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Research Papers: Fundamental Issues and Canonical Flows

Laminar Flow in Microchannels With Noncircular Cross Section

[+] Author and Article Information
Ali Tamayol

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T0A3, Canadaali_tamayol@sfu.ca

Majid Bahrami

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T0A3, Canada

J. Fluids Eng 132(11), 111201 (Nov 03, 2010) (9 pages) doi:10.1115/1.4001973 History: Received November 18, 2009; Revised June 01, 2010; Published November 03, 2010; Online November 03, 2010

Analytical solutions are presented for laminar fully developed flow in micro-/minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and hexagon. A point matching technique is used to calculate closed form solutions for the velocity distributions in the above-mentioned channel cross sections. The developed relationships for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including polygonal, rectangular, circular, elliptical, and rhombic cross sections. The present compact solutions provide a convenient and power tool for performing hydrodynamic analyses in a variety of fundamental and engineering applications such as in microfluidics, transport phenomena, and porous media.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Effect of n on the shape of the hyperellipse equation in the first quadrant, ε=0.5

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Figure 2

Different geometries covered by hyperellipse geometry, ε=1

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Figure 5

Considered geometry for modeling regular polygonal cross section

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Figure 6

Contours of constant velocity for elliptical channel with ε=0.5, (a) present model, Eq. 10; (b) model of Richardson (23)

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Figure 7

Contours of constant velocity for squared channel, (a) present model, Eq. 10; (b) Truskey (19); (c) the relative percentage difference between the present model and the model of Truskey (19)

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Figure 8

Contours of constant velocity for rectangular channel with ε=0.25, (a) present model, Eq. 10; (b) Truskey (19); (c) the relative percentage difference between the present model and the model of Truskey (19)

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Figure 9

Contours of constant velocity for a sector of triangular channel, (a) present model, Eq. 13; (b) the model of Dryden (17)

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Figure 10

Velocity contours and velocity distribution in a star-shaped channel with n=0.8 and ε=1, using Eq. 10

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Figure 11

Velocity contours and velocity distribution in a square with round corners duct, n=4, using Eq. 10

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Figure 12

f Re for different geometries using (a) hydraulic diameter and (b) square root of cross-sectional area as characteristic length scales

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Figure 13

Values of f ReA obtained from present model, Eq. 16, and existing correlations (29) for different values of n, hyperelliptical ducts

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Figure 14

Values of f ReA obtained from present model, Eq. 17, and tabulated values reported by (29) for different values of m, regular polygonal ducts

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Figure 15

Comparison of the f ReA values for rectangular channels predicted using Eq. 16 with experimental data collected from various sources

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Figure 3

Regular polygons with different number of sides, m

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Figure 4

Hyperelliptical cross-section and the boundary conditions

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