Accurate analytic solutions for the fully developed slip flow and H1 heat transfer in rectangular and equilateral triangular ducts are presented. Both velocity slip and temperature jump have significant influences on the Poiseuille and Nusselt numbers. These exact solutions serve as benchmark cases for other methods, whether analytic, approximate, or numerical.

References

References
1.
Sharipov
,
F.
, and
Seleznev
,
V.
,
1988
, “
Data on Internal Rarefied Gas Flows
,”
J. Phys. Chem. Ref. Data
,
27
, pp.
657
706
.10.1063/1.556019
2.
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
.10.1103/PhysRevLett.96.066001
3.
Yoshimura
,
A.
, and
Prudhomme
,
R. K.
,
1988
, “
Wall Slip Corrections for Couette and Parallel Flow Viscometers
,”
J. Rheol.
,
32
, pp.
53
67
.10.1122/1.549963
4.
Wang
,
C. Y.
,
2003
, “
Flow Over a Surface With Parallel Grooves
,”
Phys. Fluids
,
15
, pp.
1114
1121
.10.1063/1.1560925
5.
Sparrow
,
E. M.
, and
Lin
,
S. H.
,
1962
, “
Laminar Heat Transfer in Tubes Under Slip_flow Conditions
,”
ASME J. Heat Transfer
,
84
, pp.
363
369
.10.1115/1.3684399
6.
Ebert
,
W. A.
, and
Sparrow
,
E. M.
,
1965
, “
Slip Flow in Rectangular and Annular Ducts
,”
ASME J. Basic Eng.
,
87
, pp.
1018
1024
.10.1115/1.3650793
7.
Duan
,
Z. P.
, and
Muzychka
,
Y. S.
,
2008
, “
Slip Flow Heat Transfer in Annular Microchannels With Constant Heat Flux
,”
ASME J. Heat Transfer
,
130
, p.
092401
.10.1115/1.2946474
8.
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
, pp.
3460
3467
.10.1016/j.ijheatmasstransfer.2007.10.036
9.
Wang
,
C. Y.
,
2003
, “
Slip Flow in a Triangular Duct—An Exact Solution
,”
Z. Angew. Math. Mech.
,
83
, pp.
629
631
.10.1002/zamm.200310057
10.
Duan
,
D. P.
, and
Muzychka
,
Y. S.
,
2007
, “
Slip Flow in Elliptic Microchannels
,”
Int. J. Therm. Sci.
,
46
, pp.
1104
1111
.10.1016/j.ijthermalsci.2007.01.026
11.
Navier
,
C. L. M.
,
1827
, “
Sur les lois du mouvement des fluides
,”
C.R. Acad. Sci.
,
6
, pp.
389
440
.
12.
Colin
,
S.
,
2012
, “
Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer
,”
ASME J. Heat Transfer
,
134
, p.
020908
.10.1115/1.4005063
13.
Shah
,
R. K.
, and
London
,
A. L.
,
1978
,
Laminar Flow Forced Convection in Ducts
,
Academic Press
,
New York
.
14.
Morini
,
G. L.
, and
Spiga
,
M.
,
1998
, “
Slip Flow in Rectangular Microtubes
,”
Microsc. Thermophys. Eng.
,
2
, pp.
273
282
.10.1080/108939598199919
15.
Zhu
,
X.
,
Liao
,
Q.
, and
Xin
,
M. D.
,
2006
, “
Gas Flow in Microchannel of Arbitrary Shape in Slip Flow Regime
,”
Nanoscale Microscale Thermophys. Eng.
,
10
, pp.
41
54
.10.1080/10893950500354977
16.
Zhu
,
X.
, and
Liao
,
Q.
,
2006
, “
Heat Transfer for Laminar Slip Flow in a Microchannel of Arbitrary Cross Section With Complex Thermal Boundary Condition
,”
Appl. Therm. Eng.
,
26
, pp.
1246
1256
.10.1016/j.applthermaleng.2005.10.031
17.
Tunc
,
G.
, and
Bayazitoglu
,
Y.
,
2002
, “
Heat Transfer in Rectangular Microchannels
,”
Int. J. Heat Mass Transfer
,
45
, pp.
765
773
.10.1016/S0017-9310(01)00201-0
18.
Ghodoossi
,
L.
, and
Egrican
,
N.
,
2005
, “
Prediction of Heat Transfer Characteristics in Rectangular Microchannels for Slip Flow Regime and H1 Boundary Condition
,”
Int. J. Therm. Sci.
,
44
, pp.
513
520
.10.1016/j.ijthermalsci.2005.01.006
19.
Kuddusi
,
L.
, and
Cetegen
,
E.
,
2007
, “
Prediction of Temperature Distribution and Nusselt Number in Rectangular Microchannels at Wall Slip Condition for All Versions of Constant Heat Flux
,”
Int. J. Heat Fluid Flow
,
28
, pp.
777
786
.10.1016/j.ijheatfluidflow.2006.09.002
20.
Hooman
,
K.
,
2008
, “
Heat Transfer and Entropy Generation for Forced Convection Through a Microduct of Rectangular Cross Section: Effects of Slip, Temperature Jump, and Duct Geometry
,”
Int. Commun. Heat Mass Transfer
,
35
, pp.
1065
1068
.10.1016/j.icheatmasstransfer.2008.05.015
21.
Hooman
,
K.
,
2008
, “
A Superposition Approach to Study Slip Flow Forced Convection in Straight Microchannels of Uniform but Arbitrary Cross-Section
,”
Int. J. Heat Mass Transfer
,
51
, pp.
3753
3762
.10.1016/j.ijheatmasstransfer.2007.12.014
22.
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
.10.1115/1.3059699
23.
Yu
,
S.
, and
Ameel
,
T. A.
,
2002
, “
Slip Flow Convection in Isoflux Rectangular Microchannels
,”
ASME J. Heat Transfer
,
124
, pp.
346
355
.10.1115/1.1447932
24.
Sharipov
,
F.
,
2011
, “
Data on Velocity Slip and Temperature Jump on a Gas-Solid Interface
,”
J. Phys. Chem. Ref. Data
,
40
, p.
023101
.10.1063/1.3580290
25.
Wang
,
C. Y.
,
2003
, “
Slip Flow in Ducts
,”
Can. J. Chem. Eng.
,
81
, pp.
1058
1061
.10.1002/cjce.5450810517
26.
Tamayol
,
A.
, and
Hooman
,
K.
,
2011
, “
Slip_flow in Microchannels of Non-Circular Cross Sections
,”
ASME J. Fluids Eng.
,
133
, p.
091202
.10.1115/1.4004591
You do not currently have access to this content.