Many important problems connected to flows in micro-heat exchangers were not studied in sufficient detail. In particular, the governing physical mechanisms are still not well understood for flows in pipes and channels with hydraulic diameter ranging from 5 to 103μm, which are often defined as micro-tubes or micro-channels. Experimental and numerical results of pressure driven laminar, continuous, incompressible, flow in different scale and shape channels are analyzed to highlight variations between various studies and these discrepancies are considered. The main objective is to determine whether the classical fluid flow theory based on the Navier- Stokes equations is valid to predict velocity distribution, pressure drop and transition from laminar to turbulent flow in micro-channels. No differences were found between results in micro-channels, unaffected by fluid ionic composition and the nature of the wall, and conventional size channels. The distinctions between different experimental studies must be attributed to different initial conditions, difference between actual conditions of a given experiment and conditions corresponding to the theoretical model, and measurement accuracy.

References

References
1.
Hagen
,
G.
, 1839, “
Uber die Bewegung des Wassers in egen Zulindrischen Rohren
,”
Pogg. Ann.
46
, pp.
423
442
.
2.
Poiseuille
,
J. L. M.
, 1840, “
J. Recherches Wxperrimentelles sur le Movement des Liquids Dans les Tubes de Tres Petits Diameters
,”
Compt. Rend.
,
11
, pp.
961
967
.
3.
Tuckerman
,
D.
, and
Pease
,
R. F. W.
, 1981, “
High Performance Heat Sinking for VISI
,”
IEEE Electron Device Lett.
,
2
, pp.
126
129
.
4.
Incropera
,
F. P.
,
Liquid Cooling of Electronic Devices by Single-Phase Convection
(
Wiley
,
New York
, 1999).
5.
Stone
,
H. A.
,
Stroock
,
A. D.
, and
Ajdari
,
A.
, 2004, “
Engineering Flows in Small Devices; Microfluidies Toward a Lab-on-a-Chip
,”
Ann. Rev. Fluid Mech.
36
, pp.
381
411
.
6.
Gad-el-Hak
,
M.
, 2005, “
Differences Between Liquid and Gas Transport at the Micro-Scale
,”
Bull. Pol. Acad. Sci.: Technical Sciences
,
53
(
4
), pp.
301
316
.
7.
Celata
,
G. P.
,
Heat Transfer and Fluid Flow in Micro-Channels
(
Begell House
,
New York
, 2004).
8.
Kandlikar
,
S. G.
, 2005, “
Roughness Effects at Micro-Scale – Reassessing, Nikuradse’s Experiments on Liquid Flow in Rough Tubes
,”
Bull. Pol. Acad. Sci.: Technical Sciences
,
53
, pp.
343
349
.
9.
Yarin
,
L. P.
,
Mosyak
,
A.
,
Hetsroni
,
G.
,
Fluid Flow, Heat Transfer and Boiling in Micro-Channels
(
Springer
,
New York
, 2008).
10.
Brauner
,
N.
, and
Moalem-Maron
,
D.
, 1982, “
Identification of the Range of Small Diameter Conduits Regarding Two-Phase Flow Pattern Transitions
,”
Int. Commun. Heat Mass Transfer
19
, pp.
29
39
.
11.
Kew
,
P. A.
, and
Cornwell
,
K.
, 1997, “
Correlations for the Prediction of Boiling Heat Transfer in Small-Diameter Channels
,”
Appl. Therm. Eng.
,
17
, pp.
705
715
.
12.
Triplett
,
K. A.
,
Ghiaasian
,
S. M.
,
Abdel-Khalik
,
S. I.
, and
Sadowski
,
D. L.
, 1999,
‘Gas-Liquid Two-Phase Flow in Microchannels,”
Int. J. Multiphase Flow
,
25
, pp.
377
394
.
13.
Kandlikar
,
S. G.
, and
Grande
,
W. J.
, 2003, “
Evolution of Microchannel Flow Passages-Thermohydraulic Performance and Fabrication Technology
,”
Heat Transfer Eng.
,
21
, pp.
3
17
.
14.
Mala
,
G. M.
, and
Li
,
D.
, 1999, “
Flow Characteristics of Water in Microtubes
,”
Int. J. Heat Fluid Flow
,
20
, pp.
142
148
.
15.
Qu
,
W.
,
Mala
,
G. M.
, and
Li
,
D.
, 2000, “
Pressure Driven Water Flow in Trapezoidal Micro-Channels
,”
Int. J. Heat Mass Transfer
,
43
, pp.
353
364
.
16.
Pfund
,
D.
,
Rector
,
D.
, and
Shekarriz
,
A.
, 2000, “
Pressure Drop Measurements in a Micro-Channel
,”
AIChE J.
,
46
, pp.
1496
1507
.
17.
Li
,
Z. X.
,
Du
,
D. X.
, and
Guo
,
Z. Y.
, 2003, “
Experimental Study on Flow Characteristics of Liquid in Circular Micro-Tubes
,”
Microscale Thermophys. Eng.
,
7
, pp.
253
265
.
18.
Kandlikar
,
S. G.
,
Joshi
,
S.
, and
Tian
,
S.
, 2003, “
Effect of Surface Roughness on Heat Transfer and Fluid Flow Characteristics at Low Reynolds Numbers in Small Diameter Tubes
,”
Heat Transfer Eng.
,
24
, pp.
4
16
.
19.
Nikuradse
,
J.
, 1933, “
Strömungsgesetze in rauhen Rohren
,” (“
Laws of Turbulent Pipe Flow in Rough Pipes
”),
VDI-Forschungsheft
, Paper No. 361.
20.
Schlichting
,
H.
,
Boundary Layer Theory
(
McGraw-Hill
,
New York
, 1979).
21.
Duncan
,
A. B.
, and
Peterson
,
G. P.
1994, “
Review of Microscale Heat Transfer
,”
Appl. Mech. Rev.
,
47
, pp.
397
428
.
22.
Ho
,
C-M.
, and
Tai.
Y.-C.
, 1998, “
Micro-Electro-Mechanical Systems (MEMS) and Fluid Flows
,”
Ann. Rev. Fluid Mech.
,
30
, pp.
579
612
.
23.
Plam
,
B.
, 2000, “
Heat Transfer in Microchannels
,”
Heat Transfer and Transport Phenomena in Microscale
(
Banff
,
Alberta, Canada,
2000), pp.
54
64
.
24.
Sedov
,
L. I.
,
Similarity and Dimensional Methods in Mechanics
(
Academic
,
New York
, 1993).
25.
Loitsianskii
,
L. G.
,
Mechanics of Liquid and Gases
(
Pergamon
,
Oxford
, 1966).
26.
Schiller
,
L.
, 1923, “
Uber den Stromungswinerstand von Rohren Verschiedenen Querschnitts-and Rauhigxeitsgrades
,”
ZAMM
3
, pp.
2
13
.
27.
Nikuradse
,
J.
, 1930, “
Turbulene Stroming in Micht Krlisformigen Rohren
,”
Ing.-Arch.
1
, pp.
306
332
.
28.
Nikuradse
,
J.
, 1932,
Gesetzmässigkeit der turbulenten Strömung in glatten Rohren, Forschungsheft 356, Ausgabe B
, Vol.
3
, VDI-Verlag, Berlin.
29.
Koch
,
R.
, and
Feind
,
K.
, 1958, “
Druckverlust und Warmeubergang in Ringspaltem
,”
Chem.-Ing.-Tech.
,
30
, pp.
557
584
.
30.
Swanson
,
C. J.
,
Julian
,
B.
,
Ihas
,
G. G.
, and
Donnely
,
R. J.
, 2002, “
Pipe Flow Measurements Over a Wide Range of Reynolds Numbers Using Liquid Helium and Various Gases
,”
J. Fluid Mech.
,
461
, pp.
51
60
.
31.
Papautsky
,
I.
,
Brazzle
,
J.
,
Ameel
,
T.
, and
Frazier
,
B.
, 1999, “
Laminar Fluid Behavior in Micro-Channels Using Micro-Polar Fluid Theory
,”
Sens. Actuators
,
73
, pp.
101
108
.
32.
Brutin
,
D.
, and
Tadrist
,
L.
, 2003, “
Experimental Friction Factor of a Liquid Flow in Micro-Tubes
,”
Phys. Fluids
,
15
, pp.
653
661
.
33.
Lampert
,
S. T.
2005, “
The flow field and pressure drop in rectangular micro-channels
,” M.Sc. thesis, Technion-Israel Institute of Technology, Haifa, Israel.
34.
Xu
,
B.
,
Ooi
,
K. T.
,
Wong
,
N. T.
, and
Choi
,
W. K.
, 2000, “
Experimental Investigation of Flow Friction for Liquid Flow in Microchannels
,”
Int. J. Heat Mass Transfer
,
27
, pp.
1165
1176
.
35.
Judy
,
J.
,
Maynes
,
D.
, and
Webb
,
B. W.
, 2002, “
Characterization of Frictional Pressure Drop for Liquid Flows Through Micro-Channels
,”
Int. J Heat Mass Transfer
,
45
, pp.
3477
3489
.
36.
Maynes
,
D.
, and
Webb
,
A. R.
, 2002, “
Velocity Profile Characterization in Sub-Diameter Tubes Using Molecular Tagging Velocimetry
,”
Exp. Fluids
,
32
, pp.
3
15
.
37.
Celata
,
G. P.
,
Gumo
,
M.
, and
Zummo
,
G.
, 2004, “
Thermal-Hydraulic Characteristics of Single-Phase Flow in Capillary Pipes
,”
Exp. Therm. Fluid Sci.
,
28
, pp.
87
95
.
38.
Yang
,
C. Y.
,
Wu
,
J. C.
,
Chien
,
H. T.
, and
Lu
,
S. R.
, 2003, “
Friction Characteristics of Water, R-134a, and Air in Small Tubes
,”
Microscale Thermophys. Eng.
,
7
, pp.
335
348
.
39.
Wu
,
H. Y.
, and
Cheng
,
P.
, 2003, “
Friction Factors in Smooth Trapezoidal Silicon Micro-Channels with Different Aspect Ratio
,”
Int. J. Heat Mass Transfer
,
46
, pp.
2519
2525
.
40.
Sharp
,
K. V.
, and
Adrian
,
R. J.
, 2004, “
Transition From Laminar to Turbulent Flow in Liquid Filled Microtubes
,”
Exp. Fluids
,
36
, pp.
741
747
.
41.
Lelea
,
D.
,
Nishio
,
S.
, and
Takano
,
K.
, 2004, “
The Experimental Research on Micro-Tube Heat Transfer and Fluid Flow of Distilled Water
,”
Int. J. Heat Mass Transfer
,
47
, pp.
2817
2830
.
42.
Cui
,
H. H.
,
Silber-Li
,
Z. H.
, and
Zhu
,
S. N.
, 2004, “
Flow Characteristics of Liquids in Micro-Tubes Driven by High Pressure
,”
Phys. Fluids
,
16
, pp.
1803
1810
.
43.
Hwang
,
Y. W.
, and
Kim
,
M. S.
, 2006, “
The Pressure Drop in Microtubes and Correlation Development
,”
Int. J. Heat Mass Transfer
,
49
, pp.
1804
1812
.
44.
Li
,
Z.
,
He
,
Y.-L.
,
Tang
,
G.-H.
, and
Tao
,
W.-Q.
, 2007, “
Experimental and Numerical Studies of Liquid Flow and Heat Transfer in Microtubes
,”
Int. J. Heat Mass Transfer
,
50
, pp.
3447
3460
.
45.
Hao
,
P. F.
,
Zhang
,
X. W.
, and
Yao
,
F. He.
, 2007, “
Transitional and Turbulent Flow in Circular Micro-Tube
,”
Exp. Therm. Fluid Sci.
,
32
, pp.
423
431
.
46.
Rands
,
C.
,
Webb
,
B. W.
, and
Maynes
,
D.
, 2006, “
Characterization of Transition to Turbulence in Micro-Channels
,”
Int. J. Heat Mass Transfer
,
49
, pp.
2924
2920
.
47.
Horiuchi
,
K.
,
Dutta
,
P.
, and
Richards
,
C. D.
, 2007, “
Experiment and Simulation of Mixed Flows in a Trapezoidal Micro-Channel
,”
Microfluid. Nanofluid.
,
3
, pp.
347
358
.
48.
Travis
,
K.
,
Todd
,
B.
, and
Evans
,
D.
, 1997, “
Departure from Navier-Stokes Hydrodynamics in Confined Liquids
,”
Phys. Rev. E.
,
55
(
4
), pp.
578
584
.
49.
Trethway
,
D.
Meinhart
,
C.
, 2002, “
Apparent Fluid Slip at Hydrophobic Micro-Channel Walls
,”
Phys. Fluids
14
, pp.
L9
L12
.
50.
Morini
,
G. L.
, 2004, “
Laminar-to-Turbulent Transition in Microchannels
,”
Microscale Thermophys. Eng.
,
8
, pp.
15
30
.
51.
Meinhart
,
C. D.
,
Wereley
,
S. T.
, and
Santiago
,
J. G.
, 1999, “
PIV Measurements in Micro-Channel Flow
,”
Exp. Fluids
,
27
, pp.
414
419
.
52.
Meinhart
,
C. D.
,
Wereley
,
S. T.
, and
Santiago
,
J. G.
, 2000a, “
A PIV Algorithm for Estimating Time- Averaged Velocity Fields
,”
J. Fluids Eng.
,
122
, pp.
285
289
.
53.
Harley
,
J. C.
,
Huang
,
Y.
,
Bau
,
H. H.
, and
Zewel
,
J. N.
, 1995 “
Gas Flow in Micro-Channels
,”
J. Fluid Mech.
,
284
, pp.
257
274
.
54.
Turner
,
S. E.
,
Lam
,
L. C.
,
Faghri
,
M.
, and
Gregory
,
O. J.
, 2004, “
Experimental Investigation of Gas Flow in Microchannels
,”
J. Heat Transfer
,
126
, pp.
753
763
.
55.
Kohl
,
M. J.
,
Abdel-Khalik
,
S. I.
,
Jeter
,
S. M.
, and
Sadowski
,
D. L.
, 2005, “
An Experimental Investigation of Microchannel Flow with Internal Pressure Measurements
,”
Int. J. Heat Mass Transfer
,
48
, pp.
1518
1533
.
56.
Morini
,
G. L.
,
Lorenzini
,
M.
, and
Salvigni
,
S.
, 2006, “
Friction Characteristics of Compressible Gas Flows in Micro-Tubes
,”
Exp. Therm. Fluid Sci.
,
30
, pp.
733
744
.
57.
Guo
,
Z. Y.
, and
Li
,
Z. X.
, 2003, “
Size Effect on Single-Phase Channel Flow andHeat Transfer at Micro-Scale
,”
Int. J. Heat Mass Transfer
,
24
, pp.
284
298
.
58.
Bradshow
,
P.
, 2000, “
A Note on “Critical Roughness Height” and Transitional Roughness
,”
Phys. Fluids
,
12
, pp.
1611
1614
.
59.
Kandlikar
,
S. G.
,
Schmitt
,
D.
,
Carrano
,
A. L.
, and
Taylor
,
J. B.
, 2005, “
Characterization of Surface Roughness Effects on Pressure Drop in Single-Phase Flow in Mini-Channels
,”
Phys. Fluids
,
17
(
10
), pp.
1
11
.
60.
Herwig
,
H.
,
Gloss
,
D.
, and
Wenterod
,
T.
, 2008, “
A New Approach to Understanding and Modeling the Influence of Wall Roughness on Friction Factors for Pipe and Channel Flows
,”
J. Fluid Mech.
,
613
, pp.
35
53
.
61.
Moody
,
L. F.
, 1944, “
Friction Factor for Pipe Flow
,”
Trans. ASME
,
66
, pp.
671
684
.
62.
Gloss
,
D.
,
Dittmer
,
J.
, and
Herwig
,
H.
, 2008, “
A Systematic Approach to Wall Roughness Effects in Laminar Channel Flows: Experiments and Modeling
,” Proc. ASME ICNMM 2008.
63.
Baviere
,
R.
,
Gamrat
,
G.
,
Favre-Marinet
,
M.
, and
Le.
,
Person
,
S.
, 2006, “
Modeling of Laminar Flow in Rough-Wall Microchannels
,”
J. Fluid Eng.
,
128
, pp.
734
741
.
64.
Baviere
,
R.
,
Ayela
,
F.
,
Le Person
,
S.
, and
Favre- Marinet
,
M.
, 2004, “
An Experimental Study of Water Flow in Smooth and Rough Rectangular Micro-Channels
,” Second
International Conference
.
65.
Kleinstreuer
,
C.
Koo
,
J.
, 2004, “
Analysis of Wall Roughness Effects for Liquid Flow in Micro-Conduits
,”
ASME J. Fluids Eng.
,
126
, pp.
1
9
.
66.
Celata
,
G.
,
Gumo
,
M.
,
Guglielmi
,
M.
, and
Zummo
,
G.
, 2002, “
Experimental Investigation of Hydraulic and Single Phase Heat Transfer in 0.130 mm Capillary Tube
,”
Microscale Thermophys. Eng.
,
6
, pp.
85
97
.
67.
Obot
,
N. T.
, 2002, “
Toward a Better Understanding of Friction and Heat/Mass Transfer in Micro-Channels- A Literature Review
,”
Microscale Thermophys. Eng.
,
6
, pp.
155
173
.
68.
Bahrami
,
M.
Yovanovich
,
M. M.
Culham
,
J. R.
, 2006, “
Pressure dDrop of fFully Developed Laminar Flow in Rough Micro-Tubes
,”
ASME J. Fluids Eng.
,
128
, pp.
632
637
.
69.
Darbyshire
,
A. G.
Mullin
,
T.
, 1995, “
Transition to Turbulence in Constant-Mass-Flux Pipe Flow
,”
J. Fluid Mech.
,
289
, pp.
83
114
.
You do not currently have access to this content.