Slip flow in ducts is important in numerous contemporary applications, especially microchannel flow. This Note reviews the existing exact solutions for slip flow. These solutions serve as accuracy standards for approximate methods including numerical or semi-numerical means. Some new solutions are also introduced.
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Technical Briefs
References
1.
Sharipov
, F.
, and Seleznev
, V.
, 1988, “Data on Internal Rarefied Gas Flows
,” J. Phys. Chem. Ref. Data
, 27
, pp. 657
–706
.2.
Yoshimura
, A.
, and Prudhomme
, R. K.
, 1988, “Wall Slip Corrections for Couette and Parallel Flow Viscometers
,” J. Rheol.
, 32
, pp. 53
–67
.3.
Wang
, C. Y.
, 2003, “Flow Over a Surface With Parallel Grooves
,” Phys. Fluids
, 15
, pp. 1114
–1121
.4.
Choi
, C. H.
, and Kim
, C. J.
, 2006, “Large Slip of Aqueous Liquid Flow Over a Nanoengineered Superhydrophobic Surface
,” Phys. Rev. Lett.
, 96
, p. 066001
.5.
Navier
, C. L. M.
, 1827, “Sur les lois du Mouvement des Fluides
,” Mem. Acad. Roy. Sci. Inst. Fr.
, 6
, pp. 389
–440
.6.
Karniadakis
, G.
, Beskok
, A.
, and Narayan
, A.
, 2005, Microfluids and Nanofluids
, Springer
, New York
.7.
Beavers
, G. S.
, and Joseph
, D. D.
, 1967, “Boundary Conditions at a Naturally Permeable Wall
,” J. Fluid Mech.
, 30
, pp. 197
–207
.8.
Ebert
, W. A.
, and Sparrow
, E. M.
, 1965, “Slip Flow in Rectangular and Annular Ducts
,” ASME J. Basic Eng.
, 87
, pp. 1018
–1024
.9.
Wang
, C. Y.
, 2003, “Slip Flow in a Triangular Duct—An Exact Solution
,” Z. Angew. Math. Mech.
, 83
, pp. 629
–631
.10.
Avramenko
, A. A.
, and Kuznetsov
, A. V.
, 2009, “Instability of Slip Flow in a Curved Channel Formed by Two Concentric Cylindrical Surfaces
,” Eur. J. Mech. B/Fluids
, 28
, pp. 722
–727
.11.
Morini
, G. L.
, and Spiga
, M.
, 1998, “Slip Flow in Rectangular Microtubes
,” Microscale Thermophys. Eng.
, 2
, pp. 273
–282
.12.
Duan
, D. P.
, and Muzychka
, Y. S.
, 2007, “Slip Flow in Elliptic Microchannels
,” Int. J. Thermal Sci.
, 46
, pp. 1104
–1111
.13.
Jang
, J.
, and Kim
, Y. H.
, 2010, “Gaseous Slip Flow of a Rectangular Microchannel With Non-Uniform Slip Boundary Conditions
,” Microfl. Nanofl.
, 9
, pp. 513
–522
.14.
15.
Tamayol
, A.
, and Hooman
, K.
, 2011, “Slip-Flow in Microchannels of Non-Circular Cross Sections
,” ASME J. Fluids Eng.
, 133
, p. 091202
.16.
Tunc
, G.
, and Bayazitoglu
, Y.
, 2002, “Heat Transfer in Rectangular Microchannels
,” Int. J. Heat Mass Transfer
, 45
, pp. 765
–773
.17.
Bahrami
, M.
, Tamayol
, A.
, and Taheri
, P.
, 2009, “Slip-Flow Pressure Drop in Microchannels of General Cross Section
,” ASME J. Fluids Eng.
, 131
, p. 031201
.18.
Wang
, C. Y.
, 2011, “On Stokes Slip Flow Through a Transversely Wavy Channel
,” Mech. Res. Commun.
, 38
, pp. 249
–254
.19.
Wang
, C. Y.
, 2011, “Two-Fluid Oscillatory Flow in a Channel
,” Theor. Appl. Mech. Lett.
, 1
, p. 032007
.20.
Ng
, C. O.
, and Wang
, C. Y.
, 2011, “Oscillatory Flow Through a Channel With Stick-Slip Walls: Complex Navier’s Slip Length
,” ASME J. Fluids Eng.
, 133
, p. 014502
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by by ASME
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