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.

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.
Wang
,
C. Y.
, 2003, “
Slip Flow in Ducts
,”
Can. J. Chem. Eng.
,
81
, pp.
1058
1061
.
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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