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HierarchiesHierarchy are everywhere, including where it matters to us the most, in societySociety. Few large and many small are flowing together. HierarchyHierarchy is the visible manifestation of freedomFreedom, economies of scaleEconomies of scale, and the...

Existing energy policy proposals are approached from a demand-side perspective to solve the immediate problem of meeting existing demands defined by existing technologies. However, a constructive forward-looking policy requires a supply-side perspective. The purview of energy policy is ultimately the efficient allocation of our scarce supply of available energy for ‘exergy’. The authors outline a proposal for efficient exergy management. This supply-side orientation is based upon basic thermodynamic principles, thus offering a foundation for formation of consistent criteria for policy-oriented decision making.

This article is a review of recent work in which heat transfer enhancement, or thermal resistance minimization is achieved by optimizing the internal architecture of a heat-generating volume. When the cooling is provided by a stream that flows through the volume, it is possible to optimize the spacings between the internal features that are being cooled. When the cooling function is served by a point-size heat sink, a fixed amount of high conductivity material can be distributed through the volume to minimize its overall thermal resistance. The discovery is that any volume element can have its shape (or size) optimized such that its flow resistance is minimal. The given volume is covered in successive steps of optimization and construction. The visible portion of the optimized volume-to-point flow path that emerges is a tree network that is completely deterministic. This solution has a definite time direction: from small to large, hence the name “constructal”. Small size and slow and shapeless flow (diffusion) come first, and larger sizes and organized flows (streams) come later.

In this paper constructal theory is applied to the fundamental problem of how to arrange discrete heat sources on a wall cooled by forced convection. The global objective is to maximize the conductance between the discrete heated wall and the fluid. This is equivalent to minimizing the temperature of the hot spot on the wall, when the heat generation rate is specified. The mechanism by which the global objective is achieved is the generation of flow configuration, in this case the distribution of discrete heat sources. Two different analytical approaches are used: (i) large number of small heat sources, and (ii) small number of heat sources with finite length, which are mounted on a flat wall. Both analyses show that the heat sources should be placed nonuniformly on the wall, with the smallest distance between them near the tip of the boundary layer. If the Reynolds number is high enough, then the heat sources should be mounted flush against each near the entrance to the channel. The analytical results are validated by a numerical study of discrete heat sources that are distributed nonuniformly inside a channel formed by parallel plates.

“Empire building” is a phenomenon that dominates today’s research landscape. Large groups, national priorities and research centers dwarf the spontaneous individual investigators. Administrators and the thirst for higher rankings encourage this trend. Yet, the individuals do not disappear. This paper explains why. It attributes the emergence of the large group to the pursuit of greater visibility for the institution as a whole. The visibility (V) is modeled as a product of the production (P) of ideas in the institution, and the support (S) that the institution secures for the production of ideas. The coalescence of some investigators into a large group tends to increase S and decrease P. On the other hand, an increase in the number of individual investigators has the opposite effect. From this trade-off emerge the main and well-known features of contemporary research organization: the proportionality between the size of the large group and the size of the entire institution, the strong relationship between the visibility of an institution and its size, and the fact that large groups occurred fi rst in the largest and most research-intensive institutions. The paper also shows that as the incentives for large-group research become stronger, smaller and smaller institutions fi nd it benefi cial to abandon the individual investigator mode and seek a balance between research empires and individual investigators. The individual researcher will not disappear.

Porous materials are usually thought of as amorphous mixtures of two or more things, solids, fluids, and voids. I was drawn to the nature absent from the amorphous: the structure, flow, configuration, design, purpose, and evolution. This article is a pictorial review of the work. It begins with defining the terms: design, freedom, evolution, and prediction (theory). Vascular (tree shaped) architectures offer greater flow access than channels with only one length scale (diameter, slit, wall to wall spacing). The tendency to evolve with freedom toward flow configurations that provide greater access is everywhere in nature, bio, and non-bio. This universal phenomenon is summarized as the Constructal Law of evolution everywhere, which empowers us to predict evolution, miniaturization, high density of fluid flow and heat transfer, and scaling up (or down) of existing designs. Vascular designs are icons of the multiscale design called hierarchy. Vasculatures occur naturally because they flow more easily—they offer greater access—than one-scale designs. All movement in society is hierarchical, from city traffic to global air traffic, fuel consumption, and wealth. The future of evolutionary design everywhere points toward vascular, hierarchical flow architectures that will continue to morph with freedom and directionality.

This review article places in perspective the new work devoted both to the analysis of the thermodynamic irreversibility of heat and mass transfer components and systems and to the design of these devices on the basis of entropy generation minimization. The review focuses on the fundamental mechanisms responsible for the generation of entropy in heat and fluid flow and on the design tradeoff of balancing the heat transfer irreversibility against the fluid flow irreversibility. Applications are selected from the fields of heat exchanger design, thermal energy storage, and mass exchanger design. This article provides a comprehensive, up-to-date review of second-daw analyses published in the heat and mass transfer literature during the last decade.

This paper shows analytically and numerically how an originally uniform flow structure transforms itself into a nonuniform one when the objective is to minimize global flow losses. The flow connects one point (source, sink) to a number of points (sinks, sources) distributed uniformly over a two-dimensional domain. In the first part of the paper, the flow between neighboring points is modeled as fully developed through round tubes. It is shown that flow ‘maldistribution’ and the abandonment of symmetry are necessary for the development of flow structures with minimal resistance. The search for better flow structures can be accelerated: tubes that show a tendency of shrinking during the search can be assumed absent in future steps of structure optimization. In the second part of the paper, the flow medium is continuous and permeated by Darcy flow. The development of flow structures (channels) is modeled as a mechanism of erosion, where elements of the original medium are removed one by one, and are replaced with a more permeable medium. The elements selected for removal are identified based on two criteria: maximum pressure integrated over the element boundary, and maximum pressure gradient. The flow structures generated based on the pressure gradient criterion have consistently smaller flow resistances. As flow systems become smaller and more compact, the flow systems themselves become “designed porous media”. These design optimization trends revealed are generally applicable in constructal design, i.e., where miniaturization, global performance, compactness and complexity rule the design.

This article discusses the dynamics of the S-curve phenomenon in nature. The S-curve phenomenon and its physics principle unite the spreading flows with the collecting flows, and the animate flows with the inanimate flows. The history of the volume of heated soil versus time follows an S-shaped curve that is entirely deterministic. It is also predicted that when the invading channels are tree shaped as opposed to single pipes, the entire flow from point to volume occurs faster, more easily, along a steeper S-curve. The S-curves of nature are history records of tree-shaped spreading on areas and volumes that are eventually filled during consolidation by transversal diffusion. The prevalence of S-curve phenomena in nature rivals that of tree-shaped flows, which also unite the animate, inanimate, and human realms. This phenomenon is so common that it has generated entire fields of research that seem unrelated: the spreading of biological populations, cancer tumors, chemical reactions, contaminants, languages, news, information, innovations, technologies, infrastructure, and economic activity, and the evolution of technology performance versus cumulative R&D spending.

Technical Forum Questions in Fluid Mechanics: Natural Tree-Shaped Flows Adrian Bejan Adrian Bejan Duke University, Department of Mechanical Engineering and Materials Science, Box 90300, Durham, NC 27708-0300 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information Adrian Bejan Duke University, Department of Mechanical Engineering and Materials Science, Box 90300, Durham, NC 27708-0300 J. Fluids Eng. Sep 1998, 120(3): 429-430 (2 pages) https://doi.org/10.1115/1.2820673 Published Online: September 1, 1998 Article history Online: January 22, 2008

Hydrodynamic stability analysis of an inviscid wall jet shows that instability is possible above a characteristic disturbance wavelength which is proportional to the jet thickness. This scaling is the basis for an argument that transition occurs when the fluctuating time period of the unstable (inviscid) wall jet is of the same order as the viscous diffusion time normal to the jet. The transition must occur when the jet Reynolds number is of the order of 102. Published observations of transition along a heated vertical wall are reviewed in order to test the validity of the proposed scaling argument. Specifically, numerous observations on buoyant jets near isothermal walls, near constant-heat-flux walls, and in enclosures with vertical isothermal walls are shown to support the validity of the transition mechanism proposed

In this paper we develop an analytical and graphical formulation of the constructal law of maximization of flow access in systems with heat and fluid flow irreversibilities and freedom to change configuration. The flow system has global objective (e.g., minimization of global flow resistance) and global constraints (e.g., overall size, and total duct volume). The infinity of possible flow structures occupies a region of the two-dimensional domain of “global performance versus freedom to morph.” This region of “nonequilibrium” flow structures is bounded by a line representing the best flow structures that are possible when the freedom to morph is limited. The best of all such structures are the “equilibrium” structures: here the performance level is the highest, and it does not change even though the flow architecture continues to change with maximum freedom. The universality of this graphical and analytical presentation is illustrated with examples of flow structures from three classes: flow between two points, flow between a circle and its center, and flow between one point and an area. In sum, this paper presents an analytical and graphical formulation of the constructal principle of thermodynamic optimization of flow architecture under global constraints. The place of this new and self-standing principle in the greater framework of thermodynamics is outlined.

This paper reports a theoretical and experimental study of the effect of solid-side subcooling on the phenomenon of melting by natural convection at the vertical interface between a solid body and a pool of its own liquid. The first part of the study consists of a conjugate boundary layer analysis of the transient melting process, in which the effect of solid subcooling leads to the formation of a time-dependent conduction boundary layer in the solid. The theoretical solution documents not only the effect of solid subcooling on the melting rate, but also the effects of liquid superheating (Stefan number) and thermal diffusivity ratio. The second part of the study consists of melting experiments conducted in a rectangular enclosure heated at a constant rate from the side. The solid subcooling parameter B covers the range 0.3–6.3, as the Rayleigh number remains fixed. The experiments show that in the conduction-dominated regime the Nusselt number increases as B increases. In the convection-dominated regime, the effect of the subcooling parameter B is insignificant. It is shown that these experimental observations agree with the trends anticipated theoretically in the first part of the study.

In this article we rely on constructal theory to show that the hierarchy of universities is rigid, and that the explanation lies in the nature of education (science, news, information) as a natural fl ow system that bathes the globe most effectively. The article begins with two observations: (i) the rankings of the best engineering universities in the USA closely mirror the rankings of the universities that have the most names of researchers on the list of the most highly cited authors; and (ii) the log‐log plot of the number of highly cited authors of one school versus the rank of that school is nearly a straight line with slope between ‐1/2 and ‐1. The straight line is the same as the distribution of city sizes versus city rank throughout the history of Europe. From this follows the argument that the hierarchy of universities is tied to geography, to how each nodule of knowledge generation serves the area allocated to it. Education fl ows from point to area. The compounding of areas to cover the landscape is the origin of the hierarchical and stable arrangement of universities. The rank of a university is closely related to the visibility of its producers of ideas. The tapestry of a university on the landscape is predicted. All universities grow and improve in time (like all the river channels during the rain), but their hierarchy remains the same.

This paper reports theoretical solutions for the quasi-steady and time-dependent regimes of melting in the presence of natural convection in an enclosed phase-change material heated from the side. The first part consists of developing two boundary layer solutions for the flows near the heated wall and the solid-liquid interface, and then matching these solutions with a unique solution for the core of the liquid region. The second part of the paper outlines an analysis for the earlier, time-dependent regime, when the liquid counterflow through the slender gap convects heat in the vertical direction. This two-part analysis shows that the liquid superheat (Stefan number, Ste) has a sizeable effect on the flow and temperature fields. As Ste increases, the average melting rate decreases and the overall heat transfer rate into the enclosure increases.

Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics. These simple models are used in the optimization of real (irreversible) devices and processes, subject to finite-size and finite-time constraints. The review traces the development and adoption of the method in several sectors of mainstream thermal engineering and science: cryogenics, heat transfer, education, storage systems, solar power plants, nuclear and fossil power plants, and refrigerators. Emphasis is placed on the fundamental and technological importance of the optimization method and its results, the pedagogical merits of the method, and the chronological development of the field.

The prevailing view is that we cannot witness biological evolution because it occurred on a time scale immensely greater than our lifetime. Here, we show that we can witness evolution in our lifetime by watching the evolution of the flying human-and-machine species: the airplane. We document this evolution, and we also predict it based on a physics principle: the constructal law. We show that the airplanes must obey theoretical allometric rules that unite them with the birds and other animals. For example, the larger airplanes are faster, more efficient as vehicles, and have greater range. The engine mass is proportional to the body size: this scaling is analogous to animal design, where the mass of the motive organs (muscle, heart, lung) is proportional to the body size. Large or small, airplanes exhibit a proportionality between wing span and fuselage length, and between fuel load and body size. The animal-design counterparts of these features are evident. The view that emerges is that the evolution phenomenon is broader than biological evolution. The evolution of technology, river basins, and animal design is one phenomenon, and it belongs in physics.