This paper outlines a new direction for fundamental heat transfer: a multidisciplinary approach (combined heat transfer and strength of materials) in the conceptual design of structures that have two functions, mechanical strength and resistance (survival) in the presence of sudden thermal attack. The two functions are considered simultaneously, from the start of conceptual design. This is unlike traditional approaches, where structures are optimized for mechanical strength alone, or for thermal resistance alone. In the first part of the paper, the profile of a beam loaded in bending is optimized by maximizing the lifetime in the presence of sudden heating. The propagation of the heat wave through the beam causes softening, because of the gradual transition from elastic behavior to thermoplastic behavior. In the second part of the paper, the subject is a beam of concrete reinforced with steel bars. It is shown that the clash between the mechanical and thermal objectives of the beam generates the shape of the beam cross-section, and the position of the steel bars in the beam cross-section. The generation of optimal architecture for maximal global performance under global constraints in freely morphing systems is constructal design. On the background of the constructal architectures that have been developed so far, the present paper outlines the first steps toward the constructal design of multiobjective (multidisciplinary) architectures.
This paper documents a numerical study of time-dependent melting dominated by natural convection in a cylinder filled with a phase change material. In accord with constructal design, the search is for effective heat-flow architectures. The volume-constrained improvement of the designs for heat flow begins with assuming the simplest structure, where a single line serves as heat source. Next, the heat source is endowed with freedom to change its shape as it grows. The objective of the numerical simulations is to discover the geometric features that lead to the fastest melting process. The results show that the heat transfer rate density increases as the complexity and number of degrees of freedom of the structure are increased. Furthermore, the angles between heat invasion lines have a minor effect on the global performance compared to other degrees of freedom: number of branching levels, stem length, and branch lengths. The effect of natural convection in the melt zone is documented.
The first ever NATO Advanced Study Institute devoted to `Thermodynamics and the Optimization of Complex Energy Systems' was held in July 1998 in Neptun, Romania. The ASI unified the field by bringing together leading researchers from engineering and physics, and from West and East. This note outlines the objectives and proceedings of the Institute, which reviewed the most recent advances in exergy analysis, entropy-generation minimization and thermoeconomics. Directions for future developments (e.g. constructal theory) are also outlined.
In this article we show that the global thermal resistance to flow between a volume and one point can be reduced to unprecedented levels by shaping the external boundary of each volume element. This degree of freedom is optimized, next to internal features such as the shape and volume fraction of the high-conductivity channels. The volume is covered in a sequence of optimization and assembly steps that proceeds toward larger sizes. The resulting architecture is a leaf-like tree structure with high-conductivity nerves and low-conductivity leaf material. The same constant resistance characterizes the flow from each point on the periphery of the structure to the common sink point. Nearly optimal structures in which the leaf shapes are replaced by needle-like (triangle-in-triangle) shapes are also developed. The fractal-like character of these designs and their relevance to the trend toward fractal-like properties in natural flow structures are discussed in the concluding section of the article.
Here we propose a heat transfer framework for how human-to-human interaction spreads everything on the landscape: disease, goods, knowledge, news, technology, science, language and culture. We show that the phenomenon of “human spreading” shares key features with phenomena that are fundamental in physics (heat, electricity, species, Darcy fluid flow), which spread through continua. As example for discussion and illustration, we construct this theoretical framework by using the early phase of the coronavirus outbreak, from before May 2020. The human spreading phenomenon (S curve) is unveiled systematically by using a minimum of measurable parameters: the number of persons with whom one person comes in contact, the radial size of each step in the growth of the swept territory, the radial scale of the inhabited territory, and the directions in which infrastructure (e.g., air routes) are available for long and fast spreading. The resulting configuration of spreading is a multiscale assembly of clusters of fast channels embedded in interstices with slow diffusion. The configuration is dendritic, where each direction of long and fast spreading is covered by a finger of clusters, and each finger generates its own ramifications. The similarities between this configuration and the dendritic architectures for heat and fluid flow through heterogeneous media are discussed.
This paper describes the geometric optimization of the internal structure of a volume that generates heat at every point and is cooled by a single stream. According to the constructal method, the optimization of the cooling design is organized in a sequence of steps that begins with the smallest volume element and continues with larger assemblies (constructs) of previously optimized building blocks. Optimized at each level of assembly are the external shape of the construct and the relative thickness of each duct for fluid flow. It is shown that in the end the fluid channels form a tree network that cools every point of the given volume. Length scales smaller than the thickness of the elemental volume are reached by conduction through the solid heat-generating material. Two fluid channel geometries are optimized: parallel-plate channels and round tubes.
This study questions the view that the degree of thennodynamic imperfection (second law efficiency, η 11) of the refrigeration and liquefaction plants that have been built does not depend on the refrigeration load temperature T l . It is shown first that when plotted correctly, the empirical η II values decrease as T l decreases. Two theoretical arguments are offered as explanations for this trend. The first argument is based on a refrigeration plant model the irreversibility of which is due solely to the ‘internal’ heat transfer that passes directly through the machine all the way to T l . The second argument is based on a more refined model in which the refrigeration plant irreversibility is due to three heat transfer phenomena: the internal heat transfer (retained also in the first model), the external temperature difference between refrigeration plant and ambient, and the external temperature difference between the refrigeration load and the cold end of the refrigeration plant. It is shown that there exist optimum ways of allocating heat transfer equipment to the distinct parts of the plant, if the objective is to maximize the refrigeration capacity of the plant. Both theoretical arguments lead to the conclusion that η II generally decreases as T l . decreases.
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...
The paper presents a treatment of sensible heat energy storage units as systems intended to store useful work. An analysis of the thermodynamic irreversibilities associated with storing energy from a hot gas source as sensible heat in huge liquid baths points out two important trade-offs: 1. There exists an optimum, well-defined quantity of hot gas to be used in order to maximize the useful work stored in the liquid bath. Using more than this optimum quantity in the hope of maximizing the amount of thermal energy stored as sensible heat leads to severe thermodynamics losses. 2. There exists an optimum relationship among the gas-liquid heat exchanger design parameters which minimizes the system irreversibility while maximizing its capability of storing useful work. This relationship provides a procedure for estimating the heat exchanger optimum number of transfer units (Ntu). Increasing the Ntu above the optimum in order to upgrade the heat exchanger effectiveness and the thermal energy storage capability leads to prohibitive losses due to fluid friction in the heat exchanger channels. The existence of the two optima demonstrates that designing sensible heat units for maximum thermal energy storage does not necessarily amount to thermodynamically optimizing such systems.
This note offers a clear view of heat transfer fundamentals in terms of ‘heat tubes’, which are macroscopic architectures for the flow of energy through complex energy systems. The note focuses on heat tubes with conduction and convection, although heat tubes with radiation through stacks of radiation shields have also been treated in the literature. It is shown how to shape a heat tube and how to cool it along its length so that its thermodynamic performance evolves. Several instances of confusion are clarified along the way.
Here, I show that “entransy” has no meaning in physics, because, at bottom, it rests on the false claim that in order to transfer heat to a solid body of thermodynamic temperature T, the heat transfer must be proportional to T. Entransy “dissipation” is a number proportional to well known measures of irreversibility such as entropy generation and lost exergy (destroyed available work). Furthermore, the “principle of entransy dissipation minimization” adds nothing to existing work based on minimum entropy generation, minimum thermal resistance, and constructal law. The broader trend illustrated by the entransy hoax is that it is becoming easy to take an existing idea, change the keywords, and publish it as new.
No abstract is provided for this article.
The phenomenon of natural convection caused by combined temperature and concentration buoyancy effects is studied analytically and numerically in a rectangular slot with uniform heat and mass fluxes along the vertical sides. The analytical part is devoted to the boundary layer regime where the heat and mass transfer rates are ruled by convection. An Oseen-linearized solution is reported for tall spaces filled with mixtures characterized by Le = 1 and arbitrary buoyancy ratios. The effect of varying the Lewis number is documented by a similarity solution valid for Le >1 in heat-transfer-driven flows, and for Le <1 in mass-transfer-driven flows. The analytical results are validated by numerical experiments conducted in the range 1≤H/L≤4, 3.5×105≤Ra≤7×106, −11≤n≤9, 1≤Le≤40, and Pr=0.7, 7. “Massline” patterns are used to visualize the convective mass transfer path and the flow reversal observed when the buoyancy ratio n passes through the value −1.
In this paper, we review the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centred at O. This is a fundamental problem in energy engineering: the distribution of fluid, energy, electric power, etc., from points to surrounding areas. This problem is also fundamental in heat transfer and electronics cooling: how to bathe and cool with a single stream of coolant a disc-shaped area or volume that generates heat at every point. This paper outlines, first, a direct route to the construction of effective tree-shaped flow structures. The starting point is the optimization of the shape of each elemental area, such that the length of the flow path housed by the element is minimized. Proceeding towards larger and more complex structures—from elements to first constructs, second constructs, etc.—the paper develops tree-shaped flow structures between one point and a straight line, as an elemental problem, and a circle and its centre. We also consider the equivalent tree-shaped networks obtained by minimizing the pressure drop at every step of the construction, in accordance with geometric constraints. The construction method is applied to a fluid flow configuration with laminar fully developed flow. It is shown that there is little difference between the two methods. The minimal-length structures perform very close to the fully optimized designs. These results emphasize the robustness of optimized tree-shaped flows. Copyright © 2003 John Wiley & Sons, Ltd.
This paper addresses the fundamental problem of how to connect a heat generating volume to a point heat sink by using a finite amount of high-conductivity material that can be distributed through the volume. The problem is one of optimizing the access (or minimizing the thermal resistance) between a finite-size volume and one point. The solution is constructed by covering the volume with a sequence of building blocks, which proceeds toward larger sizes (assemblies), hence, the “constructal” name for this approach. Optimized numerically at each stage are geometric features such as the overall shape of the building block, its number of constituents, and the internal distribution of high-conductivity inserts. It is shown that in the optimal design, the high-conductivity material has a distribution with the shape of a tree. Every aspect of the tree architecture is deterministic: the shapes of the largest assembly and all its constituents, the number of branches at each level of assembly, the relative position of building blocks in each assembly, and the relative thicknesses of successive branches. The finer, innermost details of the tree architecture (e.g., the branching angle) have a negligible effect on the overall thermal resistance. The main conclusion is that the structure, working mechanism, and minimal resistance of the tree network can be obtained deterministically, and that the constrained optimization of access routes accounts for the macroscopic structure in nature.
This article illustrates the fundamental features of lateral penetration of natural convection into a horizontal porous layer in lateral communication with a heat reservoir. It is found that the important group governing the fluid mechanics of the phenomenon is the Darcy-modified Rayleigh number Ra based on longitudinal (horizontal) permeability and on transversal (vertical) thermal diffusivity. It is shown that the buoyancy-driven flow has flattened C-shaped streamlines and isotherms. The flow penetrates laterally to a distance of order H Ra1/2, where H is the height of the porous layer. The net heat exchange between the porous structure and the lateral heat reservoir is described by a Nusselt number result of the type Nu ∼ Ra1/2. The effect of horizontal wall temperature gradient on penetration length and heat transfer is discussed. The engineering importance of these findings is illustrated by examples related to the conceptual design of porous winding structures for rotating superconducting electric machines.
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