A. Heitor Reis

Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and Structure

Constructal theory and its applications to various fields ranging from engineering to natural living and inanimate systems, and to social organization and economics, are reviewed in this paper. The constructal law states that if a system has freedom to morph it develops in time the flow architecture that provides easier access to the currents that flow through it. It is shown how constructal theory provides a unifying picture for the development of flow architectures in systems with internal flows (e.g., mass, heat, electricity, goods, and people). Early and recent works on constructal theory by various authors covering the fields of heat and mass transfer in engineered systems, inanimate flow structures (river basins, global circulations) living structures, social organization, and economics are reviewed. The relation between the constructal law and the thermodynamic optimization method of entropy generation minimization is outlined. The constructal law is a self-standing principle, which is distinct from the Second Law of Thermodynamics. The place of the constructal law among other fundamental principles, such as the Second Law, the principle of least action and the principles of symmetry and invariance is also presented. The review ends with the epistemological and philosophical implications of the constructal law. DOI: 10.1115/1.2204075

Indoor Deposition and Forced Re-suspension of Respirable Particles

The rate at which particles deposit and re-suspend from indoor surfaces is an essential parameter in determining human exposure to aerosol particles. In this study, we investigate experimentally particle deposition and forced re-suspension in a cubical enclosure for three particle sizes (0.7, 1.5 and 4 m). For particle deposition, the results are presented in terms of particle deposition velocity. It was observed that the particle deposition velocity is particularly significant for the floor surface. Deposition on vertical and ceiling surfaces becomes important only when these surfaces are electrically charged. Air humidity did not influence the particle deposition apart from when it was close to saturation. Re-suspension of particles from the floor surface due to household activities was also studied. It was observed that small particles are more difficult to detach from the floor than bigger ones. Besides, there is a pressure above which re-suspension is very likely to occur (minimum re-suspension pressure). This minimum pressure is dependent on the particle size.

Design in nature, and the laws of physics: Comment on “The constructal law and the evolution of design in nature” by Adrian Bejan and Sylvie Lorente

Every day we get surprised and amazed by the huge variety of shapes and sizes of natural systems. We call it the“natural beauty” of the “wonderful mother nature” and this is nothing more than a way of expressing our inner feelingthat some order must exist behind the natural scenery. Our brain perceives it as “beauty”, which might be the firststage of a deeper and unifying perception that involves rationalization based on mathematics and principle.The previous lines might serve as a preface to the paper “The constructal law and the evolution of design in nature”[1] which is a comprehensive review in which the authors summarize recent applications of the Constructal Law. Theresults and examples provided by the authors show how a new principle sheds new light on old problems, and how itprovides a new unified understanding of complex systems.After many years of research on shape and structure of natural systems, I am pretty sure that the “Constructal Law”put forward by Adrian Bejan [2] provides the rationale for understanding the evolution of shape and structure in aunifying way in both natural and manmade systems. It is a fact that Constructal Law has been successfully applied todescribe and anticipate the unique features of a wide variety of systems [3–5]. Now, we are able to perceive naturaldesign as Nature fine art that has a rationale behind, such that our new feeling of “natural beauty” comprises also thescientific dimension of beauty. On the other hand, the Constructal Law makes it outdated and useless the “Theory ofintelligent design” put forward by some neo-creationists (see [6]).The Constructal Law is as general as the First and Second Laws of Thermodynamics but has a very different scopethat makes it unique and complementary to those laws. While the First Law points to conservation of energy, both theConstructal Law and the Second Law point to change, i.e. to a direction in time. Though both these laws share thiscommon feature, they diverge as with respects to the scope. Contrarily to the Second Law, Constructal Law appliesto systems out of equilibrium, i.e., systems that evolve in time. While the Second Law deals with state variables, theConstructal Law combines flows and design (size, shape, structure).Constructal Law provides the foundations for both natural and engineered design to be viewed in the light ofscience. It opens new avenues of research in many fields from engineering and geosciences to life and social sciences.The reason for this ubiquitous applicability of the Constructal Law is rooted in the idea that what is important is not“what flows”, but how inner flows shape and structure the systems in an evolutionary way that points to better and

Utility function estimation: The entropy approach

The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker’s preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.

Analysis of the exergy balance of green leaves

In this paper we analyse the exergy balance of green leaves. The exergy source comes from the direct and diffuse solar radiation absorbed in the leaves, while exergy destruction occurs as the consequence of evapotranspiration, of internal flows and of leaf metabolism. Exergy storage occurs namely in the form of glucose which is a result of photosynthesis and oxygen release into the environment. Based on the exergy balance equation we show how to evaluate the leaf metabolic rate and the survival threshold conditions. In the absence of the exergy source (solar radiation) we can also understand how the trees use the exergy stored for their metabolic needs. This process is similar to the discharge of a capacitor through a resistance, which is a characteristic found in every living structure.

Drying of Porous Materials

Drying is the process of thermally removing volatile substances (e.g., moisture) to yield a solid product. Mechanical methods for separating a liquid from a solid are not considered drying. When a wet solid is subjected to thermal drying, two processes occur simultaneously: transfer of energy (mostly as heat) from the surrounding environment to evaporate the surface moisture, and transfer of internal moisture to the surface of the solid and its subsequent evaporation due to the first process.

Utilisation of air-groundwater exergy potential for improvement of the performance of heat pump systems

This paper reports a study on the use of the non-flow air-groundwater exergy potential for improving heat pump performance. It is shown that for air/groundwater temperature differences of order 15°C, energy savings up to 50% may be expected for heat pumps operating either in the heating mode or in the cooling mode. It is also shown that the reduction in the energy required to drive the heat pump is proportional to the square root of the exergy potential. In the Evora region, the exergy potential peaks during wintertime and during summertime. It is concluded that the use of the non-flow air-groundwater exergy potential is attractive either for heating purposes in wintertime, when energy savings can reach 20%, or for cooling purposes during summertime when they can reach 10%.

Heart rate, arterial distensibility, and optimal performance of the arterial tree

In this study we explore the ability of a previously developed model of pulsatile flow for explaining the observed reduction of arterial distensibility with heart rate. The parameters relevant for the analysis are arterial wall distensibility together with permeability and reflection coefficients of the end capillaries. A non-specific artery and the ensemble of tissues supplied by that artery were considered in the model. The blood current within that artery was equalized to the sum of all micro currents in the tissues supplied by that artery. A formula emerged that relates changes in arterial distensibility with heart rate, and also with some particular aspects of microcirculation. Then, that formula was tested with data of distensibilities of the radial and carotid arteries observed at the heart rates of 63, 90, and 110 b.p.m. The formula correctly predicted the trend of decreased distensibility with heart rate for both arteries. Moreover, due to the fact that the carotid artery supplies the brain, and because the Blood-Brain barrier is highly restrictive to colloids in the blood, for the carotid artery the formula predicted a less marked decrease in distensibility than in the case of the radial artery feeding muscle tissue, which has a greater permeability to colloids, a trend that was confirmed by data. It was found that reduction of arterial distensibility with heart rate was greater in arteries that supply end capillaries with high permeability and low reflection coefficients.

Use of sand beds of variable permeability in beach profile engineering

Here we present a technique based on theoretical grounds for dealing with beachface dynamics in response to wave forcing. Previous work has provided a relationship involving mean sand grain size, wave height, and beachface slope for a broad range of Iribarren number. The key aspect of beach morphodynamics was shown to be the permeability of the sand bed, which may be correlated to sand grain size and sphericity, and bed porosity, through the Kozeny‐Carman equation. Therefore, we show how beach nourishment aiming at beach profile recovering must be carried out with the use of sand beds of appropriate mean grain size. The theory also illuminates beach dynamics, namely the reshaping of sandy beachfaces in response to changes in wave height.

Natural Flow Patterns and Structured People Dynamics: A Constructal View

We show here that flow patterns similar to those that emerge in nature can also be observed in flows of people and commodities and can be understood in light of the same principle—the Constructal Law. River basins are examples of naturally organized flow architectures whose scaling properties have been noticed long ago. We show that these scaling laws can be anticipated based on constructal theory, which views the pathways by which drainage networks develop in a basin not as the result of chance but as flow architectures that originate naturally as the result of minimization of the overall resistance to flow. Next we show that the planetary circulations and the main global climate zones may also be anticipated based on the same principle. Finally, we speculate that the same principle governs “rivers of people,” whose architecture develops in time to match the purpose of optimizing access within a territory.