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Research Papers: Flows in Complex Systems

Analytical and Numerical Investigations of Friction Number for Laminar Flow in Microchannels

[+] Author and Article Information
Mohamed S. El-Genk

Distinguished and Regents' Professor
Institute for Space and Nuclear Power Studies,
Nuclear Engineering Department;
Mechanical Engineering Department;
Chemical and Biological
Engineering Department,
University of New Mexico,
Albuquerque, NM 87131-0001
e-mail: mgenk@unm.edu

Mahyar Pourghasemi

Mechanical Engineering Department,
University of New Mexico,
Albuquerque, NM 87131-0001

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 14, 2017; final manuscript received July 20, 2018; published online September 26, 2018. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 141(3), 031102 (Sep 26, 2018) (15 pages) Paper No: FE-17-1806; doi: 10.1115/1.4041112 History: Received December 14, 2017; Revised July 20, 2018

Analytical and computational fluid dynamics (CFD) analyses confirmed the presence of apparent slip for water flow in microchannels with equivalent hydraulic diameter, Dh < 103μm, markedly decreasing the friction number, fRein. The determined values of the slip length, β, from reported measurements of pressure losses in microchannels with aspect ratio, α = 1, 1.74, 2, and 40, are 0.9, 3.5, 1.6, and 0.125 μm, respectively. For Dh > 103μm, the apparent slip in microchannels diminishes, and the friction number approaches the theoretical Hagen–Poiseuille with no slip. The analytical solution for fully developed flow successfully benchmarked the CFD approach, which is subsequently used to investigate fRein and the flow development length, Le, for uniform inlet velocity in microchannels. For fully developed flow, the analytical and CFD values of fRein are in excellent agreement. For microchannels with Dh < 103μm, fRein decreases below that of the theoretical Hagen–Poiseuille with no slip, almost exponentially with decreased Dh. The difference increases with decreased Dh, but increased α and β. The friction number for uniform inlet velocity is identical to that for fully developed flow when Dh ≤ 100 μm, but is as much as 9% higher for larger Dh. For uniform inlet velocity, Le negligibly depends on α and β, but increases with increased Rein. The obtained values are correlated as: Le/Dh = 0.068 Rein.

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Figures

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Fig. 1

Microchannel cross section and velocity profile for fully developed laminar flow with an apparent slip length, β, at the walls

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Fig. 2

Ratio of reported friction numbers in experiments of water flow in microchannels, fReExp, to the theoretical values for macroscale Stokes flow with no slip, fReo

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Fig. 3

Examples of the fully developed and uniform inlet velocity profiles used in CFD analyses

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Fig. 4

Numerical mesh grids used in CFD analyses of fully developed water flow in a square microchannel with an apparent slip at the walls (α = 1, Dh = 50 μm, and β = 1.0 μm): (a) coarse mesh grid, (b) fine mesh grid, and (c) finer mesh grid

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Fig. 5

Numerical mesh grids used in CFD analyses of fully developed water flow in a square microchannel with an apparent slip at the walls (α = 1, Dh = 100 μm, and β = 1.0 μm): (a) coarse mesh grid, (b) fine mesh grid, and (c) finer mesh grid

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Fig. 6

Numerical mesh grids used in CFD analyses of fully developed water flow in a rectangular microchannel with an apparent slip at the walls (α = 10, Dh = 50 μm, and β = 1.0 μm): (a) coarse mesh grid, (b) fine mesh grid, and (c) finer mesh grid

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Fig. 7

Numerical mesh grids used in CFD analyses of fully developed water flow in a rectangular microchannel with an apparent slip at the walls (α = 10, Dh = 100 μm, and β = 1.0 μm): (a) coarse mesh grid, (b) fine mesh grid, and (c) finer mesh grid

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Fig. 8

Effect of Dh, α, and β on pressure losses for fully developed laminar flow in microchannels with and without an apparent slip at the walls

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Fig. 9

Effects of changing α, β, and microchannel width (2a) on the friction number for fully developed flow in microchannels with an apparent slip at the walls

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Fig. 10

Effects of α, and microchannel width (2a) on friction number for apparent slip, β = 1 μm

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Fig. 11

Friction number grid for fully developed flow in microchannels with apparent slip at the walls

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Fig. 12

Effect of the slip length on the friction numbers in microchannels

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Fig. 13

Comparison of friction numbers for fully developed laminar flows in microchannels and microtubes with an apparent slip, β = 1 μm

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Fig. 14

Numerical and analytical friction numbers for fully developed laminar flow in microchannels

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Fig. 15

Comparisons of the analytical and CFD friction factors in microtubes and microchannels with those obtained from measurements of pressure losses in experiments [1,7,12,13,34,3638]

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Fig. 16

Effect of inlet condition on friction numbers for laminar flows in a square microchannel

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Fig. 17

Effect of flow condition on friction number in square microchannels with β = 1 μm

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Fig. 18

Effects of Dh and Rein on the ratio of friction numbers for uniform and fully developed inlet velocities in square microchannels with β = 1 μm

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Fig. 19

Determination of the development length for uniform inlet velocity laminar flow in microchannels

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Fig. 20

Flow development length and correlation for uniform inlet velocity laminar flow in microchannels

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