Publications

We start with the simplest case, that of zero flow through the fluid-saturated porous medium. For an equilibrium state the momentum equation is satisfied if (6.1) % MathType!MTEF!2!1!+- %...

This lecture outlines the basis for the entropy generation minimization method, and a series of key applications in power generation, refrigeration, and energy conservation. The lecture begins with a review of the concept of irreversibility, entropy generation, or exergy destruction. The proportionality between exergy destruction and entropy generation is used in the search for improved thermodynamic performance subject to finite-size constraints and specified environmental conditions. Examples are drawn from refrigeration, energy storage systems for sensible heat and latent heat, solar energy, and the generation of maximum power by using a stream of hot gas. It is shown that the physical structure of the system springs out of the process of global thermodynamic optimization subject to global constraints. This principle generates structure not only in engineering but also in physics and biology (constructal theory).

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Four problems are used to show how the following objectives can be pursued in a heat transfer course: the introduction of design principles along with heat transfer science, the interdisciplinary character of heat transfer engineering, and the relationship between heat transfer and other engineering disciplines. The problems address the design question of how to select the shape and material of a mechanical support that must be a good thermal insulator at the same time. They show that the mechanical and thermal functions of the system compete against one another, and that it is possible to balance these competing objectives into an optimal design.

The paper reports an experimental study of natural convection between two water reservoirs connected through a two-dimensional horizontal duct. The flow field was visualized and the velocities were measured using the thymol blue pH indicator method. The temperature field in the duct region and the heat transfer rate through the duct were also measured. It is shown that the duct flow consists of two streams in counterflow, the warmer stream occupying the upper half of the channel. The two streams are insulated from one another by a mid-depth buffer layer. The measurements demonstrate that the heat transfer mechanism differs fundamentally from the mechanism envisioned in the Bejan and Tien theory [6]. It is also suggested that the basic design of the experimental apparatus can be used in future studies of stability of shear flows in stratified fluids.

One of the anomalous thermodynamic properties of water is that the melting point of ice decreases as the pressure increases. This behavior was discovered independently by Kirchhoff and Thomson. It inspired Reynolds to speculate that the pressure-melting of ice and snow might be responsible for the low coefficient of friction experienced during skating and skiing. According to him, the pressure applied by the skate on the ice surface would cause superficial melting, which in turn would lubricate the relative motion between skate and ice. Although the pressure-melting phenomenon received some attention from early tribologists, this interest decreased after Bowden and Hughes' work, which showed that the superficial melting under the skate is due to friction (viscous dissipation) in the water film. In this note the authors consider a different fundamental aspect of the pressure-melting of ice, namely the indentation caused by a flat solid that is pressed against a block of ice. Unlike in the work referenced above, there is no lateral motion between the solid body and the ice block. The only motion that occurs is the normal progress that the solid body makes into the ice. This motion is made possible by the melting of the ice situatedmore » in front of the body. In this way, the pressure melting process is related to the contact melting process that occurs when a temperature difference ({Delta}T) is maintained between the solid body and the phase-change material.« less

This paper documents the strong relation that exists between the changing architecture of a complex flow system and the maximization of global performance under constraints. The system is a surface with uniform heating per unit area, which is cooled by a network with evaporating two-phase flow. Illustrations are based on the design of the cooling network for a skating rink. The flow structure is optimized as a sequence of building blocks, which starts with the smallest (elemental volume of fixed size), and continues with assemblies of stepwise larger sizes (first construct, second construct, etc.). The optimized flow network is tree shaped. Three features of the elemental volume are optimized: the cross-sectional shape, the elemental tube diameter, and the shape of the elemental area viewed from above. The tree that emerges at larger scales is optimized for minimal amount of header material and fixed pressure drop. The optimal number of constituents in each new (larger) construct decreases as the size and complexity of the construct increase. Constructs of various levels of complexity compete: the paper shows how to select the optimal flow structure subject to fixed size (cooled surface), pressure drop and amount of header material.

The Constructal Law is the law of physics that accounts for the universal phenomenon of evolution of flow configuration in nature. Evolution and the Constructal Law unite all the “live” systems, bio and nonbio, which are characterized by flow and freedom...

This paper describes the conceptual design and performance of balanced two-stream counterflow heat exchangers, in which each stream flows as a tree network through its allotted space. The two trees in counterflow are like two palms pressed against each other. The paper develops the relationships between effectiveness and number of heat transfer units for several tree-counterflow configurations: (i) constructal dichotomous trees covering uniformly a rectangular area, (ii) trees on a disk-shaped area, and (iii) trees on a square-shaped area. In configurations (ii) and (iii) each stream flows between the center and the periphery of the area. Configurations (i) and (ii) are trees with minimal resistance to fluid flow. Configuration (iii) is designed by minimizing the length of each duct in the network. The paper reports the formula for the number of heat transfer units in each configuration. Unlike in counterflows formed by two parallel streams, in which the longitudinal temperature gradient is constant, in the counterflow formed by two trees the longitudinal temperature gradient is steeper as one approaches the periphery of the tree canopy. The application of dendritic heat exchangers to devices with maximal transport density is discussed, e.g., electronics cooling, fuel cell architectures, etc.

Palestrante: Prof. Dr. Adrian Bejan. Instituicao: Duke University. Carolina do Norte, Estados Unidos. Resumo da palestra: Evolution is the defining phenomenon of nature. This lecture outlines the role played by freedom and evolution in physics (thermodynamics): given freedom, movement exhibits the tendency to evolve into configurations that provide greater access. The lecture traces the modern evolution of flow systems that morph with freedom toward greater flow access, in accord with the constructal law. For example, the evolution of volumetric cooling or heating is pointing toward greater heat transfer density, multiple scales and smaller dimensions. The progress is in two ways, incremental and with sudden step changes in flow configuration and performance. All this is predictable. The doctrine of evolutionary (constructal) design teaches how to predict evolution in general, and how to fast-forward technology evolution. The lecture is based on the new book: FREEDOM AND EVOLUTION: Hierarchy in Nature, Society and Science, Springer Nature, 2020.

In this paper we show that the production of ice by convection cooling followed by contact melting can be maximized by properly selecting the frequency of the intermittent freezing and removal cycle. In the first part of the paper, this principle is illustrated in three configurations: water freezing inside a tube cooled externally by convection, freezing on the outside of a tube cooled internally by convection, and freezing on a plane wall with convection cooling on the back side. The proper dimensionless groups are identified, and the optimal regime of intermittent operation is reported in dimensionless charts. The second part of the paper focuses on the contact melting process that occurs during the gravitational removal of the ice piece. This time-dependent process is the result of the coupling between the thin-film fluid mechanics, the acceleration of the ice piece and the variable length of the direct contact region. The ice fall time predicted by the contact melting analysis was validated by experiments with ice columns falling from vertical tubes heated from the side.

This paper reports a fundamental study of the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluid-saturated porous medium. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. The study contains two parts. In the first part, scale analysis shows that the natural convection phenomenon conforms to one of four possible regimes, depending on the values of buoyancy ratio N and Lewis number Le. The scales of the heat and mass transfer rates are determined for each regime. In the second part of the study, the boundary-layer problem is solved via similarity formulation in the buoyancy ratio range − 5 ⩽ N ⩽ 4 and Lewis number range 1 ⩽ Le ⩽ 100. The similarity solutions confirm the validity of the order-of-magnitude limiting results revealed by scale analysis.

Rotating electric machines generate heat volumetrically, and are cooled by forced convection aided by the self-pumping effect. In this paper we focus on the fundamental relationship between the internal flow architecture of the gas cooled winding and its thermal performance, which is represented by the nearly uniform distribution of peak temperature throughout the winding volume. We show that the cooling passages can be sized such that the volumetric cooling is most effective. From this finding follows the number of passages and their distribution through the heat generating volume. The principle is developed analytically, and it is then validated based on numerical simulations of the cooling architecture. The paper also reports the thermodynamics basis of the self-pumping effect, and its natural occurrence as free convection in general, which includes atmospheric circulation.

This paper extends to three-dimensional heat conduction the geometric “constructal” method of minimizing the overall thermal resistance between a finite-size volume and a small heat sink. The volume contains (i) low-conductivity material that generates heat at every point, and (ii) a small amount of high-conductivity material that must be distributed optimally in space. The given volume is covered in a sequence of building blocks (volume sizes) that starts with the smallest volume element, and continues toward larger assemblies. It is shown that the overall shape of each building block can be optimized for minimal volume-to-point resistance. The relative thicknesses of the high-conductivity paths can also be optimized. These optima are developed analytically and numerically for the smallest elemental volume and the first assembly. The high-conductivity paths form a tree network that is completely deterministic.

When a fluid accelerates as it sweeps a solid surface there are two consequences: the friction and the heat transfer (thermal contact) between fluid and solid increase simultaneously. This is known as the universal analogy between fluid friction and heat transfer. In thermal engineering these two effects are problematic because improved thermal contact is beneficial, and increased friction (i.e., pumping power) is detrimental to overall performance. In the present article we question whether the ‘analogy’ between these conflicting effects hampers the performance of animal movement. The theory focuses on warm-blooded swimmers and the effects (friction, heat transfer) that result from one change in the configuration of the body. Selected for analysis is a breaststroke swimmer. During gliding while reaching forward the ‘one change’ is from (a) legs spread apart, to (b) legs held tight together. The theory shows that the change from (a) to (b) has two consequences: greater swimming speed, and reduced body heat loss. In animal design both effects are beneficial, unlike in engineered flow systems. The analogy between fluid friction and heat transfer accelerated the evolution of animal design, and accounts for the 'divergent evolution' of fish and mammals.

This paper describes the fundamental mechanisms of heat transfer through a surface covered with perpendicular hair strands of uniform density. An air flow parallel to the skin seeps through the spaces created between the hair strands. It is shown that the total heat transfer rate from the surface is due to two contributions: (i) the heat conducted through the hair strands, which act as fins, and (ii) the heat convected from the bare portions of the skin. When the air flow is slow enough to conform to the Darcy regime, there exists an optimum hair strand diameter for which the total heat transfer rate is minimum. The optimum diameter increases as the square root of the length swept by the air flow, that is the linear size of the body of the animal covered with hair.

This article analyzes the organization of a city in terms of how well it enables humans to move from any point to the whole area. In accordance with Constructal Law, the natural way to assemble and connect a road and street network is to ensure that travel time is reduced at every turn and with every change in the flow design. The article also highlights that predicting the future and constructing changes based on a proven scientific principle is much faster and more economical than trial and error. Due to the modern technology, urban design expands not only outward, into suburbs, and inward, toward dense city centers, but also vertically. Experts suggest that if we can anticipate the urban features that emerge naturally from the need for greater access, we can plan ahead and design with confidence the features that not only serve the population, but do so with staying power. A city is a live flow system with freely changing architecture, many small streets, few large streets, and beltways.

This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots the intense heating that impinges on it. The vasculature is a quilt of square-shaped panels, each panel having a tree vasculature that connects the center with the perimeter. The coolant may flow in either direction, center–perimeter, or perimeter–center, although here only the center–perimeter flow direction is illustrated. Numerical simulations of conjugate heat and fluid flow in three directions show that it is possible to determine all the optimal geometric features of vasculatures with up to three levels of bifurcation (n =3). The global performance is evaluated in terms of the overall thermal resistance, pressure difference, flow resistance and pumping power. The improvements in global performance diminish as the number of bifurcation levels increases. No flow architecture is universally superior. The dendritic designs are superior at the low and high ends of the pressure difference range. The radial designs are superior at intermediate pressure difference numbers.