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.

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Fig. 1

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

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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

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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

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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.

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Fig. 5

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

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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)

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

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

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Fig. 12

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

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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



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