Research Papers: Micro/Nanoscale Heat Transfer

Design and Performance Evaluation of Constructal Microchannel Network Heatsinks

[+] Author and Article Information
Alan Lugarini

Research Center for Rheology
and Non-Newtonian Fluids,
Federal University of Technology—Paraná,
Curitiba 81280-340, Brazil
e-mail: alanlugarinisz@yahoo.com.br

Admilson T. Franco

Department of Mechanical Engineering,
Research Center for Rheology
and Non-Newtonian Fluids,
Federal University of Technology—Paraná,
Curitiba 81280-340, Brazil
e-mail: admilson@utfpr.edu.br

Marcelo R. Errera

Environmental Engineering Department,
Federal University of Paraná,
Curitiba 81531-980, Brazil
e-mail: errera@ufpr.br

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 30, 2017; final manuscript received October 16, 2017; published online January 30, 2018. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 140(5), 052403 (Jan 30, 2018) (9 pages) Paper No: HT-17-1310; doi: 10.1115/1.4038559 History: Received May 30, 2017; Revised October 16, 2017

This work presents the development and analysis of constructal microchannel network architectures for heat dissipation. The network configurations are characterized by multiple flow ramifications and changes in length and hydraulic diameter scales through each ramification level. Architectures investigated experimentally in the past years have adopted constant scaling rules throughout their ramification levels. In this study, constructal theory inspires the design of network architectures with variable scaling rules and up to three ramification levels (N). As a result, it was verified that constructal networks allowed thermal resistance reduction of 15% (N = 2) and 42% (N = 3) for a micro heat sink at a characteristic operational regime. Architecture's selection criterion using performance curves is proposed and it was also demonstrated that the bifurcated network with diameter ratio according to Hess–Murray law is not appropriate for heat dissipation purposes in miniaturized devices.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Bejan, A. , 1996, “Street Network Theory of Organization in Nature,” J. Adv. Transp., 30(2), pp. 85–107. [CrossRef]
Bejan, A. , 1997, “Constructal-Theory Network of Conducting Paths for Cooling a Heat Generating Volume,” Int. J. Heat Mass Transfer, 40(4), pp. 799–816. [CrossRef]
Bejan, A. , 1997, “Constructal Tree Network for Fluid Flow Between a Finite-Size Volume and One Source or Sink,” Rev. Gen. Therm., 36(8), pp. 592–604. [CrossRef]
West, G. B. , Brown, J. H. , and Enquist, B. J. , 1997, “A General Model for the Origin of Allometric Scaling Laws in Biology,” Science, 276(5309), pp. 122–126. [CrossRef] [PubMed]
Chen, Y. , and Cheng, P. , 2002, “Heat Transfer and Pressure Drop in Fractal Tree-Like Microchannel Nets,” Int. J. Heat Mass Transfer, 45(13), pp. 2643–2648. [CrossRef]
Pence, D. , 2003, “Reduced Pumping Power and Wall Temperature in Microchannel Heat Sinks With Fractal-Like Branching Channel Networks,” Microscale Thermophys. Eng., 6(4), pp. 319–330. [CrossRef]
Senn, S. , and Poulikakos, D. , 2004, “Laminar Mixing, Heat Transfer and Pressure Drop in Tree-Like Microchannel Nets and Their Application for Thermal Management in Polymer Electrolyte Fuel Cells,” J. Power Sources, 130(1), pp. 178–191. [CrossRef]
Haller, D. , Woias, P. , and Kockmann, N. , 2009, “Simulation and Experimental Investigation of Pressure Loss and Heat Transfer in Microchannel Networks Containing Bends and T-Junctions,” Int. J. Heat Mass Transfer, 52(11), pp. 2678–2689. [CrossRef]
Revellin, R. , Thome, J. R. , Bejan, A. , and Bonjour, J. , 2009, “Constructal Tree-Shaped Microchannel Networks for Maximizing the Saturated Critical Heat Flux,” Int. J. Therm. Sci., 48(2), pp. 342–352. [CrossRef]
Calame, J. , Park, D. , Bass, R. , Myers, R. , and Safier, P. , 2009, “Investigation of Hierarchically Branched-Microchannel Coolers Fabricated by Deep Reactive Ion Etching for Electronics Cooling Applications,” ASME J. Heat Transfer, 131(5), p. 051401. [CrossRef]
Wang, X. Q. , Xu, P. , Mujumdar, A. S. , and Yap, C. , 2010, “Flow and Thermal Characteristics of Offset Branching Network,” Int. J. Therm. Sci., 49(2), pp. 272–280. [CrossRef]
Hart, R. A. , and Da Silva, A. K. , 2011, “Experimental Thermal–Hydraulic Evaluation of Constructal Microfluidic Structures Under Fully Constrained Conditions,” Int. J. Heat Mass Transfer, 54(15), pp. 3661–3671. [CrossRef]
Yu, X. F. , Zhang, C. P. , Teng, J. T. , Huang, S. Y. , Jin, S. P. , Lian, Y. F. , Cheng, C. H. , Xu, T. T. , Chu, J. C. , Chang, Y. J. , Dang, T. , and Greif, R. , 2012, “A Study on the Hydraulic and Thermal Characteristics in Fractal Tree-Like Microchannels by Numerical and Experimental Methods,” Int. J. Heat Mass Transfer, 55(25–26), pp. 7499–7507. [CrossRef]
Zhang, C. P. , Lian, Y. F. , Hsu, C. H. , Teng, J. T. , Liu, S. , Chang, Y. J. , and Greif, R. , 2015, “Investigations of Thermal and Flow Behavior of Bifurcations and Bends in Fractal-Like Microchannel Networks: Secondary Flow and Recirculation Flow,” Int. J. Heat Mass Transfer, 85, pp. 723–731. [CrossRef]
Wang, X. Q. , Mujumdar, A. S. , and Yap, C. , 2006, “Thermal Characteristics of Tree-Shaped Microchannel Nets for Cooling of a Rectangular Heat Sink,” Int. J. Therm. Sci., 45(11), pp. 1103–1112. [CrossRef]
Hong, F. , Cheng, P. , Ge, H. , and Joo, G. T. , 2007, “Conjugate Heat Transfer in Fractal-Shaped Microchannel Network Heat Sink for Integrated Microelectronic Cooling Application,” Int. J. Heat Mass Transfer, 50(25), pp. 4986–4998. [CrossRef]
Chen, Y. , Zhang, C. , Shi, M. , and Yang, Y. , 2010, “Thermal and Hydrodynamic Characteristics of Constructal Tree-Shaped Minichannel Heat Sink,” AIChE J., 56(8), pp. 2018–2029.
Pence, D. , 2010, “The Simplicity of Fractal-Like Flow Networks for Effective Heat and Mass Transport,” Exp. Therm. Fluid Sci., 34(4), pp. 474–486. [CrossRef]
Judy, J. , Maynes, D. , and Webb, B. , 2002, “Characterization of Frictional Pressure Drop for Liquid Flows Through Microchannels,” Int. J. Heat Mass Transfer, 45(17), pp. 3477–3489. [CrossRef]
Qu, W. , and Mudawar, I. , 2002, “Experimental and Numerical Study of Pressure Drop and Heat Transfer in a Single-Phase Micro-Channel Heat Sink,” Int. J. Heat Mass Transfer, 45(12), pp. 2549–2565. [CrossRef]
Sharp, K. , and Adrian, R. , 2004, “Transition From Laminar to Turbulent Flow in Liquid Filled Microtubes,” Exp. Fluids, 36(5), pp. 741–747. [CrossRef]
Lee, P. S. , Garimella, S. V. , and Liu, D. , 2005, “Investigation of Heat Transfer in Rectangular Microchannels,” Int. J. Heat Mass Transfer, 48(9), pp. 1688–1704. [CrossRef]
Steinke, M. E. , and Kandlikar, S. G. , 2005, “Single-Phase Liquid Friction Factors in Microchannels,” ASME Paper No. ICMM2005-75112.
Zhang, C. P. , Lian, Y. F. , Yu, X. F. , Liu, W. , Teng, J. T. , Xu, T. T. , Hsu, C. H. , Chang, Y. J. , and Greif, R. , 2013, “Numerical and Experimental Studies on Laminar Hydrodynamic and Thermal Characteristics in Fractal-Like Microchannel Networks—Part B: Investigations on the Performances of Pressure Drop and Heat Transfer,” Int. J. Heat Mass Transfer, 66, pp. 939–947. [CrossRef]
Wang, L. , Wu, W. , and Li, X. , 2013, “Numerical and Experimental Investigation of Mixing Characteristics in the Constructal Tree-Shaped Microchannel,” Int. J. Heat Mass Transfer, 67, pp. 1014–1023. [CrossRef]
Hess, W. , 1913, Das Prinzip des kleinsten Kraftverbrauches im dienste hämodynamischer Forschung, Veit & Comp, Leipzig, Germany.
Murray, C. D. , 1926, “The Physiological Principle of Minimum Work—I: the Vascular System and the Cost of Blood Volume,” Proc. Natl. Acad. Sci., 12(3), pp. 207–214. [CrossRef]
Bejan, A. , 2000, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, UK.
Bejan, A. , and Lorente, S. , 2008, Design With Constructal Theory, Wiley, Hoboken, NJ. [CrossRef]
Bejan, A. , and Errera, M. R. , 2000, “Convective Trees of Fluid Channels for Volumetric Cooling,” Int. J. Heat Mass Transfer, 43(17), pp. 3105–3118. [CrossRef]
Sharp, K. , Adrian, R. , Santiago, J. , and Molho, J. , 2005, “Liquid Flows in Microchannels,” MEMS: Introduction and Fundamentals, 2nd ed., CRC Press, Boca Raton, FL. [CrossRef]
White, F. , 1991, Viscous Fluid Flow (McGraw-Hill Series in Mechanical Engineering), McGraw-Hill, New York.
Kandlikar, S. , Garimella, S. , Li, D. , Colin, S. , and King, M. R. , 2005, Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier, Oxford, UK.
Muzychka, Y. , and Yovanovich, M. , 1998, “Modeling Nusselt Numbers for Thermally Developing Laminar Flow in Non-Circular Ducts,” AIAA Paper No. 98-2586.
Phillips, R. , 1987, “Forced Convection, Liquid Cooled, Microchannel Heat Sinks,” M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/14921
Errera, M. , Frigo, A. , and Segundo, E. , 2014, “The Emergence of the Constructal Element in Tree-Shaped Flow Organization,” Int. J. Heat Mass Transfer, 78(1), pp. 181–188. [CrossRef]
Lugarini, A. , 2016, “Microchannel Net Architectures for Electronics Cooling,” Master's dissertation, Federal University of Technology—Paraná, Curitiba, Brazil.
Lee, J. , Kim, Y. , Lorente, S. , and Bejan, A. , 2013, “Constructal Design of a Comb-Like Channel Network for Self-Healing and Self-Cooling,” Int. J. Heat Mass Transfer, 66, pp. 898–905. [CrossRef]
Lee, P. S. , and Garimella, S. V. , 2006, “Thermally Developing Flow and Heat Transfer in Rectangular Microchannels of Different Aspect Ratios,” Int. J. Heat Mass Transfer, 49(17), pp. 3060–3067. [CrossRef]
Arpaci, V. S. , 1966, Conduction Heat Transfer, Addison-Wesley, Reading, MA.
Wechsatol, W. , Lorente, S. , and Bejan, A. , 2003, “Dendritic Heat Convection on a Disc,” Int. J. Heat Mass Transfer, 46(23), pp. 4381–4391. [CrossRef]
Bejan, A. , 2013, “Technology Evolution, From the Constructal Law,” Advances in Heat Transfer, Vol. 45, Academic Press, San Diego, CA, pp. 183–207. [CrossRef] [PubMed] [PubMed]
Bejan, A. , and Errera, M. R. , 2015, “Technology Evolution, From the Constructal Law: Heat Transfer Designs,” Int. J. Energy Res., 39(7), pp. 919–928. [CrossRef]
Pepe, V. R. , Rocha, L. A. , and Miguel, A. F. , 2017, “Optimal Branching Structure of Fluidic Networks With Permeable Walls,” BioMed Res. Int., 2017, p. 5284816. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Geometric configuration of an exemplary microchannel network with two ramification levels (N = 2)

Grahic Jump Location
Fig. 2

The N = 1 architecture is modeled with n1/2 different effluents for the entrance flow rate m˙in, which are distributed as xj mass fractions

Grahic Jump Location
Fig. 3

The N = 2 architecture is modeled with n2/2 different effluents for the entrance flow rate m˙in, which are distributed as xj mass fractions, and n1/2 different effluents for each ramified flow rate xim˙in, which are distributed as yj mass fractions

Grahic Jump Location
Fig. 4

Heat transfer schematics and boundary conditions in the elemental volume. The heatsink base heat flux q″ is incorporated in the two-dimensional diffusion problem as a uniform heat generation rate q″/t.

Grahic Jump Location
Fig. 5

Representation of the energy balance between heatsink base and microchannel walls. qw″ is larger than q″.

Grahic Jump Location
Fig. 6

Thermal response for N = 1 architectures and fixed input flow rate: (a) maximum temperature rise and (b) drawings of architectures marked in (a)

Grahic Jump Location
Fig. 7

Flow rate nonuniformity for N = 1 architectures and fixed input flow rate

Grahic Jump Location
Fig. 8

Pressure drop for N = 1 architectures and fixed input flow rate

Grahic Jump Location
Fig. 9

Performance curves for selected N = 1 architectures. Each curve corresponds to the best architecture for Wp=102,103, 104, and 105.

Grahic Jump Location
Fig. 10

Performance curves for selected N = 2 architectures. A constructal architecture's curve is shown for comparison.

Grahic Jump Location
Fig. 11

Drawings of architectures marked in (a) Fig. 10 and (b) Figs. 12 and 13

Grahic Jump Location
Fig. 12

Performance curves for selected N = 3 architectures with fixed scaling rules

Grahic Jump Location
Fig. 13

Performance curves for selected N = 3 architectures: (I) bifurcated net with Hess–Murray law, (II) best configuration with fixed scaling rules and (IV) constructal configuration




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