This paper outlines a completely deterministic (“constructal”) theory of why quasi‐similar street patterns exist, how they form, and how they grow in time. The function of the street network is to connect a finite area to a single destination point. The new idea is that the network of streets evolves in time , by starting with the optimization of the shape of the smallest area element that is serviced by the network. Next, the optimized area elements are assembled into a larger area element which is again optimized for shape. This sequence of optimization & organization is repeated in finite‐size steps, toward larger quasi‐similar assemblies. The optimization consists of minimizing the travel time between each point of a finite area and a common point of destination. The network is constructed (optimized, organized) in time. Every single geometric feature of the network is the result of pure, deterministic theory: the shape of each area element, the shape of each new (larger) assembly, the optimal number of parts in each assembly, the relative orientation of successive streets, and the optimal width of each street.
Since we have dealt with natural convection and forced convection in some detail, our treatment of mixed convection can be brief. It is guided by the review paper by Lai, Prasad, and Kulacki (1991). We start with a treatment of boundary layer flow on heated plane...
In the examples of forced and natural convection discussed until now, the fluid that flowed through the pores did not experience a change of phase, no matter how intense the heating or cooling effect. In the present chapter we turn our attention to situations in...
No abstract is provided for this article.
Constructal theory is the view that the generation of “designedness” in nature is a universal (physics) phenomenon that can be based on principle (the constructal law): “For a finite-size flow system to persist in time (to live) its configuration must change in time so that it provides greater and greater access to its currents”. This principle predicts natural form across the board, from river basins to animal design, engineering and social dynamics. In this introduction to the theory we show examples of vascular designs at large and small scales and multi-objective flow configurations.
We consider the problem of cooling a two-dimensional heat generating conducting volume with one heat sink, such that the smallest features of the internal structure are so small that the conventional description of conduction breaks down. The effective thermal conductivity exhibits the “size effect,” and is governed by the smallest structural dimension, which is comparable with the mean free path of the energy carriers. According to the constructal method, the development of the internal cooling structure proceeds from small to large, in steps of geometric optimization and assembly. This starts at the elemental level, where there is only one high-conductivity layer for collecting and evacuating the heat. The shape of the smallest volume can be optimized for minimal thermal resistance. Next, a first construct is formed by optimizing the number of assembled elements and the internal geometric features of the assembly. The method is repeated at the second construct level, where several first constructs are grouped so that their global thermal resistance is minimal. The construction reveals an internal multiscale structure shaped as a tree, where the spaces between the smallest branches are ruled by nanoscale heat transfer. It is shown that the transition from regions with nanoscale heat transfer to regions with conventional heat transfer is governed not only by the smallest dimensions, but also by heterogeneity (relative amounts of high- and low-conductivity materials).
No abstract is provided for this article.
The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world.
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 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.
The growth or collapse of a local normal zone in a superconducting winding structure saturated with single phase liquid helium (composite superconductor) is studied analytically. The history of a given temperature disturbance is derived from the solution to the transient heat conduction equation in a one-dimensional infinite solid with temperature dependent rate of internal heat generation, communicating laterally with a channel filled with stagnant helium. The combined diffusion by axial heat conduction and lateral heat transfer to the helium channel and its effect on the collapse or growth behaviour of a local disturbance is presented analytically. The paper develops a theoretical criterion for local stability (recovery) expressed in terms of dimensionless groups accounting for heat generation in the normal zone, metal axial conduction cooling, lateral cooling provided by the helium channel and, most importantly, the amount and spatial extent of the sudden release of energy responsible for the local disturbance.
List of Symbols Thermodynamics Concepts and Laws Definitions Closed Systems Open Systems The Momentum Theorem Useful Steps in Problem Solving The Temperature-Energy Interaction Diagram, and the Entropy Interaction-Energy Interaction Diagram Problems Entropy Generation and Exergy Destruction The Gouy-Stodola Theorem Systems Communicating with More than One Heat Reservoir Adiabatic Systems Exergy Analysis of Steady Flow Processes Exergy Analysis of Non-Flow Processes Characteristic Features of Irreversible Systems and Processes Problems Entropy Generation in Fluid Flow Relationship between Entropy Generation and Viscous Dissipation Laminar Flow Turbulent Flow The Transition Buckling Theory of Turbulent Flow Entropy Generation in Isothermal Turbulent Flow The Bernoulli Equation Entropy Generation in Heat Transfer The Local Rate of Entropy Generation in Convective Heat Transfer Fluid Friction vs. Heat Transfer Irreversibility Internal Flows External Flows Conduction Heat Transfer Convective Mass Transfer General Heat Exchanger Passage Heat Transfer Augmentation Techniques Problems Heat Exchangers Counterflow Heat Exchangers Heat Exchangers with Negligible Pressure Drop Irreversibility The Three-Part Structure of Heat Exchanger Irreversibility Two-Phase-Flow Heat Exchangers Other Heat Exchanger Entropy Generation Studies Distribution of Heat Exchanger Area on the Absolute Temperature Scale Distribution of Heat Transfer Area in Counterflow Heat Exchangers Problems Insulation Systems Power Plants and Refrigeration Plants as Insulation Systems The Generation of Entropy in an Insulation with Fixed Geometry Optimum Continuous Cooling Regime Counterflow Heat Exchangers as One-Dimensional Insulations Parallel Insulations Intermediate Cooling or Heating of Insulation Systems for Power and Refrigeration Plants Problems Storage Systems Sensible Heat Storage Optimum Heating and Cooling Processes Subject to Time Constraint Hot Storage vs. Cold Storage Latent Heat Storage Power Generation Model with Bypass Heat Leak and Two Finite-Size Heat Exchangers Power Plant Viewed as an Insulation Between Heat Source and Ambient Combined-Cycle Power Plant Optimal Combustion Chamber Temperature Other Power Plant Optimization Studies Why Maximum Power Means Minimum Entropy Generation Rate Maximum Power from Fluid Flow Problems Solar-Thermal Power Generation Models with Collector Heat Loss to the Ambient Collector-Ambient Heat Loss and Collector-Engine Heat Exchanger Collector-Ambient Heat Loss and Engine-Ambient Heat Exchanger Storage by Melting Extraterrestrial Solar Power Plant Nonisothermal Collectors Time-Varying Conditions Other Areas of Solar Power Conversion Study Problems Refrigeration Refrigeration Plant Model with Heat Transfer Irreversibilities Model with Heat Leak in Parallel with Reversible Compartment Model with Cold End Heat Exchanger and Room Temperature Heat Exchanger Minimization of the Heat-Leak Entropy Generation Problems Time-Dependent Operation Defrosting Refrigerators Cleaning the Heat Exchanger of a Power Plant Power Plants Driven by Heating from a Bed of Hot Dry Rock Maximum Rate of Ice Production Problems Appendices Local Entropy Generation Rate Variational Calculus Author Index Subject Index
In this paper we determine the fundamental relation between global performance and flow configuration (constructal design) in the case of steam power generation with superheater and reheater placed in parallel in the same stream of hot gases of combustion. The superheater heats the steam for the high pressure turbine, and the reheater supplies steam to the low pressure turbine. Both turbines operate irreversibly. We consider superheaters and reheaters with balanced counter flows and unbalanced counter flows. The total heat transfer area (or the overall number of heat transfer units) is finite. We show that the heat transfer area can be allocated to the superheater and reheater such that the overall power output is maximum. The optimal area allocation ratio is reported for two scenarios: designs with and without a maximum allowable steam temperature.
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).
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.
