Showing papers on "Constructal law published in 1999"

Constructal-theory tree networks of “constant” thermal resistance

Abstract: 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

Constructal Trees of Convective Fins

Abstract: This paper extends to the field of convective heat transfer the constructal theory of optimizing the access of a current that flows between one point and a finite-size volume, when the volume size is constrained. The volume is bathed by a uniform stream. A small amount of high-conductivity fin material is distributed optimally through the volume, and makes the connection between the volume and one point (fin root) on its boundary. The optimization proceeds in a series of volume subsystems of increasing sizes (elemental volume, first construct, second construct). The shape of the volume and the relative thicknesses of the fins are optimized at each level of assembly. The optimized structure emerges as a tree of fins in which every geometric detail is a result of minimizing the thermal resistance between the finite-size volume and the root point (source, sink). Convection occurs in the interstitial spaces of the tree. The paper shows that several of the geometric details of the optimized structure are robust, i.e., relatively insensitive to changes in other design parameters. The paper concludes with a discussion of constructal theory and the relevance of the optimized tree structures to predicting natural self-organization and self-optimization.

Two Constructal Routes to Minimal Heat Flow Resistance via Greater Internal Complexity

Abstract: We show that the geometry of the heat flow path between a volume and one point can be optimized in two fundamentally different ways. In the growth method of the original constructal theory the structure is optimized starting from the smallest volume element of fixed size. Growth, or optimal numbers of constituents assembled into larger volumes, is one route to resistance minimization. In the design method the overall volume is fixed, and the designer works inward' by optimizing the internal features of the heat flow path. The design method is new. The two methods produce comparable geometric results in which the highconductivity channels form constructal tree networks, and where the low-conductivity material fills the interstices. For simplicity, it is assumed that the high-conductivity channels and their tributaries make 90-deg angles. In both approaches, the overall resistance decreases as the internal complexity of the conductive composite increases. In the growth method the number of constituents in each assembly can be optimized. In the design method, some of the constituent numbers cannot be optimized: these numbers assume the roles of weak parameters

Three-dimensional tree constructs of “constant” thermal resistance

Abstract: This article extends to three-dimensional heat flow the constructal method of minimizing geometrically the thermal resistance between a heat-generating volume and one point. Optimized is the geometry of each volume element, and the shape and distribution of high-conductivity inserts. The new feature is the maximization of the amount of heat-generating material that operates at temperatures close to the hot-spot level (Tmax). Volume elements and subsequent constructs acquire optimal shapes where all the external surfaces are isothermal at Tmax. The same, constant thermal resistance separates each surface point (Tmax) and the common heat-sink point (Tmin). The optimized architecture is pine-cone-like, with high-conductivity nerves and low-conductivity filling (and heat-generating) material. The similarities between the constant-resistance structures and the three-dimensional tree networks found in nature are discussed. The analogy between evolutionary flow systems and evolutionary mechanical support systems is reasoned based on the same (constructal) principle of pursuing objective (purpose) subject to global and local constraints.

Constructal Flow Geometry Optimization

Abstract: In the field of heat transfer, the method of thermodynamic optimization or entropy generation minimization (EGM) brings out the inherent competition between heat-transfer and fluid-flow irreversibilities in the optimization of devices subjected to overall constraints. Consider the most elementary heat exchanger passage [1] which is represented by a duct of arbitrary cross-section (A) and arbitrary wetted perimeter (p). The engineering function of the passage is specified in terms of the heat transfer rate per unit length (q’) that is to be transmitted to the stream (m-); that is, both q’ and m are fixed. In the steady state, the heat transfer q’ crosses the temperature gap ▵T formed between the wall temperature (T + ▵T) and the bulk temperature of the stream (T). The stream flows with friction in the x direction; hence, the pressure gradient (-dP/dx) < 0