Slip flow in various noncircular microchannels has been further examined, and a simple model for a normalized Poiseuille number is proposed. As for slip flow, no solutions or graphical and tabulated data exist for most geometries; the developed simple model fills this void and can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution, and pressure drop of slip flow in noncircular microchannels by the research community for the practical engineering design of microchannels. The incompressible flow criterion for gas flow in microchannels is given. A Mach number less than 0.3 is not sufficient to ensure that the flow is incompressible. Compressibility depends on the product of two dimensionless parameters: L/L(DRe)(DRe) and Ma (Arkilic et al., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178). Some flows where Ma < 0.3 are low speed compressible flows. A fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels is proposed. If the pressure drop is less than 10% of the outlet pressure, the flow can be considered as incompressible for practical engineering applications. This paper improves and extends previous studies on slip flow in noncircular microchannels.

References

References
1.
Harley
,
J.
,
Huang
,
Y.
,
Bau
,
H.
, and
Zemel
,
J. N.
, 1995, “
Gas Flows in Micro-Channels
,”
J. Fluid Mech.
,
284
, pp.
257
274
.
2.
Arkilic
,
E. B.
,
Breuer
,
K. S.
, and
Schmidt
,
M. A.
, 1997, “
Gaseous Slip Flow in Long Microchannels
,”
J. Microelectromech. Syst.
,
6
(
2
), pp.
167
178
.
3.
Pong
,
K.
,
Ho
,
C.
,
Liu
,
J.
, and
Tai
,
Y.
, 1994, “
Nonlinear Pressure Distribution in Uniform Microchannels
,”
Application of Microfabrication to Fluid Mechanics,
ASME
,
New York
, Vol. FED-197, pp.
51
56
.
4.
Zohar
,
Y.
,
Lee
,
S. Y.
,
Lee
,
Y. L.
,
Jiang
,
L.
, and
Wong
,
P.
, 2002, “
Subsonic Gas Flow in a Straight and Uniform Microchannel
,”
J. Fluid Mech.
,
472
, pp.
125
151
.
5.
Jang
,
J.
, and
Wereley
,
S. T.
, 2004, “
Pressure Distributions of Gaseous Slip Flow in Straight and Uniform Rectangular Microchannels
,”
Microfluid. Nanofluid.
,
1
, pp.
41
51
.
6.
Maurer
,
J.
,
Tabeling
,
P.
,
Joseph
,
P.
, and
Willaime
,
H.
, 2003, “
Second-Order Slip Laws in Microchannels for Helium and Nitrogen
,”
Phys. Fluids
,
15
, pp.
2613
2621
.
7.
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
.
8.
Ewart
,
T.
,
Perrier
,
P.
,
Graur
,
I.
, and
Meolans
,
J. G.
, 2006, “
Mass Flow Rate Measurements in Gas Micro Flows
,”
Exp. Fluids
,
41
, pp.
487
498
.
9.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
, 2007, “
Slip Flow in Non-Circular Microchannels
,”
Microfluid. Nanofluid.
,
3
, pp.
473
484
.
10.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
, 2007, “
Slip Flow in Elliptic Microchannels
,”
Int. J. Therm . Sci.
,
46
, pp.
1104
1111
.
11.
Wang
,
C. Y.
, 2003, “
Slip Flow in a Triangular Duct—An Exact Solution
,”
Z. Angew. Math. Mech.
,
83
, pp.
629
631
.
12.
Morini
,
G. L.
,
Lorenzini
,
M.
, and
Spiga
,
M.
, 2005, “
A Criterion for Experimental Validation of Slip-Flow Models for Incompressible Rarefied Gases through Microchannels
,”
Microfluid. Nanofluid.
,
1
, pp.
190
196
.
13.
Niazmand
,
H.
,
Renksizbulut
,
M.
, and
Saeedi
,
E.
, 2008, “
Developing Slip Flow and Heat Transfer in Trapezoidal Microchannels
,”
Int. J. Heat Mass Transfer
51
, pp.
6126
6135
.
14.
Varoutis
,
S.
,
Naris
,
S.
,
Hauer
,
V.
,
Day
,
C.
, and
Valougeorgis
,
D.
, 2009, “
Computational and Experimental Study of Gas Flows through Long Channels of Various Cross Sections in the Whole Range of the Knudsen Number
,”
J. Vac . Sci. Technol. A
,
27
, pp.
89
100
.
15.
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
, pp.
1075
1081
.
16.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
, 2010, “
Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels
,”
ASME J. Fluids Eng.
,
132
, p.
011201
.
17.
Duan
,
Z. P.
, 2007, “
Analysis of Slip Flow in Microchannels
,” Ph.D. thesis, Memorial University, St. John’s, Newfoundland, Canada.
18.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
, 2007, “
Compressibility Effect on Slip Flow in Non-Circular Microchannels
,”
Nanoscale Microscale Thermophys. Eng.
,
11
, pp.
259
272
.
19.
Guo
,
Z. Y.
, and
Wu
,
X. B.
, 1998, “
Further Study on Compressibility Effects on the Gas Flow and Heat Transfer in a Microtube
,”
Microscale Thermophys. Eng.
,
2
, pp.
111
120
.
20.
Hong
,
C.
,
Asako
,
Y.
,
Turner
,
S. E.
, and
Faghri
,
M.
, 2007, “
Friction Factor Correlations for Gas Flow in Slip Flow Regime
,”
ASME J. Fluids Eng.
,
129
, pp.
1268
1276
.
21.
Yan
,
X. H.
, and
Wang
,
Q. W.
, 2009, “
Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes
,”
ASME J. Fluids Eng.
,
131
, p.
101201
.
22.
Karniadakis
,
G. E.
,
Beskok
,
A.
, and
Aluru
,
N.
, 2005,
MicrofloMicroflows and Nanoflowsws and Nanoflows
,
Springer
,
New York.
You do not currently have access to this content.