• Energy Research

Abstract This paper shows that it is possible to distribute a finite amount of insulation in an optimal way that minimizes the overall heat transfer rate from a nonisothermal wall to the ambient. The optimal insulation thickness for a plane wall varies as the square root of the local wall-ambient temperature difference. Corresponding variational-calculus results are developed for cylindrical walls covered with insulation. The heat loss reduction associated with using the optimal thickness is greater when the wall is plane, as opposed to cylindrical, and when the wall temperature variation in the x direction has a greater second derivative, d 2 T / dx 2 . It is shown finally that the best insulation for a single-phase stream suspended in an environment of different temperature is the insulation with uniform thickness.

Abstract This paper describes a hierarchical strategy to developing the optimal internal structure of a round heat-generating body cooled at its center with the help of optimally distributed inserts of high-conductivity material. The sequence begins with optimizing the geometry of the smallest heat generating entity – a sector-shaped elemental volume with the smallest dimension, and a single high-conductivity insert. Many such elements are assembled into disc-shaped constructs, or into sector-shaped constructs in which the elemental volumes are grouped into a formation shaped as a fan. When several sector-shaped constructs are assembled into a disc, they constitute a quasi-radial heat-flow structure in which each high-conductivity insert exhibits one branching. Every geometric detail of the optimized two-material conductive structures is determined based on principle – the minimization of global resistance subject to global constraints (total volume, total volume of high-conductivity material). The inserts of high-conductivity material form structures shape as trees. The global thermal resistance of each tree-shaped construct is reported. The minimization of global thermal resistance is the criterion for choosing between a design with radial inserts and one with branched inserts.

Abstract 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.

Abstract Here we explore the idea that the highest heat transfer rate between two fluids in a given volume is achieved when plate channel lengths are given by the thermal entrance length, i.e., when the thermal boundary layers meet at the exit of each channel. The overall design can be thought of an elemental construct of a dendritic heat exchanger, which consists of two tree-shaped streams arranged in cross flow. Every channel is as long as the thermal entrance length of the developing flow that resides in that channel. The results indicate that the overall design will change with the total volume and total number of channels. We found that the lengths of the surfaces swept in cross flow would have to decrease sizably as number of channels increases, while exhibiting mild decreases as total volume increases. The aspect ratio of each surface swept by fluid in cross flow should be approximately square, independent of total number of channels and volume. We also found that the minimum pumping power decreases sensibly as the total number of channels and the volume increase. The maximized heat transfer rate per unit volume increases sharply as the total volume decreases, in agreement with the natural evolution toward miniaturization in technology.

In this paper we explore the opportunity to maximize the production of power in a steam-turbine power plant by properly configuring the hardware at the interface between the stream of hot gas produced by the furnace and the steam that circulates through the power producing cycle. The interface consists of four heat exchangers, superheaters and reheaters, in parallel flow and counter flow. The search for better configurations is based on constructal design, and consists of searching for the distribution of heat exchanger surface (number of heat exchangers, types, sizes) such that the total power output of the turbines is maximum, subject to fixed total size for the heat transfer surface, and fixed maximum allowable steam heat exchanger wall temperature. The emergence of the more effective configurations is documented along with the migration of the spot of maximum temperature along the flow path.

Abstract This paper describes the optimization of a tree-shaped system of insulated pipes for the distribution of a stream of hot water over an area. The area is covered uniformly by users who must receive the same flow rate of hot water. The network of pipes is developed in steps. Each step consists of attaching to an existing network an extension (one new user) that is placed in the position that maximizes the temperature of the water received by the new user. The network grows `one-by-one', i.e., by one new user at a time. Networks with up to 16 users are optimized in this manner, and their geometric features and thermo-fluid performance are documented. These one-by-one trees of hot water flows are compared with corresponding `constructal' trees that are obtained in steps of pairing (doubling), i.e., connecting together two identical area constructs of the same size. It is shown that although the constructal trees perform the best (uniform water delivery at the highest temperature), the one-by-one trees approach the same level of performance as they become more complex. It is also shown that the geometry of the insulated tree structure is relatively insensitive to how the insulation is distributed over all the pipes. The thermal performance of the structure is relatively insensitive to how finely the distribution of pipe sizes and insulation radii is optimized.

In this paper constructal theory is applied to the fundamental problem of how to arrange discrete heat sources on a wall cooled by forced convection. The global objective is to maximize the conductance between the discrete heated wall and the fluid. This is equivalent to minimizing the temperature of the hot spot on the wall, when the heat generation rate is specified. The mechanism by which the global objective is achieved is the generation of flow configuration, in this case the distribution of discrete heat sources. Two different analytical approaches are used: (i) large number of small heat sources, and (ii) small number of heat sources with finite length, which are mounted on a flat wall. Both analyses show that the heat sources should be placed nonuniformly on the wall, with the smallest distance between them near the tip of the boundary layer. If the Reynolds number is high enough, then the heat sources should be mounted flush against each near the entrance to the channel. The analytical results are validated by a numerical study of discrete heat sources that are distributed nonuniformly inside a channel formed by parallel plates. 2004 Elsevier Ltd. All rights reserved.

Recent developments in thermodynamic optimization are reviewed by focusing on the generation of optimal geometric form (shape, structure, topology) in flow systems. The flow configuration is free to vary. The principle that generates geometric form is the pursuit of maximum global performance (e.g., minimum flow resistance, minimum irreversibility) subject to global finiteness constraints (volume, weight, time). The resulting structures constructed in this manner have been named constructal designs. The thought that the same objective and constraints principle accounts for the optimally shaped flow paths that occur in natural systems (animate and inanimate) has been named constructal theory. Examples of large classes of applications are drawn from various sectors of mechanical and civil engineering: the distribution of heat transfer area in power plants, optimal sizing and shaping of flow channels and fins, optimal aspect ratios of heat exchanger core structures, aerodynamic and hydrodynamic shapes, tree-shaped assemblies of convective fins, tree-shaped networks for fluid flow and other currents, optimal configurations for streams that undergo bifurcation or pairing, insulated pipe networks for the distribution of hot water and exergy over a fixed territory, and distribution networks for virtually everything that moves in society (goods, currency, information). The principle-based generation of flow geometry unites the thermodynamic optimization developments known in mechanical engineering with lesser known applications in civil engineering and social organization. This review extends thermodynamics, because it shows how thermodynamic principles of design optimization account for the development of optimal configurations in civil engineering and social organization.