901 publications from this institution
This lecture reviews a series of recent results based on the geometric minimization of the resistance to flow between one point (source, sink) and a volume or an area (an infinity of points). Optimization is achieved by varying the geometric features of the flow path subject to volume constraints. The method is outlined by using the problem of steady volume-point conduction. Optimized first is the smallest elemental volume, which is characterized by volumetric heat generation in a low-conductivity medium, and one-dimensional conduction through a high-conductivity 'channel'. Progressively larger volumes are covered by assemblies of previously optimized constructs. Tree-shaped flow structures spring out of this objective and constraints principle. Analogous problems of fluid flow, and combined heat and fluid flow (convection, trees of fins) are also discussed. The occurrence of similar tree structures in nature may be reasoned based on the same principle (constructal theory) (Bejan, 2000). Copyright © 2003 John Wiley & Sons, Ltd.
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.
