Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 11 2 2007 10.5194/hess-11-753-2007 http://www.hydrol-earth-syst-sci.net/11/753/2007/ http://www.hydrol-earth-syst-sci.net/11/753/2007/hess-11-753-2007.html http://www.hydrol-earth-syst-sci.net/11/753/2007/hess-11-753-2007.pdf 753 768 2007-01-17 Constructal theory of pattern formation A. Bejan abejan@duke.edu Duke University, Durham, North Carolina, USA This review article shows that the occurrence of macroscopic flow configuration is a universal natural phenomenon that can be explained and predicted on the basis of a principle of physics (the constructal law): "For a flow system to persist in time (to survive) it must evolve in such a way that it provides easier and easier access to the currents that flow through it". The examples given in this article come from natural inanimate flow systems with configuration: duct cross-sections, open channel cross-sections, tree-shaped flow architectures, and turbulent flow structure (e.g., eddies, laminar lengths before transition). Other examples that are treated in the literature, and which support the constructal law, are the wedge-shape of turbulent shear layers, jets and plumes, the frequency of vortex shedding, Bénard convection in fluids and fluid-saturated porous media, dendritic solidification, the coalescence of solid parcels suspended in a flow, global atmospheric and oceanic circulation and climate, and virtually all architectural features of animal design. The constructal law stresses the importance of reserving a place for pure theory in research, and for constantly searching for new physics – new summarizing principles that are general, hence useful. Bejan, A.: Entropy Generation through Heat and Fluid Flow, Wiley, New York, 1982. Bejan, A.: Heat Transfer, Wiley, New York, 1993. Bejan, A.: Entropy Generation Minimization, CRC Press, Boca Raton, FL, 1996a. Bejan, A.: Street network theory of organization in Nature, J. Adv. Transport., 30, 85–107, 1996b. Bejan, A.: Constructal-theory network of conducting paths for cooling a heat generating volume, Int. J. Heat Mass Trans., 40, 799–816, 1997a (published 1 November 1996). Bejan, A.: Theory of organization in Nature: Pulsating physiological processes, Int. J. Heat Mass Trans., 40, 2097–2104, 1997b. Bejan, A.: Constructal tree network for fluid flow between a finite-size volume and one source or sink, Int. J. Thermal Sci., 36, 592–604, 1997c. Bejan, A.: Advanced Engineering Thermodynamics, 2nd ed., Wiley, New York, 1997d. Bejan, A.: Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, UK, 2000. Bejan, A.: Convection Heat Transfer, 3rd ed., Wiley, Hoboken, NJ, 2004. Bejan, A.: Advanced Engineering Thermodynamics, 3rd ed., Wiley, Hoboken, NJ, 2006. Bejan, A. and Errera, M. R.: Deterministic tree networks for river drainage basins, Fractals, 6, 245–261, 1998. Bejan, A. and Gobin, D.: Constructal theory of droplet impact geometry, Int. J. Heat Mass Trans., 49, 2412–2419, 2006. Bejan, A. and Lorente, S.: Thermodynamic formulation of the constructal law, Int. Mech. Eng. Congress and Expo, ASME Paper IMECE2003-41167, 2003. Bejan, A. and Lorente, S.: The constructal law and the thermodynamics of flow systems with configuration, Int. J. Heat Mass Trans., 47, 3203–3214, 2004. Bejan, A. and Lorente, S.: La Loi Constructale, L'Harmattan, Paris, 2005. Bejan, A. and Marden, J. H.: Unifying constructal theory for scale effects in running, swimming and flying, J. Exp. Biol., 209, 238–248, 2006. Bejan, A. and Reis, A. H.: Thermodynamic optimization of global circulation and climate, Int. J. Energy Res., 29, 303–316, 2005. Bejan, A., Dincer, I., Lorente, S., Miguel, A. F., and Reis, A. H.: Porous and Complex Flow Structures in Modern Technologies, Springer, New York, 2004. Bejan, A., Lorente, S., Miguel, A. F., and Reis, A. H.: Constructal theory of distribution of river sizes, Sect 13.5, in: Bejan, A.: Advanced Engineering Thermodynamics, 3rd ed., Wiley, Hoboken, NJ, 2006. Carrigan, C. R.: Two-component magma transport and the origins of composite intrusions and lava flows, ch. 14 in: Magmatic Systems, edited by: Ryan, M. P., Academic Press, New York, 319–353, 1994. Carrigan, C. R. and Eichelberger, J. C.: Zoning of magmas by viscosity in volcanic conduits, Nature, 343, 248–251, 1990. Chorley, R. J., Schumm, S. A., and Sugden, D. E.: Geomorphology, Methuen, London, 1984. Dewar, R.: Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states, J. Phys. A: Math. Gen., 36, 631–641, 2003. Hess, W. R.: Das Prinzip des kleinsten Kraftverbrauchs im Dienste hämodynamischer Forschung, Archiv. Anat. Physiol., 1913, see Weibel, 2000. Kockman, N., Kiefer, T., Engler, M., and Woias, P.: Channel networks for optimal heat transfer and high throughput mixers, ECI Int. Conf. Heat Transfer and Fluid Flow in Microscale, Castelvecchio Pascoli, Italy, 25–30 September 2005. Ledezma, G. A., Bejan, A., and Errera, M. R.: Constructal tree networks for heat transfer, J. Appl. Phys., 82, 89–100, 1997. Leopold, L. B., Wolman, M. G., and Miller, J. P.: Fluvial Processes in Geomorphology, Freeman, San Francisco, 1964. Lewins, J.: Bejan's constructal theory of equal potential distribution, Int. J. Heat Mass Trans., 46, 1541–1543, 2003. Lin, C. A.: An extremal principle for a one-dimensional climate model, Geophys. Res. Lett., 9, 716–718, 1982. Lorente, S. and Bejan, A.: Svelteness, freedom to morph, and constructal multi-scale flow structures, Int. J. Thermal Sci., 44, 1123–1130, 2005. Lorentz, R. D., Lunine, J. I., McKay, C. P., and Withers, P. G.: Titan, Mars and Earth: entropy production by latitudinal heat transport, Geophys. Res. Lett., 25, 415–418, 2001. Lundell, F., Thonon, B., and Gruss, J. A.: Constructal networks for efficient cooling/heating, 2nd Conference on Microchannels and Minichannels, Rochester, NY, 2004. Malkus, W. V. R.: The heat transport and spectrum of turbulence, Prof. R. Soc. Ser. A., 225, 196–212, 1954. Murray, C. D.: The physiological principle of minimal work, in the vascular system, and the cost of blood-volume, Proc. Acad. Nat. Sci., 12, 207–214, 1926. Neagu, M. and Bejan, A.: Constructal-theory tree networks of "constant" thermal resistance, J. Appl. Phys., 86, 1136–1144, 1999. Nield, D. A. and Bejan, A.: Convection in Porous Media, Springer, New York, 1992. Nield, D. A. and Bejan, A.: Convection in Porous Media, 3rd ed., Springer, New York, 2006. North, G. R.: Energy balance climate models, Rev. Geophys. Space Phys., 19, 91–121, 1981. Paltridge, G. W.: Global dynamics and climate, Quart. J. Roy. Meteorol. Soc., 101, 475–484, 1975. Parker, R. S.: Experimental study of drainage basin evolution and its hydrologic implications, Hydrology Paper 90, Colorado State University, Fort Collins, CO, 1977. Poirier, H.: Une théorie explique l'intelligence de la nature, Science & Vie, 1034, 44–63, 2003. Reis, A. H. and Bejan, A.: Constructal theory of global circulation and climate, Int. J. Heat Mass Trans., 49, 1857–1875, 2006. Reis, A. H., Miguel, A. F., and Bejan, A.: Constructal theory of particle agglomeration and design of air-cleaning devices, J. Phys. D., 39, 2311–2318, 2006. Rodriguez-Iturbe, I., Rinaldo, A., Rigon, R., Bras, R. L., Marani, A., and Ijjasz-Vasquez, E.: Energy dissipation, runoff production, and the three-dimensional structure of river basins, Water Resour. Res., 28, 1095–1103, 1992. Rodriguez-Iturbe, I. and Rinaldo, A.: Fractal River Basins, Cambridge University Press, Cambridge, UK, 1997. Rosa, R. N., Reis, A. H., and Miguel, A. F.: Bejan's Constructal Theory of Shape and Structure, Évora Geophysics Center, University of Évora, Portugal, 2004. Scheidegger, A. E.: Theoretical Geomorphology, 2nd ed., Springer-Verlag, Berlin, 1970. Swenson, R.: Emergent attractors and a law of maximum entropy production: foundations to a theory of general evolution, Syst. Res., 6, 187–197, 1989. Thompson, D. A.: On Growth and Form, Cambridge University Press, Cambridge, UK, 1942. Torre, N.: La Natura, vi svelo le formule della perfezione, La Macchina del Tempo, No. 1–2, Year 5, 36–46, 2004. West, G. B. and Brown, J. H.: Constructing a theory of scaling and more, Physics Today, 20–21, July 2005. West, G. B., Brown, J. H., and Enquist, B. J.: A general model for the origin of allometric scaling laws in biology, Science, 276, 122–126, 1997. Whitfield, J.: Order out of chaos, Nature, 436, 905–907, 2005. Weibel, E. R.: Symmorphosis, Harvard University Press, Cambridge, MA, 2000.