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

Abstract

SUMMARY 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.

A design rule for constant depth microfluidic networks for power-law fluids

“…Murray's original relationship was derived for fully developed flow of Newtonian fluids in circular ducts to match the basic shape of most biological distribution systems, such as the vascular system, and can be considered as a particular case of constructal theory (Bejan 2005;Bejan and Lorente 2006). Considering a symmetric bifurcating network where φ 1 = φ 2 , it follows that Murray's law can be generalised (Emerson et al 2006;Barber and Emerson 2008) for designing microfluidic manifolds that have specific fluidic conditions, by modifying the relationship (2) with the use of a branching parameter, X:…”

The evolution of speed, size and shape in modern athletics

“…More recently, a broader view of the commonality of animal locomotion has been emerging (Ahlborn, 2004;Bejan, 2000;Bejan, 2005;Bejan and Marden, 2006;Bejan and Lorente, 2008;Hoppeler and Weibel, 2005;Marden and Allen, 2002;Muller and van Leeuwen, 2004;Taylor et al, 2003;Weibel, 2000). For example, according to constructal theory, animal locomotion is a rhythm of body motion constructed such that the animal achieves a balance between two expenditures of useful energy: lifting weight on the vertical, and overcoming drag while progressing on the horizontal (this analysis is reviewed in the Appendix).…”

Minimum mass vascular networks in multifunctional materials

“…Later work reported by Sherman & Popel (1989) and originally derived by Milsum & Roberge (1973) showed that the predicted total power demand is relatively insensitive to radius close to the Murray optimum; a 10% change in radius from the optimum was found to increase the power requirement by only 3-5%. Bejan (2000Bejan ( , 2005Bejan et al 2000) has used constructal theory-the concept that the survival of a flow network relies on continued evolution to minimize flow resistance-to theoretically investigate fluid flow in networks by minimizing the hydraulic resistance with the network volume constrained. Agreement with Murray's law was shown.…”