A solution of the problem of Poiseuille slip flow through an eccentric cylindrical annulus is obtained in bipolar coordinates. The solution is in excellent agreement with the two published limiting cases of slip flow through concentric annuli and no-slip flow through eccentric annuli. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average velocity (flow rate) under the same pressure gradient and slip conditions. For a given channel geometry, the average velocity varies linearly with Knudsen number except for small aspect ratio. It is also shown that the extrema of the friction factor Reynolds number product is determined by how this product is defined or scaled.

References

1.
Wang
,
C. Y.
,
2015
, “
On Viscous Flow in Semi-Elliptic Ducts
,”
ASME J. Fluids Eng.
,
137
(
11
), p.
114502
.
2.
Alassar
,
R. S.
, and
Abushoshah
,
M. A.
,
2012
, “
Hagen–Poiseuille Flow in Semi-Elliptic Microchannels
,”
ASME J. Fluids Eng.
,
134
(
12
), p.
124502
.
3.
Yovanovich
,
M.
, and
Muzychka
,
Y.
,
1997
, “
Solution of Poisson Equation Within Singly and Doubly Connected Prismatic Domains
,”
National Heat Transfer Conference
, Baltimore, MD, Aug. 10–12.
4.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
,
2007
, “
Slip Flow in Non-Circular Microchannels
,”
Microfluid. Nanofluid.
,
3
(
4
), pp.
473
484
.
5.
Duan
,
Z. P.
,
2012
, “
Slip Flow in Doubly Connected Microchannels
,”
Int. J. Therm. Sci.
,
58
, pp.
45
51
.
6.
Char
,
M.
, and
Tai
,
B.
,
2010
, “
Effects of Viscous Dissipation on Slip-Flow Heat Transfer in a Micro Annulus
,”
Int. J. Heat Mass Transfer
,
53
(7–8), pp.
1402
1408
.
7.
MacDonald
,
D. A.
,
1982
, “
Fully Developed Incompressible Flow Between Non-Coaxial Circular Cylinders
,”
J. Appl. Math. Phys. (ZAMP)
,
33
(6), pp.
738
751
.
8.
Wang
,
C. Y.
,
2011
, “
Slip Flow in Doubly Connected Ducts
,”
Can. Soc. Chem. Eng.
,
89
(
3
), pp.
469
474
.
9.
Avci
,
M.
, and
Aydin
,
O.
,
2008
, “
Laminar Forced Convection Slip-Flow in a Micro-Annulus Between two Concentric Cylinders
,”
Int. J. Heat Mass Transfer
,
51
(13–14), pp.
3460
3467
.
10.
Coelho
,
P. M.
, and
Pinho
,
F. T.
,
2006
, “
Fully-Developed Heat Transfer in Annuli With Viscous Dissipation
,”
Int. J. Heat Mass Transfer
,
49
(
19–20
), pp.
3349
3359
.
11.
Avcı
,
M.
, and
Aydin
,
O.
,
2006
, “
Laminar Forced Convection With Viscous Dissipation in a Concentric Annular Duct
,”
Comptes Rendus Mec.
,
334
(
3
), pp.
164
169
.
12.
Tosun
,
I.
,
1984
, “
Axial Laminar Flow in an Eccentric Annulus: An Approximate Solution
,”
AICHE J.
,
30
(
5
), pp.
877
878
.
13.
Escudier
,
M. P.
,
Oliveira
,
P. J.
, and
Pinho
,
F. T.
,
2002
, “
Fully Developed Laminar Flow of Purely Viscous Non-Newtonian Liquids Through Annuli, Including the Effects of Eccentricity and Inner-Cylinder Rotation
,”
Int. J. Heat Fluid Flow
,
23
(
1
), pp.
52
73
.
14.
Snyder
,
W. T.
, and
Goldstein
,
G. A.
,
1965
, “
An Analysis of Fully Developed Laminar Flow in an Eccentric Annulus
,”
AICHE J.
,
12
(
3
), pp.
462
467
.
15.
Snyder
,
W. T.
,
1963
, “
An Analysis of Slug Flow Heat Transfer in an Eccentric Annulus
,”
AICHE J.
,
9
(
4
), pp.
503
506
.
16.
Jonsson
,
V. K.
, and
Sparrow
,
E. M.
,
1965
, “
Results of Laminar Flow Analysis and Turbulent Flow Experiments for Eccentric Annular Ducts
,”
AICHE J.
,
11
(
6
), pp.
1143
1145
.
17.
Cheng
,
K. C.
, and
Hwang
,
G. J.
,
1968
, “
Laminar Forced Convection in Eccentric Annuli
,”
AICHE J.
,
14
(
3
), pp.
510
512
.
18.
Wilson
,
J. T.
,
1978
, “
Fully Developed Laminar Incompressible Flow in an Eccentric Annulus
,”
AICHE J.
,
24
(
4
), pp.
733
735
.
19.
Usui
,
H.
, and
Tsuruta
,
K.
,
1980
, “
Analysis of Fully Developed Turbulent Flow in an Eccentric Annulus
,”
J. Chem. Eng. Jpn.
,
13
(
6
), pp.
445
450
.
20.
Moon
,
P.
, and
Spencer
,
D. E.
,
1988
,
Field Theory Handbook, Including Coordinate Systems, Differential Equations and Their Solutions
, 2nd ed.,
Springer-Verlag
,
New York
, pp.
1
48
.
21.
Alassar
,
R. S.
, and
El-Gebily
,
M. A.
,
2009
, “
Inviscid Flow Past two Cylinders
,”
ASME J. Fluids Eng.
,
131
(
5
), p.
054501
.
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