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,
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.

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Fig. 1

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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



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