Closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections. To achieve this goal, starting from the general solution of the Poisson’s equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall. Then the application of boundary conditions for three different types of cross sections is examined. While the model is general enough to be extended to almost any arbitrary cross section, microchannels of polygonal (with circular as a limiting case), rectangular, and rhombic cross sections are analyzed in this study. The results are then successfully compared to the existing data in the literature.

References

References
1.
Antohe
,
B. V.
,
Lage
,
J. L.
,
Price
,
D. C.
, and
Weber
,
R. M.
, 1996, “
Numerical Characterization of Micro Heat Exchangers Using Experimentally Tested Porous Aluminum Layers
,”
Int. J. Heat Fluid Flow
,
17
(
6
), pp.
594
603
.
2.
Ho
,
C. M.
, and
Tai
,
Y. C.
, 1998, “
Micro-Electro-Mechanical–Systems (MEMS) and Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
, pp.
579
612
.
3.
Cha
,
S. W.
,
O’Hayre
,
S.
, and
Prinz
,
F. B.
, 2004, “
The Influence of Size Scale on the Performance of Fuel Cells
,”
Solid State Ionics
,
175
, pp.
789
795
.
4.
Morini
,
G. L.
, 2006, “
Scaling Effects for Liquid Flows in Microchannels
,”
Heat Transfer Eng.
,
27
(
4
), pp.
64
73
.
5.
Merrikh
,
A. A.
, and
Lage
,
J. L.
, 2005, “
The Role of Red Cell Movement on Alveolar Gas Diffusion
,”
Materialwiss. Werkstofftech.
,
36
(
10
), pp.
497
504
.
6.
Morini
,
G. L.
, 2004, “
Viscous Heating in Liquid Flows in Micro-Channels
,”
Int. J. Heat Mass Transfer
,
48
(
17
), pp.
3637
3647
.
7.
Herwig
,
H.
, and
Hausner
,
O.
, 2003, “
Critical View on “New Results in Micro-Fluid Mechanics”: An Example
,”
Int. J. Heat Mass Transfer
,
46
(
5
), pp.
935
937
.
8.
Hooman
,
K.
,
Hooman
,
F.
and
Famouri
,
M.
, 2009, “
Scaling Effects for Flow in Micro-Channels: Variable Property, Viscous Heating, Velocity Slip, and Temperature Jump
,”
Int. Commun. Heat Mass Transfer
,
36
(
2
), pp.
192
196
.
9.
Gad-El-Hak
,
M.
, 2006, “
Gas and Liquid Transport at the Microscale
,”
Heat Transfer Eng.
,
27
(
4
), pp.
13
29
.
10.
Pfahler
,
J.
,
Harley
,
J.
,
Bau
,
H.
, and
Zemel
,
J.
, 1991, “
Liquid Transport in Micron and Submicron Channels
,”
Sens. Actuators, A
,
22
, pp.
431
434
.
11.
Ebert
,
W. A.
, and
Sparrow
,
E. M.
, 1965, “
Slip Flow in Rectangular and Annular Ducts
,”
J. Basic Eng.
,
87
, pp.
1018
1024
.
12.
Harley
,
J. C.
,
Huang
,
Y. F.
,
Bau
,
H. H.
, and
Zemel
,
J. N.
, 1995, “
Gas-Flow in Microchannels
,”
J. Fluid Mech.
,
284
, pp.
257
274
.
13.
Morini
,
G. L.
,
Lorenzini
,
M.
, and
Salvigni
,
S.
, 2006, “
Friction Characteristics of Compressible Gas Flows in Microtubes
,”
Exp. Therm. Fluid Sci.
,
30
(
8
), pp.
733
744
.
14.
Hooman
,
K.
, 2008, “
A Superposition Approach to Study Slip-Flow Forced Convection in Microchannels of Arbitrary Cross–Section
,”
Int. J. Heat Mass Transfer
,
51
, pp.
3753
3762
.
15.
Hooman
,
K.
, 2009, “
Slip Flow Forced Convection in a Microporous Duct of Rectangular Cross-Section
,”
Appl. Therm. Eng.
,
29
, pp.
1012
1019
.
16.
Hooman
,
K.
, 2007, “
Entropy Generation for Microscale Forced Convection: Effects of different Thermal Boundary Conditions, Velocity Slip, Temperature Jump Viscous Dissipation, and Duct Geometry
,”
Int. Commun. Heat Mass Transfer
,
34
(
8
), pp.
945
957
.
17.
Hooman
,
K.
, and
Ejlali
,
A.
, 2010, “
Effects of Viscous Heating, Fluid Property Variation, Velocity Slip, and Temperature Jump on Convection Through Parallel Plate and Circular Microchannels
,”
Int. Commun. Heat Mass Transfer
,
37
(
1
), pp.
34
38
.
18.
Duan
,
Z.
, and
Musychka
,
Y. S.
, 2007, “
Slip Flow in Non-Circular Microchannels
,”
Microfluids Nanofluids
,
3
, pp.
473
484
.
19.
Bahrami
,
M.
,
Tamayol
,
A.
, and
Taheri
,
P.
, 2009, “
Slip-Flow Pressure Drop in Microchannels of General Cross Section
,”
ASME J. Fluids Eng.
,
131
, pp.
1036
1044
.
20.
Arkilic
,
E. B.
,
Schmidt
,
M. A.
, and
Breuer
,
K. S.
, 1997, “
Gaseous Slip Flow in Long Microchannels
,”
J. Microelectromech. Syst.
,
6
(
2
), pp.
167
178
.
21.
Araki
,
T.
,
Kim
,
M. S.
, and
Iwai
,
H.
, 2002, “
An Experimental Investigation of Gaseous Flow Characteristics in Microchannels
,”
Microscale Thermophys. Eng.
,
6
(
2
), pp.
17
30
.
22.
Colin
,
S.
,
Lalonde
,
P.
, and
Caen
,
R.
, 2004, “
Validation of a second-order slip flow model in rectangular microchannels
,”
Heat Transfer Eng.
,
25
, pp.
23
30
.
23.
Delgado
,
M. A.
,
Franco
,
J. M.
,
Partal
,
P.
, and
Gallegos
,
C.
, 2005, “
Experimental Study of Grease Flow in Pipelines: Wall Slip and Air Entrainment Effects
,”
Chem. Eng. Process.
,
44
(
7
), pp.
805
817
.
24.
Kim
,
M. S.
,
Araki
,
T.
,
Inaoka
,
K.
, and
Suzuki
,
K.
, 2000, “
Gas Flow Characteristics in Microtubes
,”
JSME Int. J., Ser. B
,
43
(
4
), pp.
634
639
.
25.
Taheri
,
P.
, and
Struchtrup
,
H.
, 2010,
“An Extended Macroscopic Transport Model for Rarefied Gas Flows in Long Capillaries With Circular Cross Section,”
Phys. Fluids
,
22
, p.
112004
.
26.
Hadjiconstantinou
,
N. G.
, and
Simek
,
O.
, 2002, “
Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels
,”
ASME J. Heat Transfer
,
124
(
2
), pp.
356
364
.
27.
Bird
,
G. A.
, 1983, “
Definition of Mean Free Path for Ideal Gases
,”
Phys. Fluids
,
26
, pp.
3222
3223
.
28.
Morini
,
G. L.
,
Spiga
,
M.
, and
Tartarini
,
P.
, 2004, “
The Rarefaction Effect on the Friction Factor of Gas Flow in Microchannels
,”
Superlattices Microstruct.
,
35
, pp.
587
599
.
29.
Sparrow
,
E. M.
, and
Hajisheikh
,
A.
, 1966, “
Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions
,”
ASME J. Heat Transfer
,
88
(
4
), pp.
351
358
.
30.
Tamayol
,
A.
, and
Bahrami
,
M.
, 2010, “
Parallel Flow Through Ordered Fibers: An Analytical Approach
,”
ASME J. Fluids Eng.
,
132
(
11
), p.
114502
.
31.
Tamayol
,
A.
, and
Bahrami
,
M.
, 2010, “
Laminar Flow in Microchannels With Non-Circular Cross-Section
,”
ASME J. Fluids Eng.
,
132
(
11
), p.
111201
.
32.
Shams
,
M.
,
Shojaeian
,
M.
,
Aghanajafi
,
C.
, and
Dibaji
,
S. A. R.
, 2009, “
Numerical Simulation of slip Flow Through Rhombus Microchannels
,”
Int. Commun. Heat Mass Transfer
,
36
(
10
), pp.
1075
1081
.
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