The fractal characterization of surface topography by using Cantor set structures is introduced to quantify the microchannel surface. Based on this fractal characterization of surface, a model of laminar flow in rough microchannels is developed and numerically analyzed in this paper. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all discussed. The results indicate that the presence of roughness leads to the form of detachment, and the eddy generation is observed at the shadow of the roughness elements. The pressure drop in the rough microchannels along the flow direction is larger than that in the smooth channel. It is no longer in a linear fashion and the fluctuation in pressure drop along the stream due to the vortex near the wall is found. Differing from the smooth channel, the Poiseuille number for laminar flow in rough microchannels is no longer only dependent on the cross-sectional shape of the channel, but also strongly influenced by the Reynolds number, roughness height, and fractal dimension (spectrum) of the surface.

References

References
1.
Taylor
,
J. B.
,
Carrano
,
A. L.
,and
Kandlikar
,
S. G.
, 2006, “
Characterization of the Effect of Surface Roughness and Texture on Fluid Flow: Past, Present, and Future
,”
Int. J. Therm. Sci.
,
45
(
10
), pp.
962
968
.
2.
Kandlikar
,
S. G.
, 2008, “
Exploring Roughness Effect on Laminar Internal Flow Are We Ready for Change
,”
Nanoscale Microscale Thermophys. Eng.
,
12
(
1
), pp.
61
82
.
3.
Pfund
,
D.
,
Rector
,
D.
,and
Shekarriz
,
A.
, 2000, “
Pressure Drop Measurements in a Microchannel
,”
AIChE J.
,
46
(
8
), pp.
1496
1507
.
4.
Shen
,
S.
,
Xu
,
J. L.
,
Zhou
,
J. J.
,and
Chen
,
Y.
, 2006, “
Flow and Heat Transfer in Microchannels With Rough Wall Surface
,”
Energy Convers. Manage.
,
47
(
11-12
), pp.
1311
1125
.
5.
Celata
,
G. P.
,
Cumo
,
M.
,
McPhail
,
S.
,and
Zummo
,
G.
, 2006, “
Characterization of Fluid Dynamic Behaviour and Channel Wall Effects in Microtube
,”
Int. J. Heat Fluid Flow
,
27
(
1
), pp.
135
143
.
6.
Croce
,
G.
,and
Agaro
,
P. D.
, 2004, “
Numerical Analysis of Roughness Effect on Microtube Heat Transfer
,”
Superlattices Microstruct.
,
35
(
3-6
), pp.
601
616
.
7.
Wang
,
M.
, and
Kang
,
Q. J.
, 2009, “
Electrokinetic Transport in Microchannels With Random Roughness
,”
Anal. Chem.
,
81
(
8
), pp.
2953
2961
.
8.
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 Minichannels
,”
Phys. Fluids
,
17
(
10
), pp.
1
11
.
9.
Xu
,
J. L.
,
Gan
,
Y. H.
,
Zhang
,
D. C.
,and
Li
,
X. H.
, 2005, “
Microscale Heat Transfer Enhancement Using Thermal Boundary Redeveloping Concept
,”
Int. J. Heat Mass Transfer
,
48
(
9
), pp.
1662
1674
.
10.
Xu
,
J. L.
,
Song
,
Y. X.
,
Zhang
,
W.
,
Zhang
,
H.
,and
Gan
,
Y. H.
, 2008, “
Numerical Simulations of Interrupted and Conventional Microchannel Heat Sinks
,”
Int. J. Heat Mass Transfer
,
51
(
25-26
), pp.
5906
5917
.
11.
Guo
,
Z. Y.
,and
Li
,
Z. X.
, 2003, “
Size Effect on Microscale Single-Phase Flow and Heat Transfer
,”
Int. J. Heat Mass Transfer
,
46
(
1
), pp.
149
159
.
12.
Bahrami
,
M.
,
Yovanovich
,
M. M.
,and
Culham
,
J. R.
. 2006, “
Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes
,”
J. Fluids Eng.
,
128
(
3
), pp.
632
637
.
13.
Chen
,
Y. P.
,and
Cheng
,
P.
, 2003, “
Fractal Characterization of Wall Roughness on Pressure Drop in Microchannels
,”
Int. Commun. Heat Mass Transfer
,
30
(
1
), pp.
1
11
.
14.
Sayles
,
R. S.
,and
Thomas
,
T. R.
, 1978, “
Surface Topography as a Nonstationary Random Process
,”
Nature (London)
,
271
(
5644
), pp.
431
434
.
15.
Warren
,
T. L.
,and
Krajcinovic
,
D.
, 1995, “
Fractal Models of Elastic-Perfectly Plastic Contact of Rough Surfaces Based on the Cantor Set
,”
Int. J. Solids Struct.
,
32
(
19
), pp.
2907
2922
.
16.
Warren
,
T. L.
,
Majumdar
,
A.
,and
Krajcinovic
,
D. A.
, 1996, “
A Fractal Model for the Rigid-Perfectly Plastic Contact of Rough Surfaces
,”
J. Appl. Mech.
,
63
(
1
), pp.
47
54
.
17.
Warren
,
T. L.
,and
Krajcinovic
,
D.
, 1996, “
Random Cantor Set Models for the Elastic-Perfectly Plastic Contact of Rough Surface
,”
Wear
,
196
(
1-2
), pp.
1
15
.
18.
Chen
,
Y. P.
,
Fu
,
P. P.
,
Zhang
,
C. B.
,and
Shi
,
M. H.
, 2010, “
Numerical Simulation of Laminar Heat Transfer in Microchannels With Rough Surfaces Characterized by Fractal Cantor Structures
,”
Int. J. Heat Fluid Flow
,
31
(
4
), pp.
622
629
.
19.
Mandelbrot
,
B. B.
, 1983,
The Fractal Geometry of Nature, Freeman
,
New York
.
20.
Majumdar
,
A.
, and
Tien
,
C. L.
, 1990, “
Fractal Characterization and Simulation of Rough Surface
,”
Wear
,
136
(
2
), pp.
313
327
.
21.
Voss
,
R. F.
, 1988,
Fractals in Nature: From Characterization to Simulation
,
Springer-Verlag
,
New York
.
22.
White
,
F. M.
, 2003,
Fluid Mechanics
,
5th
ed.,
Mc-Graw Hill
,
New Delhi
.
23.
Kandlikar
,
S. G.
, 2005, “
Roughness Effects at Microscale—Reassessing Nikuradse’s Experiments on Liquid Flow in Rough Tubes
,”
Bull. Pol. Acad. Sci.: Tech. Sci.
,
53
(
4
), pp.
343
349
. Available at http://bulletin.pan.pl/vol53iss4.htmlhttp://bulletin.pan.pl/vol53iss4.html and http://bulletin.pan.pl/(53-4)343.pdfhttp://bulletin.pan.pl/(53-4)343.pdf.
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