As an alternative to the mechanistic point of view expressed in Carathe´odory’s axioms, it is shown that the laws and concepts of thermodynamics are covered also by two statements made from a purely heat transfer perspective: Axiom I′—The heat transfer is the same in all zero-work processes that take a system from a given initial state to a given final state. Axiom II′—In the immediate neighborhood of every state of a system there are other states that cannot be reached from the first via a zero-work process. The primary concepts of this formulation are heat transfer, temperature, entropy, and zero-work boundary. Axiom I′ is used to define the property “energy,” and to deduce the secondary (derived) concept of “work transfer.” Axiom II′ is used to define the thermodynamic properties of “volume” and “pressure.” In this new heat transfer-based scheme, the analog of the Kelvin–Planck statement of the second law is: “∮δW < 0 is impossible” for an integral number of cycles executed by a closed system while in communication with no more than one pressure reservoir.
This article describes the generation of dendritic flow architectures that provide maximum side-to-side flow access, across a vascularized body. The flow architecture consists of trees that alternate with upside-down trees (a,b,a,b,…). If in tree “a” the flow is from root to canopy, in tree “b” the flow is from canopy to root. This means that the flow proceeds in the same direction through all the trees, i.e., the flow is oriented side-to-side, or line-to-line. The channel cross sections are rectangular, and they all have the same depth. The article shows under what conditions the tree vascularization offers greater flow access than parallel single-scale channels oriented perpendicularly to the two parallel lines. The analytical part of the work is based on the assumption of fully developed laminar flow in every channel. The numerical part consists of simulations of three-dimensional laminar flow through the entire tree architecture and its many bifurcations. It is shown that tree vascularization is more attractive than parallel channels when the number of bifurcation levels increases, the global porosity of the vascularized body decreases, and the global svelteness (Sv) of the flow architecture increases. The nonuniformity (maldistribution) of flow rates through ramifications of the same rank becomes nonnegligible when the pressure drop number (Be) exceeds 109. The optimal step in the sizes of cross-sectional areas from one channel to the channel of the next rank is closely approximated by 22∕3 even when the cross section is not square or round. The agreement between analysis and numerical simulation and optimization is good.
This paper shows that the main architectural features of a counterflow heat exchanger can be determined based on thermodynamic optimization subject to volume constraint. It is assumed that the channels are formed by parallel plates, the two fluids are ideal gases, and the flow is fully developed, laminar or turbulent. In the first part of the paper, it is shown that the irreversibility of the heat exchanger core is minimized with respect to (1) the ratio of the two-channel spacings, and (2) the total heat transfer area between the two streams. In the second part, the entropy generation rate also accounts for the irreversibility due to discharging the spent hot stream into the ambient. It is shown that the design can be optimized with respect to (1), (2) and (3) the ratio of the capacity rates of the two streams. The optimized features of the geometry are robust with respect to whether the external discharge irreversibility is included in the entropy generation rate calculation. Copyright © 2000 John Wiley & Sons, Ltd.
Humans and technology are not in symbiosis. They are one species, not two. Humans, enveloped in artefacts of many kinds and ages (from writing, to airplanes), are evolving as one species, the ‘human & machine species’. This evolution is visible and recorded in our lifetime. Here, I illustrate the evolution of the human & machine species by focusing on commercial aircraft, the cooling of electronics, and modern athletics, which is a special laboratory for witnessing the evolution of animal locomotion. I show that these evolutionary forms of flow organization are in accord with, and can be predicted based on the law of physics that governs evolution in nature, bio and non-bio: the constructal law. Evolution, life and the human & machine species are physics.
The problem of mixed convection on a wedge in a saturated porous medium is analyzed using the Darcy flow formulation and three different methods of solution. Nonsimilar solutions are obtained for several wedge angles. The nonsimilarity technique is applied to the boundary layer formulation, and the finite element method is used in both formulations. It is shown that both formulations produce results that agree well for Pe = 1 and uniform wall temperature in the range 0.1 < Ra/Pe < 100. The local and average Nusselt numbers are calculated for several geometries. Relative to the progress documented in the literature, new solutions are presented for m = 1 /3, 1/2 and 1 (i.e., wedge half angles 7 = 45, 60, and 90). It is shown that the overall heat-transfer rate is the largest when the wedge angle is zero, and the walls are oriented vertically.
This article discusses various aspects of snowflake architectures. It is certain that every snowflake conforms to only one architecture: a flat star with six fishbones connected at the center. The latent heat of solidification, which is released by the water vapor that becomes solid at the bead surface. There comes a critical time when the spherical bead is no longer an efficient architecture for dissipating heat. The principle calls for design change, toward faster heat release and solidification. The growth of ice morphs abruptly into a ball continued in one plane by needles. Because of the configuration of the water molecule, the needles grow in six directions. The flat star transfers heat to the surroundings more easily than a spherical bead with the same diameter. In order to give credit to the view that every snowflake is unique, the actual configuration depends on many secondary effects, which are of random origin.
This paper described numerical the procedure used to determine the optimum configuration of two rows of pin fins so that the total heat transfer rate is maximized. The heat transfer across the fins is by laminar forced convection bathed by a free-stream that is uniform and isothermal. The optimization is subjected to fixed volume of fin materials. The dimensions of the optimized configuration are the result of balancing conduction along the fins with convection transversal to the fins. Numerical results on the effect of dimensionless pressure drop and the thermal conductivity ratio on the optimal configuration are reported. Results obtained from numerical analyses are comparable to those in the open literature. The results also show that the flow structure performs best when the fin diameters and heights are non-uniform.
This paper describes analytically the process in which a body of glass is heated, softened and eroded (‘melted’ away) by direct contact with a solid surface of much higher temperature. This surface can slide relative to the body of glass. The glass is modelled as a liquid the viscosity of which varies as T −n , where T is the absolute temperature and n is a number in the range 10–20. The temperature and velocity distributions in the thin layer of hot (soft) glass are determined. Simple calculation procedures are developed for the rate at which the block of glass is eroded, and for the general relationship between the forces exerted on the block and the combined heat transfer and lubrication phenomenon that governs the glass removal process.
This article explores the causal relationship between freedom, the imagined (perfection), and the observed design in nature (diversity). The presentation is with familiar examples of perfection and diversity over space and in time: the configurations and rhythms of moving and changing designs of people, animals, athletes, technologies, universities, and science itself: divergent evolution hand-in-glove with convergent evolution.
A new edition of the bestseller on convection heat transfer A revised edition of the industry classic, Convection Heat Transfer, Fourth Edition, chronicles how the field of heat transfer has grown and prospered over the last two decades. This new edition is more accessible, while not sacrificing its thorough treatment of the most up-to-date information on current research and applications in the field. One of the foremost leaders in the field, Adrian Bejan has pioneered and taught many of the methods and practices commonly used in the industry today. He continues this book's long-standing role as an inspiring, optimal study tool by providing: Coverage of how convection affects performance, and how convective flows can be configured so that performance is enhanced, how convective configurations have been evolving, from the flat plates, smooth pipes, and single-dimension fins of the earlier editions to new populations of configurations: tapered ducts, plates with multiscale features, dendritic fins, duct and plate assemblies (packages) for heat transfer density and compactness, etc. New, updated, and enhanced examples and problems that reflect the author's research and advances in the field since the last edition. Complete with hundreds of informative and original illustrations, Convection Heat Transfer, Fourth Edition is the most comprehensive and approachable text for students in schools of mechanical engineering.
In this paper we show that the sizes (weights) of heat and fluid flow systems that function on board vehicles such as aircraft can be derived from the maximization of overall (system level) performance. The total weight of the aircraft dictates its fuel requirement. The principle owes its existence to two effects that compete for fuel. Components, power plants and refrigeration plants operate less irreversibly when they are larger. Less irreversibility means less fuel needed for their operation. On the other hand, larger sizes add more to the mass of the aircraft and to the total fuel requirement. This tradeoff pinpoints optimal sizes. The principle is illustrated based on three examples: a power plant the size of which is represented by a heat exchanger, a counterflow heat exchanger without fluid flow irreversibility, and a counterflow heat exchanger with heat transfer and fluid flow irreversibilities. The size optimization principle is applicable to the organs of all flow systems, engineered (e.g., vehicles) and natural (e.g., animals).
In this paper we use thermodynamics to show why larger flow systems are more efficient than smaller flow systems. This trend is visible across the board, from power generation and refrigeration, to vascular design and animal design. The reason is that larger systems have larger flow passages and heat transfer surfaces, and do not strangle the flow of the currents that must flow. Three fundamental examples show how to predict this trend: a power plant with fluid friction and finite heat transfer area, a vascular body with building blocks optimized at every level of assembly, and a vascular body designed based on a duct-pairing algorithm. The examples show that the performance improves as the size increases, and that the architecture changes with the size. These constructal-design features constitute the basis for scaling up and scaling down the configurations of flow systems, from desktop models to life size installations.
This paper describes a structured procedure to optimize the internal structure (relative sizes, spacings), single cells thickness, and external shape (aspect ratios) of a polymer electrolyte membrane fuel cell (PEMFC) stack so that net power is maximized. The constructal design starts from the smallest (elemental) level of a fuel cell stack (the single PEMFC), which is modeled as a unidirectional flow system, proceeding to the pressure drops experienced in the headers and gas channels of the single cells in the stack. The polarization curve, total and net power, and efficiencies are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed stack total volume. There are two levels of optimization: (i) the internal structure, which accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, together with the single cells thickness, and (ii) the external shape, which accounts for the external aspect ratios of the PEMFC stack. The flow components are distributed optimally through the available volume so that the PEMFC stack net power is maximized. Numerical results show that the optimized single cells internal structure and stack external shape are “robust” with respect to changes in stoichiometric ratios, membrane water content, and total stack volume. The optimized internal structure and single cells thickness, and the stack external shape are results of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the stack headers and single-cell gas channels. It is shown that the twice maximized stack net power increases monotonically with total volume raised to the power 3/4, similarly to metabolic rate and body size in animal design.
In this paper we use the constructal method to determine the optimal distribution and sizes of discrete heat sources in a vertical open channel cooled by natural convection. Two classes of geometries are considered: (i) heat sources with fixed size and fixed heat flux, and (ii) single heat source with variable size and fixed total heat current. In both classes, the objective is the maximization of the global thermal conductance between the discretely heated wall and the cold fluid. This objective is equivalent to minimizing temperature of the hot spot that occurs at a point on the wall. The numerical results show that for low Rayleigh numbers (∼102), the heat sources select as optimal location the inlet plane of the channel. For configuration (i), the optimal location changes as the Rayleigh number increases, and the last (downstream) heat source tends to migrate toward the exit plane, which results in a non-uniform distribution of heat sources on the wall. For configuration (ii) we also show that at low and moderate Rayleigh numbers (Ra M ∼102 and 103) the thermal performance is maximized when the heat source does not cover the entire wall. As the flow intensity increases, the optimal heat source size approaches the height of the wall. The importance to free the flow geometry to morph toward the configuration of minimal global resistance (maximal flow access) is also discussed.
This is a fundamental study of the phenomenon of natural convection in the region formed by a vertical warm wall rising above a cold horizontal wall, or in the region between a cold vertical wall extending downward from a warm horizontal surface. The study consists of scale analysis, numerical simulations, and an asymptotic solution of the low Rayleigh number limit. The scale analysis predicts the persistence of a single cell in the corner region, regardless of Rayleigh number. The cell migrates toward the corner as the Rayleigh number RaH increases: the flow rate and the net heat transfer rate vary as Ra1/7H. The scale analysis is verified qualitatively and quantitatively by means of numerical experiments in the range RaH =103–107, Pr=0.7–7, H/L=1–4, where Pr is the Prandtl number and H/L is the height/length ratio of the corner region. Additional numerical simulations are presented for cases where one or both walls have uniform heat flux; in these cases, the heat transfer rate shows nearly the same behavior as when the corner walls are both isothermal. The asymptotic solution for the RaH→0 limit shows that the flow field is relatively insensitive to whether the wall temperature varies continuously or discontinuously through the corner point.
Technical Briefs Mass Transfer to Natural Convection Boundary Layer Flow Driven by Heat Transfer K. R. Khair, K. R. Khair Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 Search for other works by this author on: This Site PubMed Google Scholar A. Bejan A. Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information K. R. Khair Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 A. Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 J. Heat Transfer. Nov 1985, 107(4): 979-981 (3 pages) https://doi.org/10.1115/1.3247535 Published Online: November 1, 1985 Article history Received: October 31, 1984 Online: October 20, 2009
