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Research Papers: Fundamental Issues and Canonical Flows

Slip-Flow in Microchannels of Non-Circular Cross Sections

[+] Author and Article Information
A. Tamayol1

School of Engineering Science,  Simon Fraser University, Surrey, BC, V3T 0A3, Canada

K. Hooman

School of Mechanical and Mining Engineering,  The University of Queensland, Brisbane, QL, 4072, Australia

1

Corresponding Author: A. Tamayol, Mailing Address: 250−13450 102nd Avenue, Surrey, BC, Canada, V3T0A3., Tel: [778] 782 8587, Email: ali_tamayol@sfu.ca

J. Fluids Eng 133(9), 091202 (Sep 08, 2011) (8 pages) doi:10.1115/1.4004591 History: Received July 23, 2010; Revised June 05, 2011; Published September 08, 2011; Online September 08, 2011

Closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections. To achieve this goal, starting from the general solution of the Poisson’s equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall. Then the application of boundary conditions for three different types of cross sections is examined. While the model is general enough to be extended to almost any arbitrary cross section, microchannels of polygonal (with circular as a limiting case), rectangular, and rhombic cross sections are analyzed in this study. The results are then successfully compared to the existing data in the literature.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Polygons with different number of sides, m

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Figure 2

Rectangular cross section

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Figure 3

Rhombus cross section

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Figure 4

The considered portion of the cross section in polygonal ducts

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Figure 5

The considered portion of the cross section in rectangular ducts

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Figure 6

The considered portion of the cross section in rhombic ducts

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Figure 7

Contours of constant dimensionless velocity in a sector of a squared cross section (a) Kn = 0, (b) Kn = 0.01, (c) Kn = 0.05, and (d) Kn = 0.1

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Figure 8

Contours of constant dimensionless velocity in a sector of a triangular (polygon with three sides) cross section: (a) Kn = 0, (b) Kn = 0.01, (c) Kn = 0.05, and (d) Kn = 0.1

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Figure 9

Comparison of reduction of friction coefficient under slip condition calculated from the present solution with experimental data of Kim [24] for circular channels

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Figure 10

The present solution for polygonal ducts in different Knudsen numbers; (a) Poiseuille number, (b) α where σ = 1

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Figure 11

Comparison of the Poiseuille numbers obtained from the present solution (lines) with the numerical results of Morini [28] (symbols) for rectangular channels

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Figure 12

Comparison of the Poiseuille numbers obtained from the present solution (lines) with the numerical results of Shams [32] (symbols) for rhombus channels

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