0
Research Papers: Micro/Nanoscale Heat Transfer

Constructal Microdevice Manifold Design With Uniform Flow Rate Distribution by Consideration of the Tree-Branching Rule of Leonardo da Vinci and Hess–Murray Rule

[+] Author and Article Information
Erdal Cetkin

Department of Mechanical Engineering,
Izmir Institute of Technology,
Urla,
Izmir 35430, Turkey
e-mail: erdalcetkin@iyte.edu.tr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 28, 2016; final manuscript received January 20, 2017; published online April 11, 2017. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 139(8), 082401 (Apr 11, 2017) (9 pages) Paper No: HT-16-1611; doi: 10.1115/1.4036089 History: Received September 28, 2016; Revised January 20, 2017

In this paper, we show how the design of a microdevice manifold should be tapered for uniform flow rate distribution. The designs based on the tree-branching rule of Leonardo da Vinci and the Hess–Murray rule were considered in addition to the constructal design. Both da Vinci and Hess–Murray designs are insensitive to the inlet velocity, and they provide better flow uniformity than the base (not tapered) design. However, the results of this paper uncover that not only pressure drop but also velocity distribution in the microdevice play an integral role in the flow uniformity. Therefore, an iterative approach was adopted with five degrees-of-freedom (inclined wall positions) and one constraint (constant distribution channel thickness) in order to uncover the constructal design which conforms the uniform flow rate distribution. In addition, the effect of slenderness of the microchannels (Svelteness) and inlet velocity on the flow rate distribution to the microchannels has been documented. This paper also uncovers that the design of a manifold should be designed with not only the consideration of pressure distribution but also dynamic pressure distribution especially for non-Svelte microdevices.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Tonomura, O. , Tanaka, S. , Noda, M. , Kano, M. , Hasebe, S. , and Hashimoto, I. , 2004, “ CFD-Based Optimal Design of Manifold in Plate-Fin Microdevices,” Chem. Eng. J., 101(1–3), pp. 397–402. [CrossRef]
Lagally, E. T. , Medintz, I. , and Mathies, R. A. , 2001, “ Single-Molecule DNA Amplification and Analysis in an Integrated Microfluidic Device,” Anal. Chem., 73(3), pp. 565–570. [CrossRef] [PubMed]
Sanders, G. H. W. , and Manz, A. , 2000, “ Chip-Based Microsystems for Genomic and Proteomic Analysis,” TrAC, 19(6), pp. 364–378.
Lee, D. , Kim, Y. T. , Jee, J. W. , Kim, D. H. , and Seo, T. S. , 2016, “ An Integrated Direct Loop-Mediated Isothermal Amplification Microdevice Incorporated With an Immunochromatographic Strip for Bacteria Detection in Human Whole Blood and Milk Without Sample Preparation Step,” Biosens. Bioelectron., 79, pp. 273–279. [CrossRef] [PubMed]
Sweeney, J. , Whitney, C. , and Wilson, C. G. , 2009, “ A Plasma Spectroscopic Microdevice for On-Site Water Monitoring,” IEEE Sensors, Vol. 1–3, pp. 2005–2008.
Sanchez, Z. , Tani, A. , Suzuki, N. , Kariyama, R. , Kumon, H. , and Kimbara, K. , 2013, “ Assessment of Change in Biofilm Architecture by Nutrient Concentration Using a Multichannel Microdevice Flow System,” J. Biosci. Bioeng., 115(3), pp. 326–331. [CrossRef] [PubMed]
Xie, Y. , Shen, Z. , Zhang, D. , and Lan, J. , 2014, “ Thermal Performance of a Water-Cooled Microchannel Heat Sink With Grooves and Obstacles,” ASME J. Electron. Packag., 136(2), p. 021001. [CrossRef]
Wibel, W. , Schygulla, U. , and Brandner, J. J. , 2011, “ Micro Device for Liquid Cooling by Evaporation of R134a,” Chem. Eng. J., 167(2–3), pp. 705–712. [CrossRef]
Xia, G. D. , Jiang, J. , Zhai, Y. L. , and Ma, D. D. , 2015, “ Effects of Different Geometric Structures on Fluid Flow and Heat Transfer Performance in Microchannel Heat Sinks,” Int. J. Heat Mass Transfer, 80, pp. 439–447. [CrossRef]
Bello-Ochende, T. , Liebenberg, L. , and Meyer, J. P. , 2007, “ Constructal Cooling Channels for Micro-Channel Heat Sinks,” Int. J. Heat Mass Transfer, 50(21–22), pp. 4141–4150. [CrossRef]
Kosar, A. , and Peles, Y. , 2005, “ Thermal-Hydraulic Performance of MEMS-Based Pin Fin Heat Sink,” ASME J. Heat Transfer, 128(2), pp. 121–131. [CrossRef]
Lee, Y. J. , Lee, P. S. , and Chou, S. K. , 2013, “ Numerical Study of Fluid Flow and Heat Transfer in the Enhanced Microchannel With Oblique Fins,” ASME J. Heat Transfer, 135(4), p. 041901. [CrossRef]
Khan, M. G. , and Fartaj, A. , 2011, “ Heat Exchanger: A Review on Microchannel Heat Exchangers and Potential Applications,” Int. J. Energy Res., 35(7), pp. 553–582. [CrossRef]
Wei, X. , Joshi, Y. , and Patterson, M. K. , 2007, “ Experimental and Numerical Study of a Stacked Microchannel Heat Sink for Liquid Cooling of Microelectronic Devices,” ASME J. Heat Transfer, 129(10), pp. 1432–1444. [CrossRef]
Toohey, K. S. , Sottos, N. R. , Lewis, J. A. , Moore, J. S. , and White, S. R. , 2007, “ Self-Healing Materials With Microvascular Networks,” Nat. Mater., 6(8), pp. 581–585. [CrossRef] [PubMed]
White, S. R. , Sottos, N. R. , Geubelle, P. H. , Moore, J. S. , Kessler, M. R. , Sriram, S. R. , Brown, E. N. , and Viswanathan, S. , 2001, “ Autonomic Healing of Polymer Composites,” Nature, 409(6822), pp. 794–797. [CrossRef] [PubMed]
Cetkin, E. , 2015, “ Constructal Vascular Structures With High-Conductivity Inserts for Self-Cooling,” ASME J. Heat Transfer, 137(11), p. 111901. [CrossRef]
Yenigun, O. , and Cetkin, E. , 2016, “ Experimental and Numerical Investigation of Constructal Vascular Channels for Self-Cooling: Parallel Channels, Tree-Shaped and Hybrid Designs,” Int. J. Heat Mass Transfer, 103, pp. 1155–1165. [CrossRef]
Cetkin, E. , Lorente, S. , and Bejan, A. , 2010, “ Natural Constructal Emergence of Vascular Design With Turbulent Flow,” J. Appl. Phys., 107(11), p. 114901. [CrossRef]
Cetkin, E. , 2014, “ Emergence of Tapered Ducts in Vascular Designs With Laminar and Turbulent Flows,” J. Porous Media, 17(8), pp. 715–722. [CrossRef]
Huang, C.-H. , Wang, C.-H. , and Kim, S. , 2016, “ A Manifold Design Problem for a Plate-Fin Microdevice to Maximize the Flow Uniformity of System,” Int. J. Heat Mass Transfer, 95, pp. 22–34. [CrossRef]
Bejan, A. , 1997, Advanced Engineering Thermodynamics, 2nd ed., Wiley, New York.
Lorenzini, G. , Machado, B. S. , Isoldi, L. A. , dos Santos, E. D. , and Rocha, L. A. O. , 2016, “ Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows,” ASME J. Heat Transfer, 138(10), p. 102501. [CrossRef]
Bejan, A. , 2015, “ Constructal Law: Optimization as Design Evolution,” ASME J. Heat Transfer, 137(6), p. 061003. [CrossRef]
Rocha, L. A. O. , Lorente, S. , and Bejan, A. , 2002, “ Constructal Design for Cooling a Disc-Shaped Area by Conduction,” Int. J. Heat Mass Transfer, 45(8), pp. 1643–1652. [CrossRef]
Muzychka, Y. S. , 2005, “ Constructal Design of Forced Convection Cooled Microchannel Heat Sinks and Heat Exchangers,” Int. J. Heat Mass Transfer, 48(15), pp. 3119–3127. [CrossRef]
Azoumah, Y. , Neveu, P. , and Mazet, N. , 2007, “ Optimal Design of Thermochemical Reactors Based on Constructal Approach,” AIChe J., 53(5), pp. 1257–1266. [CrossRef]
Miguel, A. F. , 2006, “ Constructal Pattern Formation in Stony Corals, Bacterial Colonies and Plant Roots Under Different Hydrodynamics Conditions,” J. Theor. Biol., 242(4), pp. 954–961. [CrossRef] [PubMed]
Bejan, A. , Lorente, S. , and Lee, J. , 2008, “ Unifying Constructal Theory of Tree Roots, Canopies and Forests,” J. Theor. Biol., 254(3), pp. 529–540. [CrossRef] [PubMed]
Lucia, U. , Ponzetto, A. , and Deisboeck, T. S. , 2014, “ A Thermo-Physical Analysis of the Proton Pump Vacuolar-ATPase: The Constructal Approach,” Sci. Rep., 4, p. 6763. [CrossRef] [PubMed]
Reis, A. H. , 2006, “ Constructal View of Scaling Laws of River Basins,” Geomorphology, 78(3–4), pp. 201–206. [CrossRef]
Bejan, A. , 2007, “ Constructal Theory of Pattern Formation,” Hydrol. Earth Syst. Sci., 11(2), pp. 753–768. [CrossRef]
Bejan, A. , and Merkx, G. W. , 2007, Constructal Theory of Social Dynamics, Springer, New York.
Lui, C. H. , Fong, N. K. , Lorente, S. , Bejan, A. , and Chow, W. K. , 2012, “ Constructal Design for Pedestrian Movement in Living Spaces: Evacuation Configurations,” J. Appl. Phys., 111(5), p. 054903. [CrossRef]
Reis, A. H. , Miguel, A. F. , and Aydin, M. , 2004, “ Constructal Theory of Flow Architectures of the Lungs,” Med. Phys., 31(5), pp. 1135–1140. [CrossRef] [PubMed]
Bejan, A. , and Zane, J. P. , 2013, Design in Nature, Anchor Books, New York.
Bejan, A. , 2016, Physics of Life, St. Martin's Press, New York.
Cetkin, E. , and Oliani, A. , 2015, “ The Natural Emergence of Asymmetric Tree-Shaped Pathways for Cooling of a Non-Uniformly Heated Domain,” J. Appl. Phys., 118(2), p. 024902. [CrossRef]
COMSOL, 2014, “COMSOL Multiphysics 5.0,” COMSOL Inc., Burlington, MA.
Bejan, A. , and Lorente, S. , 2008, Design With Constructal Theory, Wiley, Hoboken, NJ.
Richter, J. , 1970, The Notebooks of Leonardo da Vinci, Dover, New York.
Minamino, R. , and Tateno, M. , 2014, “ Tree Branching: Leonardo da Vinci`s Rule Versus Biomechanical Models,” PLoS One, 9(4), p. e93535. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Comparison of Vi/V¯ ratio for each channel in current study and Ref. [1]

Grahic Jump Location
Fig. 2

(a) Geometry of the manifold with tapered distributing channel with the branching rule of da Vinci and (b) flow rate in each channel divided by the average flow rate for tapered collecting channel (triangle), tapered distributing channel (square), and tapered distributing and collecting channels (diamond), and nontapered design of Fig. 1 (circle) with 1.5-mm microchannel length and 1 m/s inlet velocity

Grahic Jump Location
Fig. 3

(a) Geometry of the manifold with tapered distributing channel with Hess–Murray rule and (b) flow rate in each channel divided by the average flow rate for tapered distributing channel with 1.5-mm microchannel length and 1 m/s inlet velocity

Grahic Jump Location
Fig. 4

Flow rate in each channel divided by the average flow rate for four competing designs: design of Fig. 1 (circle), da Vinci (square), Hess–Murray with 21/6 thickness ratio (diamond), and constructal design (cross) with the inlet velocities of (a) 0.5 m/s, (b) 1 m/s, and (c) 2 m/s

Grahic Jump Location
Fig. 5

Sum of the deviations and maximum deviations for the competing designs with the inlet velocities of (a) 0.5 m/s, (b) 1 m/s, and (c) 2 m/s

Grahic Jump Location
Fig. 6

Flow rate in each channel divided by the average flowrate for four competing designs with inlet velocities of (a) 0.5 m/s, (b) 1 m/s, and (c) 2 m/s

Grahic Jump Location
Fig. 7

Flow rate in each channel divided by the average flow rate for three competing designs: Type B-O and Type OPT1 of Ref. [21] and the constructal design

Grahic Jump Location
Fig. 8

Flow rate in each channel divided by the average flow rate for four competing designs when the microchannel length is 13.5 mm with inlet velocities of (a) 0.5 m/s, (b) 1 m/s, and (c) 2 m/s

Grahic Jump Location
Fig. 9

Maximum deviation of the designs with maximum (base) and minimum deviations (constructal) with 2 m/s inlet velocity for length of channels of 1.5 mm, 4.5 mm, and 13.5 mm

Grahic Jump Location
Fig. 10

(a) Geometry of a manifold with 5 identical length microchannels and (b) flow rate in each channel divided by the average flow rate for the base design, the constructal design, and the design of Fig. 10(a) with 1.5-mm microchannel length and 1 m/s inlet velocity

Grahic Jump Location
Fig. 11

Velocity, pressure, and overall pressure (summation of static and dynamic pressures) contours of the designs of Figs. 1, 4, and 10(a) with 1 m/s inlet velocity

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In