Skip to main content
SpringerLink
Log in

Tree-Shaped Flow Networks in Nature and Engineered Systems

  • Chapter
  • First Online:
Tree-Shaped Fluid Flow and Heat Transfer

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSAPPLSCIENCES))

  • 552 Accesses

Abstract

Our world is made up of things that have shapes. The apparently endless diversity of shapes can be ranked and compared. Similar patterns and forms in natural systems abound, from the honeycomb configuration in living tissue and cell aggregates to the tree-shape configuration in lightning, neurons, plant roots and branches, blood distribution systems, and river basins. Tree architecture is ubiquitous, both in small- and large-scale systems, in systems that have nothing in common apart from the purpose of allowing something to flow.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Arion V, Cojocari A, Bejan A (2003) Constructal tree shaped networks for distribution of electrical power. Energy Convers Manage 44:867–891

    Article  Google Scholar 

  • Azoumah Y, Neveu P, Mazet N (2004) Constructal network for heat and mass transfer in a solid-gas reactive porous medium. Int J Heat Mass Transf 47:2961–2970

    Article  Google Scholar 

  • Azoumah Y, Neveu P, Mazet N (2007) Optimal design of thermochemical reactors based on constructal approach. AIChE J 53:1257–1266

    Article  Google Scholar 

  • Baieth HEA (2008) Physical parameters of blood as a non-Newtonian fluid. Int J Biomed Sci 4:323–329

    Google Scholar 

  • Barber RW, Emerson DR (2008) Optimal design of microfluidic networks using biologically inspired principles. Microfluid Nanofluid 4:179–191

    Article  Google Scholar 

  • Bejan A (1997) Constructal-theory network of conducting paths for cooling a heat generating volume. Trans ASME J Heat Transf 40:799–816

    MATH  Google Scholar 

  • Bejan A (2000) Shape and structure, from engineering to nature. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Bejan A, Ledezma GA (1998) Streets tree networks and urban growth: optimal geometry for quickest access between a finite-size volume and one point. Phys A 255:211–217

    Article  Google Scholar 

  • Bejan A, Lorente S (2008) Design with constructal theory. Wiley, Hoboken

    Book  Google Scholar 

  • Bejan A, Rocha LAO, Lorente S (2000) Thermodynamic optimization of geometry: T and Y-shaped constructs of fluid streams. Int J Therm Sci 39:949–960

    Article  Google Scholar 

  • Bejan A, Lorente S, Miguel AF, Reis AH (2006) Constructal theory of distribution of river sizes. In: Bejan A (ed) Advanced engineering thermodynamics, 3rd edn. Wiley, Hoboken, pp 779–782

    Google Scholar 

  • Biswas AK, Cordeiro NV, Brage BPF (eds) (1999) Management of Latin American river basins: Amazon, Plata, and San Francisco. Water resources management and policy series. United Nations University, New York

    Google Scholar 

  • Calamas D, Baker J (2013) Tree-like branching fins: performance and natural convective heat transfer behavior. Int J Heat Mass Transf 62:350–361

    Article  Google Scholar 

  • Chen YP, Cheng P (2002) Heat transfer and pressure drop in fractal tree-like microchannel nets. Int J Heat Mass Transf 45:2643–2648

    Article  Google Scholar 

  • Chen YP, Cheng P (2005) An experimental investigation on the thermal efficiency of fractal tree-like microchannel nets. Int Commun Heat Mass Transf 32:931–938

    Article  Google Scholar 

  • Chen YP, Yao F, Huang X (2015) Mass transfer and reaction in methanol steam reforming reactor with fractal tree-like microchannel network. Int J Heat Mass Transf 87:279–283

    Article  Google Scholar 

  • Cheng SJ, Miao JM, Tai CH (2012) Numerical simulation applied to study the effects of fractal tree-liked network channel designs on PEMFC performance. Adv Mater Res 488–489:1219–1223

    Article  Google Scholar 

  • Cohn DL (1954) Optimal systems: I. The vascular system. Bull Math Biophys 16:59–74

    Article  Google Scholar 

  • Combelles L, Lorente S, Anderson R, Bejan A (2012) Tree-shaped fluid flow and heat storage in a conducting solid. J Appl Phys 111:014902

    Article  Google Scholar 

  • da Silva AK, Lorente S, Bejan A (2004) Constructal multi-scale tree-shaped heat exchanger. J Appl Phys 96:1709–1718

    Article  Google Scholar 

  • Damiri HS, Bardaweel HK (2015) Numerical design and optimization of hydraulic resistance and wall shear stress inside pressure-driven microfluidic networks. Lab Chip 15:4187–4196

    Article  Google Scholar 

  • Daneshi M, Zare M, Salimpour MR (2013) Micro- and nanoscale conductive tree-structures for cooling a disk-shaped electronic piece. ASME J Heat Transf 135:031401

    Article  Google Scholar 

  • Emerson DR, Cieslicki K, Gu X, Barber RW (2006) Biomimetic design of microfluidic manifolds based on a generalized Murray’s law. Lab Chip 6:447–454

    Article  Google Scholar 

  • Gaughan C, Panos AL (2009) Anatomy of lungs. In: Salerno TA (ed) Principles of pulmonary protection in heart surgery. Springer, New York, pp 3–8

    Google Scholar 

  • Ghodoossi L, Egrican N (2003) Exact solution for cooling of electronics using constructal theory. J Appl Phys 93:4922–4929

    Article  Google Scholar 

  • Hack JT (1957) Studies of longitudinal profiles in Virginia and Maryland. USGS Professional Papers 294-B, Washington DC, pp. 46–97

    Google Scholar 

  • Hess WR (1917) Über die periphere Regulierung der Blutzirkulation. Pflüger’s Archiv für die gesamte Physiologie des Menschen und der Tiere 168:439–490

    Article  Google Scholar 

  • Horsfield K, Relea FG, Gumming G (1976) Diameter, length and branching ratios in the bronchial tree. Respir Physiol 26:351–356

    Article  Google Scholar 

  • Horton RE (1945) Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology. Geol Soc Am Bull 56:275–370

    Article  Google Scholar 

  • Huang HQ, Nanson GC (2000) Hydraulic geometry and maximum flow efficiency as products of the principle of least action. Earth Surf Process Landf 25:1–16

    Article  Google Scholar 

  • Huang H-F, Liu S-Y, Guo W (2012) A hierarchical tree shaped power distribution network based on constructal theory for EBG structure power plane. Prog Electromagn Res B 36:173–191

    Article  Google Scholar 

  • Kasimova RG, Tishin D, Kacimov AR (2014) Streets and pedestrian trajectories in an urban district: Bejan’s constructal principle revisited. Phys A 410:601–608

    Article  MathSciNet  Google Scholar 

  • Kjelstrup S, Coppens M-O, Pharoah JG, Pfeifer P (2010) Nature-inspired energy- and material-efficient design of a polymer electrolyte membrane fuel cell. Energy Fuels 24:5097–5108

    Article  Google Scholar 

  • Ledezma GA, Bejan A, Errera MR (1997) Constructal tree networks for heat transfer. J Appl Phys 82:89–100

    Article  Google Scholar 

  • Liu H, Li P, Lew JV (2010) CFD study on flow distribution uniformity in fuel distributors having multiple structural bifurcations of flow channels. Int J Hydrogen Energy 35:9186–9198

    Article  Google Scholar 

  • Lorente S, Wechsatol W, Bejan A (2003) Optimization of tree shaped flow distribution structures over a disc-shaped area. Int J Energy Res 27:715–723

    Article  Google Scholar 

  • Lorenzini G, Rocha LAO (2006) Constructal design of Y-shaped assembly of fins. Int J Heat Mass Transf 49:4552–4557

    Article  Google Scholar 

  • Mamdouh S (1985) Hydrology of the Nile river basin. Elsevier, New York

    Google Scholar 

  • Mandelbrot BB (1975) Les objects fractals: forme, hasard et dimension. Flammarian, Paris

    MATH  Google Scholar 

  • Mandelbrot BB (1983) The fractal geometry of nature. Freeman, New York, WH

    Google Scholar 

  • Matos RS, Laursen TA, Vargas JVC, Bejan A (2004) Three-dimensional optimization of staggered finned circular and elliptic tubes in forced convection. Int J Therm Sci 43:477–487

    Article  Google Scholar 

  • McCulloh KA, Sperry JS, Adler FR (2003) Water transport in plants obeys Murray’s law. Nature 421:939–942

    Article  Google Scholar 

  • McCulloh KA, Sperry JS, Adler FR (2004) Murray’s law and the hydraulic vs mechanical functioning of wood. Funct Ecol 18:931–938

    Article  Google Scholar 

  • Melton MA (1959) A derivation of Strahler’s channel-ordering system. J Geol 67:345–346

    Article  Google Scholar 

  • Miguel AF (2012) Lungs as a natural porous media: architecture, airflow characteristics and transport of suspended particles. In: Delgado J (ed) Heat and mass transfer in porous media, advanced structured materials series, vol 13. Springer, Berlin, pp 115–137

    Chapter  Google Scholar 

  • Miguel AF (2013) The emergence of design in pedestrian dynamics: locomotion, self-organization, walking paths and constructal law. Phys Life Rev 10:168–190

    Article  Google Scholar 

  • Miguel AF (2015) Fluid flow in a porous tree-shaped network: optimal design and extension of Hess–Murray’s law. Phys A 423:61–71

    Article  MathSciNet  Google Scholar 

  • Miguel AF (2016a) Toward an optimal design principle in symmetric and asymmetric tree flow networks. J Theor Biol 389:101–109

    Article  MathSciNet  Google Scholar 

  • Miguel AF (2016b) Scaling laws and thermodynamic analysis for vascular branching of microvessels. Int J Fluid Mech Res 43:390–403

    Google Scholar 

  • Miguel AF (2018) Constructal branching design for fluid flow and heat transfer. Int J Heat Mass Transf 122:204–211

    Article  Google Scholar 

  • Moreau B, Mauroy B (2015) Murray’s law revisited: Quémada’s fluid model and fractal tree. J Rheol 59:1419

    Article  Google Scholar 

  • Murray CD (1926a) The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA 12:207–214

    Article  Google Scholar 

  • Murray CD (1926b) The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9:835–841

    Article  Google Scholar 

  • Omori T, Ishikawa T, Barthès-Biesel D, Salsac A-V, Imai Y, Yamaguchi T (2012) Tension of red blood cell membrane in simple shear flow. Phys Rev E 86:056321

    Article  Google Scholar 

  • Panda-Jonas S, Jonas JB, Jakobczyk M, Schneider U (1994) Retinal photoreceptor count, retinal surface area, and optic disc size in normal human eyes. Ophthalmology 101:519–523

    Article  Google Scholar 

  • Pepe VR, Rocha LAO, Miguel AF (2017) Optimal branching structure of fluidic networks with permeable walls. Biomed Res Int 2017:528481

    Article  Google Scholar 

  • Pries AR, Neuhaus D, Gaehtgens P (1992) Blood viscosity in tube flow: dependence on diameter and hematocrit. Dtsch Arch Klin Med 169:212–222

    Google Scholar 

  • Pries AR, Reglin B, Secomb TW (2003) Structural response of microcirculatory networks to changes in demand: information transfer by shear stress. Am J Physiol Heart Circ Physiol 284:H2204–H2212

    Article  Google Scholar 

  • Reddy BVK, Ramana PV, Narasimhan A (2008) Steady and transient thermo-hydraulic performance of disc with tree-shaped micro-channel networks with and without radial inclination. Int J Therm Sci 47:1482–1489

    Article  Google Scholar 

  • Reis AH, Miguel AF, Aydin M (2004) Constructal theory of flow architecture of the lungs. Med Phys 31:1135–1140

    Article  Google Scholar 

  • Revellin R, Rousset F, Baud D, Bonjour J (2009) Extension of Murray’s law using a non-Newtonian model of blood flow. Theor Biol Med Model 6:7

    Article  Google Scholar 

  • Rivera-Alvarez A, Bejan A (2003) Constructal geometry and operation of adsorption processes. Int J Therm Sci 42:983–994

    Article  Google Scholar 

  • Rocha LAO, Lorente S, Bejan A (2002) Constructal design for cooling a disc-shaped area by conduction. Int J Heat Mass Transf 45:1643–1652

    Article  Google Scholar 

  • Schumm SA (1956) Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey. Geol Soc Am Bull 67:597–646

    Article  Google Scholar 

  • Senn SM, Poulikakos D (2004) Tree network channels as fluid distributors constructing double-staircase polymer electrolyte fuel cells. J Appl Phys 96:842–852

    Article  Google Scholar 

  • Senn SM, Poulikakos D (2006) Pyramidal direct methanol fuel cells. Int J Heat Mass Transf 49:1516–1528

    Article  Google Scholar 

  • Serrenho A, Miguel AF (2013) Accessing the influence of Hess-Murray law on suspension flow through ramified structures. Defect Diff Forum 334:322–328

    Article  Google Scholar 

  • Stephenson C, Lyon D, Hüblera A (2017) Topological properties of a self-assembled electrical network via ab initio calculation. Sci Rep 7:41621

    Article  Google Scholar 

  • Su Y, Chen G, Kenig EY (2015) An experimental study on the numbering-up of microchannels for liquid mixing. Lab Chip 15:179–187

    Article  Google Scholar 

  • Thoma R (1901) Über den verzweigungsmodus der arterien. Archiv für Entwicklungsmechanik der Organismen 2:352–413

    Article  Google Scholar 

  • Toksvang LN, Berg RM (2013) Using a classic paper by Robin Fahraeus and Torsten Lindqvist to teach basic hemorheology. Adv Physiol Educ 37:129–133

    Article  Google Scholar 

  • Tüber K, Oedegaard A, Hermann M, Hebling C (2004) Investigation of fractal flow-fields in portable proton exchange membrane and direct methanol fuel cells. J Power Sour 131:175–181

    Article  Google Scholar 

  • Tuma RF, Duran WN, Ley K (2008) Handbook of physiology: microcirculation. Academic Press, San Diego

    Google Scholar 

  • Uylings HBM (1977) Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol 39:509–519

    Article  Google Scholar 

  • Vesalius A, Richardson WF, Carman JB (2002) On the fabric of the human body. Book III, The veins and arteries. Book IV, The nerves: a translation of De humani corporis fabrica libri septem. Norman anatomy series. Norman, Novato

    Google Scholar 

  • Wechsatol W, Lorente S, Bejan A (2001) Tree-shaped insulated designs for the uniform distribution of hot water over an area. Int J Heat Mass Transf 44:3111–3123

    Article  Google Scholar 

  • Wechsatol W, Lorente S, Bejan A (2003) Dendritic convection on a disc. Int J Heat Mass Transf 46:4381–4391

    Article  Google Scholar 

  • Weibel ER, Gomez DM (1962) Architecture of human lung. Science 137:577–585

    Article  Google Scholar 

  • Xu P, Wang XQ, Mujumdar AS, Yap C, Yu BM (2009) Thermal characteristics of tree-shaped microchannel nets with/without loops. Int J Therm Sci 48:2139–2147

    Article  Google Scholar 

  • Xu P, Yu BM, Yuan MJ, Zou MQ (2006) Heat conduction in fractal tree-like branched networks. Int J Heat Mass Transf 49:3746–3751

    Article  Google Scholar 

  • Young T (1809) On the functions of the heart and arteries. Philos Trans Royal Soc Lond 99:1–31

    Article  Google Scholar 

  • Yu B, Li B (2006) Fractal-like tree networks reducing the thermal conductivity. Phys Rev E 73:066302

    Article  Google Scholar 

  • Yue J, Boichot R, Luo L, Gonthier Y, Chen G, Yuan Q (2010) Flow distribution and mass transfer in a parallel microchannel contactor integrated with constructal distributors. AIChE J 56:298–317

    Google Scholar 

  • Zheng X, Shen G, Wang C, Li Y, Dunphy D, Hasan T, Brinker CJ, Su B-L (2017) Bio-inspired Murray materials for mass transfer and activity. Nat Commun 8:14921

    Article  Google Scholar 

  • Zhou S, Chen L, Sun F (2007) Constructal entropy generation minimization for heat and mass transfer in a solid-gas reactor based on triangular element. J Phys D Appl Phys 40:3545–3550

    Article  Google Scholar 

  • Zimparov VD, da Silva AK, Bejan A (2006) Constructal tree-shaped parallel flow heat exchangers. Int J Heat Mass Transf 49:4558–4566

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Évora, Évora, Portugal

    António F. Miguel

  2. Graduate Program in Mechanical Engineering, University of Vale do Rio dos Sinos, UNISINOS, São Leopoldo, Rio Grande do Sul, Brazil

    Luiz A. O. Rocha

Authors
  1. António F. Miguel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luiz A. O. Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 The Author(s)

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Miguel, A.F., Rocha, L.A.O. (2018). Tree-Shaped Flow Networks in Nature and Engineered Systems. In: Tree-Shaped Fluid Flow and Heat Transfer. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-73260-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73260-2_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73259-6

  • Online ISBN: 978-3-319-73260-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation