This paper addresses the fundamental problem of how to facilitate the flow of heat across a conducting slab heated from one side. Available for distribution through the system is a small amount of high-conductivity material. The constructal method consists of optimizing geometrically the distribution of the high-conductivity material through the material of lower conductivity. Two-dimensional distributions (plate inserts) and three-dimensional distributions (pin inserts) are optimized based on the numerical simulation of heat conduction in a large number of possible configurations. Results are presented for the external and internal features of the optimized architectures: spacings between inserts, penetration distances, tapered inserts and constant-thickness inserts. The use of optimized pin inserts leads consistently to lower global thermal resistances than the use of plate inserts. The side of the slab that is connected to the high-conductivity intrusions is in effect a “rough” surface. This paper shows that the architecture of a rough surface can be optimized for minimum global contact resistance. Roughness can be designed.
This is a review of a new class of fundamental results concerning the optimal spacing of parallel heat generating boards arranged in a stack of fixed volume. The cooling is by single-phase laminar flow, in natural convection or forced convection. Several board models...
This paper is a study of the optimal geometric layout of schemes for distributing hot water uniformly over an area. Constrained are the amount of insulation material, the volume of all the pipes, and the amount of pipe wall material. Unknown are the distribution of insulation over all the links of the network, and the configuration of the network itself. The main focus is on how the geometric configuration may be selected in the pursuit of maximized global performance, and how closely a non-optimal configuration performs to the highest level. Three global optimization criteria are considered, and they all yield similar results with respect to the distribution of insulation: the maximization of the temperature of the hot water received by the farthest user, the minimization of the total heat loss of the network, and the maximization of the delivery temperature averaged over all the users. Three configurations are optimized: (a) an area covered by a coiled stream, where all the users are aligned on the same stream, (b) a sequence of tree-shaped flows on square areas in which each area construct is made up of four smaller area constructs, and (c) a sequence of tree-shaped flows where each area construct is made up of two smaller area constructs. It is shown that the tree-shaped designs (b) and (c) outperform consistently and significantly the coiled stream design (a). The tree designs obtained by pairing (c) are better than the square tree constructs (b) and, in addition, they deliver water at the same temperature to all the users spread over the territory. The optimized tree networks (b) and (c) approach the same high level of global performance as their complexity increases. Optimized tree-shaped flow designs are robust.
In this paper we use constructal theory to determine the 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 total volume of fin materials. The dimensions of the optimized configuration are the result of balancing conduction along the fins with convection transversal to the fin. The resulting flow structure has multiple scales that are distributed non-uniformly through the flow structure. Numerical results on the effect of Reynolds number and the thermal conductivity ratio on the optimal configuration are reported. The results predicted based on scale analysis are in good agreement with the numerical results. The results also show that the flow structure performs best when the fin diameters and heights are non-uniform.
This paper explores the application of constructal design to tree-shaped networks for cold storage. The objective is the maximization of ice production per unit volume, for specified operating conditions (temperature difference, pressure drop, storage time, construction material). Constructal design starts from the smallest scale (elemental volume) and proceeds toward larger and more complex assemblies of elements. Two geometries were optimized at the smallest scale: ice production on parallel plates and on parallel cylinders. The cylindrical geometry offers a greater ice production density. At the next larger scale, the ice production was maximized on arrays of tubes assembled as ‘Z-shaped registers’. The optimization of geometry yielded the spacing between tubes, and the tube diameter and length. The road toward larger and more complex assemblies, and the emergence of dendritic flow architecture are discussed.
This paper documents the process of determining the internal geometric configuration of a component by optimizing the global performance of the installation that uses the component. The example chosen is the crossflow heat exchanger used in the environmental control system of a modern aircraft. The optimization of global performance is achieved by minimizing the total entropy generation rate of the installation. There are three degrees of freedom in the heat exchanger configuration (the length-to-width and height-to-width aspect ratios, and the separator plate spacing ratio), which is subjected to two global constraints: total component volume, and total wall material volume (or weight/density) of wall material. Numerical results show how the optimal configuration responds to changes in specified external parameters such as volume, weight, Mach number, diffuser inlet cross-sectional area, and the pressure at which the cabin air is initially bled from the engine compressor. It is shown that the optimal configuration is robust and that major features such as the ratios of channel spacings and flow lengths are relatively insensitive to changes in some of the external parameters. It is also shown that the optimal heat exchanger geometry is insensitive to the thermodynamic irreversibility caused by discharging the used ram air into the ambient.
Constructal theory is the thought that the generation of flow configurations is a phenomenon of physics. Flow configuration, such as the trees of river basins, lungs and city traffic unite the natural with the engineered, and the animate with the inanimate. The physics principle that accounts for the generation of flow configuration everywhere is the constructal law (Bejan, 1997 Bejan, A. 1997. Advanced Engineering Thermodynamics, 2nd, New York: Wiley. [Google Scholar], p. 807): “For a finite-size flow system to persist (to survive) it must morph in time such that it provides easier access to the currents that flow through it”. Why is the constructal law relevant to green energy? For lack of an official definition of “green energy”, we assume that green energy means “man going about his business without changing the environment much”. This thought defines the plane on which constructal theory is relevant. How can human action change the environment the least? The answer is delivered by the constructal law, which prescribes the ways in which humans can engineer machines that use minimal fossil fuels. Everything that Sadi Carnot (1824) Carnot, S. 1824. Reflections on the Motive Power of Fire, and on Machines Fitted to Develop that Power, Paris: Bachelier. [Google Scholar] said about making better machines is the constructal law, and is relevant to green energy. To persist in time (to survive), our flows must flow most easily (most efficiently) and be optimally matched to (i.e., in harmony with) the flows of the environment. Our trees of energy production, economics, business and garbage disposal must “mate” optimally with the trees of the environment (river basins, atmospheric and oceanic circulation).
No abstract is provided for this article.
: This report describes the friction and heat transfer characteristics of a solid surface covered with flexible fibers. The work consisted of analysis, numerical simulations, and laboratory experiments. Chapter 1 documents the pressure drop and heat transfer through bundles of parallel cylinders in a domain that has been overlooked, namely, low Reynolds numbers, arrays that are long in the direction of flow such that the flow is hydraulically and thermally fully developed, and cylinders inclined relative to the flow direction. The heat transfer, friction and mechanical (elastic) interaction between an external laminar flow and a solid surface covered by a layer of fibers is documented in Chapter 2. The flow is initially perpendicular to the surface, and the fibers can bend. The effect of fiber bending,
The rotating superconducting windings of large ac machines must be supplied with enough refrigeration at an adequate temperature. The problems associated with bringing liquid helium to the rotating winding structure are analysed. Existing designs as well as newly proposed systems are used to draw the general guidelines for the design concepts of cooling systems for rotating superconducting windings.
TheDiversity disciplineDiscipline of the scienceScience of formForm also accounts for why objectsObject look similar. In geometryGeometry, the concept is called similitudeSimilitude, and it has strict rulesRules. ObjectsObject and images that are not similar in the...
This article unveils the connection between design in nature and a classic mathematics problem from 1696 to 1697: the brachistochrone. Some flow designs seem to act as obstacles to flow (cataracts, waterfalls, and roll waves), in contradiction with the natural tendency to facilitate flow (round ducts, bifurcated channels, animal speeds, and frequencies). The brachistochrone problem is to determine the curve of shortest-time descent without friction. The connection communicated in this article is that cataracts, roll waves, and the curve of shortest-time descent are about one natural phenomenon, which is predictable. This is demonstrated by comparing two ways for water to flow downhill: (i) on a stepped path (free fall over a dam, followed by accumulation in a large and nearly stagnant pool) and (ii) on a straight incline. We find that (i) is faster than (ii). In conclusion, brachistochrone-like paths are naturally occurring flow configurations, in accord with common observations of natural flow configurations that facilitate access.
This paper outlines a newly emerging body of work that relies on exergy analysis and thermodynamic optimization in the design of energy systems for modern aircraft. Exergy analysis establishes the theoretical performance limit. The minimization of exergy destruction brings the design as closely as permissible to the theoretical limit. The system architecture springs out of this constrained optimization principle. A key problem is the extraction of maximum exergy from a hot gaseous stream that is gradually cooled and eventually discharged into the ambient. The optimal configuration consists of a heat transfer surface with a temperature that decays exponentially in the flow direction. This configuration can be achieved in a counterflow heat exchanger with an optimal imbalance of flow capacity rates. The same optimal configuration emerges when the surface is minimized subject to specified exergy extraction rate. Similar opportunities for optimally matching components and streams exist in considerably more complex systems for power and refrigeration. They deserve to be pursued, and can be approached first at the conceptual level, based on exergy analysis and thermodynamic optimization. The application of such principles in aircraft energy system design also sheds light on the “constructal” design principle that generates all the systems that use powered flight, engineered and natural, cf. constructal theory.
The heat transfer through vertical partitions surrounded by thermally-stratified fluids is studied theoretically and experimentally. The theory is based on the Oseen linearization method. The analytical results show the effect of thermal stratification on the partition temperature, fluid flow and heat flux. The relationship between overall heat transfer (Nusselt number) and the degrees of thermal stratification on both sides of the partition is determined. The experimental part of the study confirms the heat transfer features predicted analytically. In particular, it is shown that the theoretical Nusselt number calculation is in good agreement with experimental measurements. It is shown also that the net heat transfer between the two ends of a rectangular enclosure is proportional to (1 + n)−0.61, where n is the number of vertical partitions inserted in the middle of the enclosure.
Attention is drawn to constructal theory and design, which relies on global maximization of performance in the pursuitofe owsystem architecture. Exergy analysisestablishesthetheoreticalperformancelimit.Thermodynamic optimization (orentropygenerationminimization )bringsthedesignascloselyaspermissibletothetheoreticallimit. The design is destined to remain imperfect because of constraints (e nite sizes, times, and costs ). Improvements are registered by spreading the imperfection, for example, e ow resistances, through the system. Resistances compete againsteach otherand must be optimized together. Optimal spreading meansgeometricform. System architecture is generated by the constructal principle: constrained global optimization and constraints in a morphing e ow medium. In e ows that connect a volume (or area) with one point, the resulting structure is a tree of low-resistance links, and high-resistance interstices. These structures are robust, diverse, and everywhere. A key example is the extraction of maximum exergy from a hot-gas stream that is cooled and discharged into the ambient. The optimal cone guration consists ofa heat transfer surface with a temperaturethat decays exponentially in the e owdirection. Additional examples show that the complete structure of a heat exchanger for an environmental control system can be derived based on this method.
