Showing papers on "Constructal law published in 2005"

The constructal law of organization in nature: tree-shaped flows and body size

Abstract: The constructal law is the statement that for a flow system to persist in time it must evolve in such a way that it provides easier access to its currents. This is the law of configuration generation, or the law of design. The theoretical developments reviewed in this article show that this law accounts for (i) architectures that maximize flow access (e.g. trees), (ii) features that impede flow (e.g. impermeable walls, insulation) and (iii) static organs that support flow structures. The proportionality between body heat loss and body size raised to the power 3/4 is deduced from the discovery that the counterflow of two trees is the optimal configuration for achieving (i) and (ii) simultaneously: maximum fluid-flow access and minimum heat leak. Other allometric examples deduced from the constructal law are the flying speeds of insects, birds and aeroplanes, the porosity and hair strand diameter of the fur coats of animals, and the existence of optimal organ sizes. Body size and configuration are intrinsic parts of the deduced configuration. They are results, not assumptions. The constructal law extends physics (thermodynamics) to cover the configuration, performance, global size and global internal flow volume of flow systems. The time evolution of such configurations can be described as survival by increasing performance, compactness and territory.

Constructal multi‐scale and multi‐objective structures

Abstract: SUMMARY This is a review of recent progress on constructal design made in two directions: multi-scale flow structures, and multi-objective design. The first direction is associated with the maximization of heat transfer rate density in a fixed volume in the limit of decreasing length scales, where boundary layers touch, and optimized channels are no longer slender. In the first example of this type, spacings are optimized based on the intersection of asymptotes method. In the second, the heat transfer density is further increased by placing progressively smaller plates in the entrances of the channels formed by the first generation of plates. In the third example, the placement of discrete heat sources on a vertical wall with natural and forced convection is optimized. The second direction is the discovery of architectures that result from two competing objectives, for example, mechanical strength and thermal insulation. It is shown that the internal configuration of a cavernous brick wall can be deduced from the clash between the two objectives. The same concept can be used to optimize the shape and structure of support beams that must be strong and, at the same time, must resist sudden attack by intense heating. Copyright # 2005 John Wiley & Sons, Ltd.

A Constructal Approach to the Optimal Design of Photovoltaic Cells

Abstract: The constructal law is used for the minimization of the photovoltaic cells (PVC) electrical series resistance. In this paper we report a theoretical, step by step construction of optimal PVC, from the smallest, elemental cell to the largest assembly that relies on the minimisation of the maximum voltage drop subject to volume (material) constraints. This completely deterministic approach produces optimal geometric shape for each assembly level, the optimal number and orientation of constituents within each new, higher order assembly and the optimal size of each new collector (metallic) path.

Thermodynamic optimization of global circulation and climate

Abstract: SUMMARY The constructal law of generation of flow structure is used to predict the main features of global circulation and climate. The flow structure is the atmospheric and oceanic circulation. This feature is modelled as convection loops, and added to the earth model as a heat engine heated by the Sun and cooled by the background. It is shown that the dissipation of the power produced by the earth engine can be maximized by selecting the proper balance between the hot and cold zones of the Earth, and by optimizing the thermal conductance of the circulation loops. The optimized features agree with the main characteristics of global circulation and climate. The robustness of these predictions, and the place of the constructal law as a selfstanding principle in thermodynamics, are discussed. Copyright # 2005 John Wiley & Sons, Ltd.

Constructal Design of Forced Convection Cooled Microchannel Heat Sinks and Heat Exchangers

Abstract: Heat transfer from arrays of circular and non-circular ducts subject to finite volume and constant pressure drop constraints is examined. It is shown that the optimal duct dimension is independent of the array structure and hence represents an optimal construction element. Solutions are presented for the optimal duct dimensions and maximum heat transfer per unit volume for the parallel plate channel, rectangular channel, elliptic duct, circular duct, polygonal ducts, and triangular ducts. Approximate analytical results show that the optimal shape is the isosceles right triangle and square duct due to their ability to provide the most efficient packing in a fixed volume. Whereas a more exact analysis reveals that the parallel plate channel array is in fact the superior system. An approximate relationship is developed which is very nearly a universal solution for any duct shape in terms of the Bejan number and duct aspect ratio. Finally, validation of the relationships is provided using exact results from the open literature.Copyright © 2005 by ASME

Emergence of asymmetry in constructal tree flow networks

Abstract: In this paper, we demonstrate that asymmetry in fluid distribution tree networks emerges from power requirement minimization, under global volume constraint. We have discovered several levels of asymmetry in optimal trees: different pipe lengths at the same level of branching, different mass flow rates at junctions or bifurcations, and different main branches to build the optimal dendrite. The emergence of asymmetry in optimal tree networks (man-made or natural) is a result of the optimization: it is not an assumption or a modeling feature. The constructal method that we used to discover asymmetry is predictive, and this distinguishes it from descriptive methods such as fractal geometry.

Constructal theory of energy-system and environment flow configurations

Abstract: This paper outlines the place occupied by the constructal law in thermodynamics, and provides a vision of the future development of energy engineering as a transdisciplinary science of systems of systems. Natural and man-made flow systems do not exist in isolation. The optimal balance between engineered flow systems and their surroundings is achieved through the optimal distributing of thermodynamic imperfections. The paper traces the development of constructal theory from a principle of maximisation of flow access in morphing configurations to engineering discoveries, such as optimal internal spacings, tree-shaped flow networks, machine flight, and multi-scale flow structures for maximal heat transfer density. The introduction of constructal theory and design in thermodynamics education is also discussed.

Tree-shaped structures for cold storage

Abstract: 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.

Constructal Optimization of Top Contact Metallization of a Photovoltaic Solar Cell

Abstract: A top contact metallization of a photovoltaic solar cell collects the current generated by incident solar radiation. Several power-loss mechanisms are associated with the current flow through the front contact grid. The design of the top metal contact grid is one of the most important areas of efficient photovoltaic solar cell design. In this paper, an approach based on the constructal theory is proposed to design the grid pattern in a photovoltaic solar cell, minimizing total resistive losses. Constructal theory explains the geometric form (shape and structure) of most volume-to-point systems in nature. In this paper, the applicability of the constructal theory to design top contact metallization for a photovoltaic solar cell has been extended.

Constructal Theory of the Minimum Requirements for Forced Convection Cooling Solutions

Abstract: The advances in microfluidics and microelectronics bring with them the need to provide new cooling solutions for many applications. A number of technologies are under development for forced convection cooling at the microscale. This short paper, through the new constructal theory of Bejan, presents the minimum velocity requirements of any such technology to be truly useful in a new design. Thus the theory presented in this paper, should form the first step in the design process of any new forced cooling technology for mini-micro scale applications. Furthermore, it is demonstrated that the use of the constructal theory provides a heightened level of understanding to the problem of forced convection, while simultaneously deriving the empirical correlations proposed in the literature over the past number of decades.Copyright © 2005 by ASME

Sveltness, Freedom to Morph, and the Constructal Design of Multi-Scale Flow Structures

Abstract: This paper reviews recent progress on constructal theory and design The emphasis is on the development of multi-scale, nonuniformly distributed flow structures that offer increased compactness (eg, heat transfer density) Examples are counterflow heat exchangers with tree-shaped hot and cold streams, and tree architectures on a disc Every flow system has a global property called sveltness (Sv), which is the ratio between its external (global) length scale and its internal length scale (V1/3 ), where V is the volume occupied by all the ducts Emphasis is placed on the development of simple strategies for decreasing the computational cost required by the development of such structures The generation of multi-scale flow configurations is a process that can be projected on a diagram having global performance on the abscissa and degrees of freedom on the ordinate This process rules the development (evolution) of all flow configurations for systems with global objective, global constraints and freedom to morphCopyright © 2005 by ASME

The Optimal Shape for a Unit PEM Fuel Cell

Abstract: This paper develops a mathematical model and a structured procedure to optimize the internal structure (relative sizes, spacings) and external shape (aspect ratios) of a unit PEM fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the unit PEM fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels of optimization: (i) the internal structure, which basically accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, and (ii) the external shape, which accounts for the external aspect ratios of a square section plate that contains all unit PEM fuel cell components. The available volume is distributed optimally through the system so that the net power is maximized. Temperature and pressure gradients play important roles, especially as the fuel and oxidant flow paths increase. Numerical results show that the optimized internal structure is “robust” with respect to changes in external shape. The optimized internal structure and external shape are results of the optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the gas channels. Directions for future improvements at the PEM fuel cell stack level in constructal geometric optimization are discussed.Copyright © 2005 by ASME

Constructal Design: The Generation of Multi-Scale Heat and Fluid Flow Structures

Abstract: This is a new constructal design concept for generating multi-scale structures in natural convection with the objective of maximizing the heat transfer density, or the heat transfer rate per unit of volume. The flow volume is filled with vertical equidistant heated blades of decreasing lengths. The spacings between the blades are optimized for maximal heat transfer density. Smaller blades are installed in the center plane between two adjacent longer blades, in the entrance region where the boundary layers are thin and the fluid is unheated. New generations of smaller blades are added stepwise to the multi-scale structure. Constructal theory is applied to each new generation of blades. The above figures show the dimensionless numerical temperature distribution inside a flow volume composed of four main channels, for optimized structures with one, two and three length scales, at Ra = 10 and Pr = 0.7. The temperature ranges between two main colors, red ( T~ = 1) and blue ( T~ = 0). As the number of length scales increases, the color red is distributed more uniformly, illustrating the progress towards maximal heat transfer rate density, i.e. the constructal principle of \"optimal distribution of imperfection\". The average heat transfer density increases by 12% from the simplest structure (one length scale) to two length scales, and by 6% from two to three length scales. ______________ * Corresponding Author: (akd3@duke.edu) Tel.: +1 (919) 660-5299 Fax: +1 (919) 660-8963