual conclusions. These conclusions provided both applications of and tests to the theories. The key features were the introduction of descriptive, mathematical models and their application by means of deduction. The next step in the scientific method would be the transition from informal mathematical theories to formal analytic models, one of the benefits of formalisation being that it makes the models more accessible to machine processing.
Science can be thought of as a process of Observation-Hypothesis-Test. According to Karl Popper, the essence of scientific proof is testing under the Principle of Falsification.In other words a hypothesis cannot be proven to be true, but can be proven to be false or not, by confronting its predictions against the real world. Under these logical conditions, any test that confirms a hypothesis establishes "truth" on a conditional basis only, always subject to further testing and possible falsification. The result is a gradually expanding edifice of conditional truth.
Engineering is a similar self-correcting search process. However, in this case, it can be viewed as a trial-and-error process of Observation - Design - Test. The emphasis on design in the place of hypothesis confers to engineering a different motive force, but its method is essentially the same as that of science. In contrast to science, Engineering can be envisaged as a creative search process for what works by combining existing scientific principles and technologies into new products or processes to achieve defined purposes. Engineering is therefore the practical application of the scientific method, where a design replaces a hypothesis, and the principle of falsification takes the form of testing a prototype design.
From these convergent and overlapping views, one draws the conclusion that the foundations of technical creation and of scientific discovery are coincident and that, intertwined, the two creative processes reflect the dialectic relation of the very natural phenomena and of our understanding of them. Da Vinci, Bacon, Galileo, Pascal, Newton, Faraday, Darwin, are just a few of the exponents of that epistemological progress in which invention and discovery can hardly by differentiated, and only by methodological intention can be separated.

The duality nature-machine

The metaphor of Nature as a machine has captivated scientists’ minds for centuries to this day. The machines of the XVII century were characterized by their powers to transmit and modify actions initiated from some mechanical source. Mechanistic philosophers of that era found in Nature's workings the display of innate capacities to transmit or modify actions initiated from an external source. The universe would be a Cosmic Machine in which smaller machines are embedded in larger ones.
The revolutionary advances in biochemistry since the 1950’s, and of nanoscience in the 1990’s, have perpetuated that metaphor of Nature as machine and is feeding the dream of the Machine akin to Nature. Today, we confront new domains which challenge traditional distinctions between machines and non-machines. Nanostructures provide insight into both the emergence of life and the fabrication of innovative materials.
We face again the puzzling challenge of the identity of machine, the real or apparent distinction between Machine and Nature. Machine/Nature duality appears grounded in that scientific progress is assisted by technical advances and technological innovation is assisted by scientific discovery, whereas both share in having in Nature inspiration and the object of inquiry or action. In human evolution, our understanding of Nature and technical achievements appear closely associated. Throughout history no single demarcation line between machines and non-machines has withstood the emergence of major technological innovations or scientific findings.

Causes and effects. Teleology

Some highlight the harmony observed in the natural world to argue that the whole Universe and living beings in particular are necessarily products of external actions. Biological structures, their optimal arrangements and organized societies, would point to some sort of purpose or design. On the contrary, others appeal to chance and a huge span of time and argue that the harmony and optimal arrangements have arisen by necessity out of chance. These appeal to natural forces alone, albeit unknown, acting over huge spans of time, to attain those ordered configurations.
In classical times, teleologists were those appealing to the role of external causes in achieving a purpose, thereby making sense of otherwise unaccountable phenomena. Among them were wise men such as Socrates, Plato and Aristotle. The non-teleologists were men equally wise such as Democritus, Leucippus and Epicurus. Their views would later influence the European philosophy from the XVII century onwards. This debate, more that 25 centuries old, has captured the minds of the greatest thinkers of all times. The debate assumed later the form of opposition between idealists and materialists and continues up to the present time.
Kant did not regard teleology and mechanism as opposites, but rather as explanatory modes complementary to each other. He was committed to the idea that all objects in Nature, either organic or inorganic, are completely controlled by mechanical laws. However, a mechanical explanation could be given only when the separation between cause and effect would be clear. In complex systems, causes and effects are inextricably mixed, and explanations require external or unknown causes to be invoked. External causes are required only to the extent that our understanding of the whole context is incomplete, their epistemological role being transitory.
Even the evolution of a deterministic world cannot be completely understood in terms of its governing laws alone. The initial conditions and the boundary conditions must be specified too. These constraints might be unknown in which case its change and evolution cannot be predicted. Not predicted yet.

Optimization principles as natural laws

The law of reflection of light was known since classical times. Heron of Alexandria realized that as in free propagation, the reflection path obeys likewise a minimal principle of length. The law governing the refraction of light proved more difficult to discover. Only in 1621, Willebrord Snell stated it in correct mathematical form.
Pierre de Fermat (1657-62) assumed that light travels at a finite speed and at slower pace in a denser medium. He realised that both the laws of reflection and refraction could then be derived from the same principle that is, the light travelling along a path would take the least possible transit time. Fermat placed the propagation of light into the arena of four-dimensional space-time, like geodesic paths, a remarkable premonition of important elements of both special and general relativity.
Nearly a century later (1747) Pierre Louis Moreau de Maupertuis invoked his “principle of least action” to derive Snell's law of light refraction. In his view, the “least action” principle would be an all-encompassing principle governing all areas of physics. Natural processes should proceed in just such a way as to “minimize the quantity of action”, an assertion closely akin to Fermat's principle of “least time”.
The notion that the phenomena of nature must follow some “best” course was not new. Plato already quoted Socrates stating what we could now call a “best possible” principle for the natural phenomena. The innovation of Maupertuis was to offer a quantitative measure for the vague notion of what is “best" for nature, and to demonstrate that this kind of reasoning can produce predictive results. Lagrange later clarified the concept and named it.
The modern formulation of Fermat’s Principle has proven to be a remarkably useful approach to the formulation of all kinds of physical problems involving motion and change. Newton's Mechanics is contained in Hamilton's principle of least action. Water running downhill seeks the steepest descent; and when running into a basin distributes itself so as its surface rests at the lowest level, thereby minimizing the potential energy. The path of a body in a gravitational field is a geodesic in relativistic mechanics. Feynman's formulation of quantum mechanics is based on a least-action principle applied to path integrals.
All processes of macroscopic change are irreversible. The entropy concept has been coined in thermodynamics to capture just this fundamental feature of nature. At the same time it allows to make quantitative statements about the efficiency of energetic and material transformations. Its origins goes back to the XIX century, when practitioners, engineers and scientists like Watt, Carnot and Clausius meant to understand and increase the efficiency of steam engines. By now, the original notion of entropy has been greatly generalized and applied in many different contexts outside classical thermodynamics. The principles of entropy maximization and of free-energy minimization, notwithstanding being formulations of the laws of thermodynamics in two particular contexts of closed systems, are further examples of optimal principle formulations, which had great historical reach.

The Constructal Theory of Adrian Bejan

Thermodynamics is a powerful tool that scientists and engineers can use to attain a deeper understanding of how naturally organized systems arise and evolve. More important, engineers have applied the principles of thermodynamics, fluid mechanics, and heat and mass transfer to construct models that account for the inherent irreversibility of processes executed by systems, both natural and man-made. In particular, entropy-generation minimization is an approach to thermodynamic optimization that provides considerable insight into the organization of the natural world. In the process of performing such analyses, engineers determine the entropy that a system generates as a function of its parameters, including size, shapes, and materials. Engineers can go on to optimize the system's performance given their constraints.
When engineers design a device or system, they must first understand its purpose. The device must perform a function, subjected to given constraints. The engineer conceives and designs it, optimizes its design, constructs it, makes it work and optimizes its performance. The unique understanding that engineers can offer in the search for the origins and evolution of naturally occurring structures is that many designs for such structures have nearly the same overall performance as the optimal design engineers could conceive, even though they may differ in their details. This engineering insight helps to account for the evolution of naturally occurring systems governed by energy and mass flow and subjected to geometric and size constraints.
When a heat source and current is imposed, minimization of the entropy generation amounts to minimizing the resistance to the heat flow. In an elementary passage of a heat exchanger, the generation of entropy is due to both heat differential and pressure drop, which compete against one another. The hydraulic diameter must be selected such that the sum of the two irreversibilities is minimized. To cool an electronic package, both the volume and the heat-generation rate over its volume are given. Heat is removed by a stream under natural or forced convection. The geometric arrangement of heat-generating components can be optimized such that the hot-spot temperature is minimal. Optimal package architecture can be attained.
In the case of minimizing the overall thermal resistance between a fixed heat-generating volume and one sink point, every subsystem of the given volume can have its shape optimized. This principle is applied first at the smallest volume scale, where a single high-conductivity fibber removes the heat generated by the low-conductivity material from each smallest element. The same geometric-optimization principle applies at larger scales. The next volume is an optimized assembly of optimized volume elements. The process of construction and shape optimization continues stepwise to larger scales until the given volume is fully covered. The high-conductivity paths form a tree, and the low-conductivity paths fill the infinity of points of the given volume.
Tree networks, as the one stated above, abound in nature in both animate and inanimate flow systems. We find them everywhere: plants, leaves, roots, lungs, vascular tissues, river drainage basins and dendritic crystals clusters. Every detail of every natural tree can be anticipated through the construction and optimization method illustrated by the heat flow tree. In fluid trees, the smallest-scale volumetric flow is by slow viscous diffusion, while the larger scale flow is organized into faster channelled streams which form a tree like structure. Most important, the method of defining each feature of the evolving tree is deterministic.
Volume-to-point constructs have a definite time direction: from small to large, and from diffusion to structure (ramifications, channels and streams). Determinism results only if this time arrow is respected. The optimized geometry formed by combining low- and high-conductivity flow regimes unites all the volume-to-point flows. Artificial constructs as well as natural structures, such as the internal arrangement of components in a computer or the arterial-vascular system in animals, require the same cooperation between slow and fast heat transfer mechanisms, with the slow mode operating at the smallest scale.
Tree networks in living communities are also observed and can be explained by the principle of minimization of the travel time between one point and a finite-size area of infinite destinations. Travellers have access to more than one mode of locomotion, starting at the slowest speed (walking) from lanes to streets and from streets to boulevards and proceeding toward faster modes of locomotion over longer distances. The given area is covered in steps of increasingly larger constructs. Each construct can be optimized for overall shape and angle between assembly and constituents. This predicts urban growth, from alleys to streets, avenues, and highways and drives multimodal transport systems that are set up to minimize travel time over long distances. Minimizing time travel of people flow determines geometric shape and flow regimes.
The minimization of travel time has been invoked to account for the trajectory of light and urban organization. Minimizing travel time such as minimizing resistance to flows, suggests a generalization, that is: For a finite-size system to persist it must evolve and organize in such a way that it provides easier access to the imposed currents that flow through it. This statement recognizes the natural tendency of imposed currents to construct paths of optimal access through constrained open systems. It also accounts for the evolution of these paths, which occurs in an identifiable direction that can be aligned with time. This is the Constructal Principle that Adrian Bejan proposes to the scientific community.

Adrian Bejan and the University of Évora

For some years now, Prof. Adrian Bejan has maintained a close relationship with the University of Évora, a relationship by which we feel greatly honoured. In addition to his scientific collaboration with some of this University’s faculty members, Prof. Adrian Bejan was the coordinator of the “School on Porous and Complex Flow Structures in Modern Technologies” that took place at the University in June 2002. And in May 2004, he will return as Chairman of the 2nd International Conference on Applications of Porous Media.
Our University highly appreciates the generous availability and the continued collaboration of Prof. Adrian Bejan not only in terms of scientific research but also in terms of the promotion of conditions affirming this University as a nationally-renown centre for engineering studies with international recognition.
Considering Professor Adrian Bejan’s highly relevant contributions to the general progress of scientific knowledge with his academic pursuits of inspiring and vast interdisciplinary repercussions, as well as his distinguishing this University with his valuable collaboration, the Scientific Council and the University Senate unanimously approved conferring to Professor Adrian Bejan an Honorary Doctorate from this University of Évora. The honorary degree was awarded in solemn academic plenary section on the 1st November 2003. The award took place in the main academic hall, which dates back to the foundation of the University of Évora in 1559.
In addition to that academic tribute to Prof. Adrian Bejan as an eminent scientist and world expert in mechanical and thermal engineering, the University of Évora organized a one day Symposium on “Bejan’s Constructal Theory of Shape and Structure” which was held on October the 31st 2003, with invited papers by Sylvie Lorente (INSA, France), Ibrahim Dincer (University of Ontario, Canada), Ventsislav Dzimparov (Gabrovo Technical University, Bulgaria), Vitor Costa (University of Aveiro, Portugal), Rui Rosa, António F. Miguel and A. Heitor Reis (University of Évora, Portugal) and Adrian Bejan himself. That was a memorable occasion for those who participated or attended the overview, albeit partial, of applications of the Constructal Principle.
In the present volume we collected the papers offered by our speakers. We feel that in bringing them to a wider audience, the University of Évora is also contributing to make the Constructual Theory more widely known so that it might inspire further researchers in a growing number of fields of knowledge.

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