In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.
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e-mail: mbahrami@sfu.ca
e-mail: ata42@sfu.ca
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March 2009
Research Papers
Slip-Flow Pressure Drop in Microchannels of General Cross Section
M. Bahrami,
M. Bahrami
Assistant Professor
Mechatronic Systems Engineering, School of Engineering Science,
e-mail: mbahrami@sfu.ca
Simon Fraser University
, BC, V3T 0A3, Canada
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A. Tamayol,
A. Tamayol
Ph.D. Student
Mechatronic Systems Engineering, School of Engineering Science,
e-mail: ata42@sfu.ca
Simon Fraser University
, BC, V3T 0A3, Canada
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P. Taheri
P. Taheri
Ph.D. Candidate
Department of Mechanical Engineering,
University of Victoria
, P.O. Box 3055, Stn. CSC, Victoria, BC, V8W 3P6, Canada
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M. Bahrami
Assistant Professor
Mechatronic Systems Engineering, School of Engineering Science,
Simon Fraser University
, BC, V3T 0A3, Canadae-mail: mbahrami@sfu.ca
A. Tamayol
Ph.D. Student
Mechatronic Systems Engineering, School of Engineering Science,
Simon Fraser University
, BC, V3T 0A3, Canadae-mail: ata42@sfu.ca
P. Taheri
Ph.D. Candidate
Department of Mechanical Engineering,
University of Victoria
, P.O. Box 3055, Stn. CSC, Victoria, BC, V8W 3P6, CanadaJ. Fluids Eng. Mar 2009, 131(3): 031201 (8 pages)
Published Online: February 5, 2009
Article history
Received:
April 9, 2008
Revised:
October 2, 2008
Published:
February 5, 2009
Citation
Bahrami, M., Tamayol, A., and Taheri, P. (February 5, 2009). "Slip-Flow Pressure Drop in Microchannels of General Cross Section." ASME. J. Fluids Eng. March 2009; 131(3): 031201. https://doi.org/10.1115/1.3059699
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