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Review Article

Transport Phenomena and Properties in Treelike Networks

[+] Author and Article Information
Peng Xu

College of Science,
China Jiliang University,
258 Xueyuan Street,
Hangzhou 310018, China
e-mail: xupeng@cjlu.edu.cn

Agus Pulung Sasmito

Department of Mining and Materials Engineering,
McGill University,
3450 University Street,
Montreal, QC H3A2A7, Canada
e-mail: agus.sasmito@mcgill.ca

Boming Yu

School of Physics,
Huazhong University of Science and Technology,
1037 Luoyu Road,
Wuhan 430074, China
e-mail: yubm_2012@hust.edu.cn

Arun Sadashiv Mujumdar

Department of Mining and Materials Engineering,
McGill University,
3450 University Street,
Montreal, QC H3A2A7, Canada
e-mail: arunmujumdar123@gmail.com

1Corresponding author.

Manuscript received January 17, 2016; final manuscript received June 15, 2016; published online July 12, 2016. Assoc. Editor: Ellen Kuhl.

Appl. Mech. Rev 68(4), 040802 (Jul 12, 2016) (17 pages) Paper No: AMR-16-1007; doi: 10.1115/1.4033966 History: Received January 17, 2016; Revised June 15, 2016

Treelike structures abound in natural as well as man-made transport systems, which have fascinated multidisciplinary researchers to study the transport phenomena and properties and understand the transport mechanisms of treelike structures for decades. The fluid flow and heat transfer in treelike networks have received an increasing attention over the past decade as the highly efficient transport processes observed in natural treelike structures can provide useful hints for optimal solutions to many engineering and industrial problems. This review paper attempts to present the background and research progress made in recent years on the transport phenomenon in treelike networks as well as technological applications of treelike structures. The subtopics included are optimization of branching structures, scaling laws of treelike networks, and transport properties for laminar flow, turbulent flow, heat conduction, and heat convection in treelike networks. Analytical expressions for the effective transport properties have been derived based on deterministic treelike networks, and the effect of branching parameters on the transport properties of treelike networks has also been discussed. Furthermore, numerical simulation results for treelike microchannel networks are presented as well. The proposed transport properties may be beneficial to understand the transport mechanisms of branching structures and promote the applications of treelike networks in engineering and industry.

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Figures

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Fig. 1

The sketches for (a) animal vascular network, (b) plant pipe model, and (c) branching topology structure with five generations

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Fig. 2

Research schematic for transport phenomena in treelike networks

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Fig. 3

(a) Publication and citation numbers and (b) discipline distribution of publications on transport in treelike network since 1990–2015 (data from Scopus)

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Fig. 4

(a) A schematic graph of bifurcation structure, (b) structural changes induced by an infinitesimal increment of the parent branch, (c) structural changes induced by one of the daughter branches infinitesimal increment

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Fig. 5

Fractal treelike networks: (a) Y-shaped network with fractal dimension Dl = 1.357 (n = 2, m = 7, and θ = 75 deg) and (b) H-shaped network with fractal dimension Dl = 2.0 (n = 2, m = 9, and θ = 180 deg)

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Fig. 6

Schematic diagram for (a) a typical fractal treelike network (n = 2, m = 4, and θ = 60 deg) and (b) kth branching structure

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Fig. 7

The thermal–electrical analogy on treelike network: (a) Y-shaped network and (b) H-shaped network

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Fig. 8

Sandwich structures of treelike microchannel network cooling system: (a) rectangular heat sink with H-shaped treelike network and (b) circular heat sink with Y-shaped treelike network [139]

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Fig. 9

Temperature contours on the middle plane of channels for (a) treelike microchannel network without loops under partial blockages at four outlets and (b) treelike microchannel network with loops under partial blockages at six outlets [139]

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