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Research Papers: Fundamental Issues and Canonical Flows

Micro-Channels: Reality and Myth

[+] Author and Article Information
G. Hetsroni1

 Department of Mechanical Engineering, Technion- Israel Institute of Technology, Haifa 32000, Israelhetsroni@techunix.technion.ac.il

A. Mosyak, E. Pogrebnyak, L. P. Yarin

 Department of Mechanical Engineering, Technion- Israel Institute of Technology, Haifa 32000, Israel

1

Corresponding author.

J. Fluids Eng 133(12), 121202 (Dec 20, 2011) (14 pages) doi:10.1115/1.4005317 History: Received May 01, 2011; Revised October 10, 2011; Published December 20, 2011; Online December 20, 2011

Many important problems connected to flows in micro-heat exchangers were not studied in sufficient detail. In particular, the governing physical mechanisms are still not well understood for flows in pipes and channels with hydraulic diameter ranging from 5 to 103   μm, which are often defined as micro-tubes or micro-channels. Experimental and numerical results of pressure driven laminar, continuous, incompressible, flow in different scale and shape channels are analyzed to highlight variations between various studies and these discrepancies are considered. The main objective is to determine whether the classical fluid flow theory based on the Navier- Stokes equations is valid to predict velocity distribution, pressure drop and transition from laminar to turbulent flow in micro-channels. No differences were found between results in micro-channels, unaffected by fluid ionic composition and the nature of the wall, and conventional size channels. The distinctions between different experimental studies must be attributed to different initial conditions, difference between actual conditions of a given experiment and conditions corresponding to the theoretical model, and measurement accuracy.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Map of gas flow regime. The domains A and B correspond to continuous and rarefied fluids, respectively.

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Figure 2

Effect of diameter uncertainty on Po error, Celata [37]

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Figure 3

Poiseuille number for distilled and tap water using tubes of 152 μm and 262 μm diameter (Brutin and Tadrist [32])

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Figure 4

Measured number with viscosity based on: (a) average tube fluid temperature and (b) inlet temperature for fused silica square microchannel with isopropanol (Judy [35])

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Figure 5

Parameter C as a function of pressure for isopropanol in 10 μm tube (Cui [41])

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Figure 6

Revised parameter C as a function of pressure for isopropanol in 10 μm tube (Cui [42])

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Figure 7

Dependence of Poiseuille number on Reynolds number (Rands [46])

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Figure 8

Measured rms of the centerline velocity, averaged over x, divided by the measured velocity, versus Re (Sharp and Adrian [40])

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Figure 9

Velocity profiles versus y/R for Re = 500, 740, 1240 and 1600 (Maynes and Webb [36])

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Figure 10

Velocity profile in a 30 × 300 μm channel. The solid line is the analytical solution for Newtonian flow through a rectangular channel (Meinhart [51]).

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Figure 11

Depth-wise averaged velocity profile in pressure driven flow for (a) Channel 1 and (b) Channel 2 presented in Table 4 for dP/dx =− 9319 N/m3 . For comparison, numerical results of depth-wise averaged velocity distribution for rectangular micro-channels are also presented for the same pressure gradient (Horiuchi [47]) (a) channel No 1-depth 12 μm, (b) channel No 2 -depth 8 μm.

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Figure 12

Influence of rarefaction on the local friction factor (Turner [54])

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Figure 13

Influence of compressibility on local friction factor for air (Turner [54])

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Figure 14

Regular roughness. (a) Two-dimensional (b) Three dimensional: (1) symmetrical arrangement (2) asymmetrical arrangement.

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Figure 15

Types of roughness: (a) irregular roughness, (b) equivalent sand grain roughness, (c) maximum profile peak height Rp, mean spacing of profile irregularities Sm, and floor distance to mean line Fp, and (d) actual profile rough-wall pipe

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Figure 16

Schematics of dependence of the friction factor on the Reynolds number I – laminar flow, II – transition from laminar to turbulent flow, III – developed turbulent flow. (1) Stoke’s law; (2) laminar flow in rough-wall pipe; (3) Blasius law. IIIa-domain where relative roughness plays dominant role; IIIb-domain where friction factor depends on the relative roughness plays dominant role; IIIb-domain where friction factor depends on the relative roughness and the Reynolds number; a – a-above this line the friction factor depends only on the relative roughness.

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Figure 17

Poiseuille number as a function of relative wall roughness. S-type roughness Δ – Eq. 17, ○ – Calculation by Herwig [60].

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Figure 18

Dependence of the Poiseuille number on the Reynolds number for laminar pipe flow (Herwig [60])

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Figure 19

Experimental data and numerical results for laminar flow between two disks (Herwig [60])

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Figure 20

Experimental data [26] and numerical results [60] for three different pipes with rough walls

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Figure 21

Poiseuille number. Comparison of numerical computations and analytical model with experimental results (Baviere [64]). ○ Experimental results; ♦ Numerical computations, k = 5 μm; analytical model, dotted lines indicate k = 6.2 μm, thick lines indicate 7.2 μm, dashed lined indicate 8.2 μm, dash-dotted lines indicate Po = 24.

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