0
Research Papers: Fundamental Issues and Canonical Flows

Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels

[+] Author and Article Information
Zhipeng Duan

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadazpduan@uwaterloo.ca

Y. S. Muzychka

Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s, NL, A1B 3X5, Canada

J. Fluids Eng 132(1), 011201 (Dec 21, 2009) (13 pages) doi:10.1115/1.4000692 History: Received December 26, 2008; Revised November 06, 2009; Published December 21, 2009

Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product fRe for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Effect of ξ on the development of velocity profiles for Kn∗=0.01 for circular tubes

Grahic Jump Location
Figure 2

Entrance length for which U(0,ξ)=0.99Ufd(0) for circular tubes

Grahic Jump Location
Figure 3

Effect of Kn∗ on fapp Re for developing laminar flow for circular tubes

Grahic Jump Location
Figure 4

Effect of ξ on the development of velocity profiles for Kn∗=0.005 for parallel plates

Grahic Jump Location
Figure 5

Entrance length for which U(0,ξ)=0.99Ufd(0) for parallel plates

Grahic Jump Location
Figure 6

Entrance length comparison for the Barber and Emerson (23) numerical model

Grahic Jump Location
Figure 7

Effect of Kn∗ on fapp Re for developing laminar flow for parallel plates

Grahic Jump Location
Figure 8

Comparison of fapp Re for different Kn∗ between circular tubes and parallel plates

Grahic Jump Location
Figure 9

Comparison of fapp Re for the numerical data by Renksizbulut (35) for Re=100

Grahic Jump Location
Figure 10

Fully developed f ReDh for noncircular ducts (37)

Grahic Jump Location
Figure 11

Fully developed f ReA for noncircular ducts (37)

Grahic Jump Location
Figure 12

Comparison of f ReA for polygonal ducts

Grahic Jump Location
Figure 13

Comparison of f ReA for circular tubes

Grahic Jump Location
Figure 14

Comparison of f ReA for the numerical data by Niazmand (44)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In