Abstract

The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement.

1.
Yang
,
C.
,
Wu
,
J.
,
Chien
,
H.
, and
Lu
,
S.
, 2003, “
Friction Characteristics of Water, R-134a, and Air in Small Tubes
,”
Microscale Thermophys. Eng.
1089-3954,
7
, pp.
335
348
.
2.
Morini
,
G. L.
, 2004, “
Laminar-To-Turbulent Flow Transition in Microchannels
,”
Microscale Thermophys. Eng.
1089-3954,
8
, pp.
15
30
.
3.
Tuckerman
,
D. B.
, and
Pease
,
R. F.
, 1981, “
High-Performance Heat Sinking For VLSI
,”
IEEE Electron Device Lett.
0741-3106,
5
, pp.
126
129
.
4.
Pfund
,
D.
,
Rector
,
D.
,
Shekarriz
,
A.
,
Popescu
,
A.
, and
Welty
,
J.
, 2000, “
Pressure Drop Measurements in a Microchannel
,”
AIChE J.
0001-1541,
46
(
8
), pp.
1496
-
1507
.
5.
Bahrami
,
M.
,
Yovanovich
,
M. M.
, and
Culham
,
J. R.
, 2006, “
Pressure Drop of Fully-Developed, Laminar Flow in Rough Microtubes
,”
ASME J. Fluids Eng.
0098-2202,
128
, pp.
632
637
.
Also
ASME 3rd International Conference on Microchannels
, 2005, Paper No. ICMM 2005-75108, July 13–15, Univ. of Toronto, Toronto, Canada.
6.
Liu
,
D.
, and
Garimella
,
S.
, 2004, “
Investigation of Liquid Flow in Microchannels
,”
J. Thermophys. Heat Transfer
0887-8722,
18
(
1
), pp.
65
72
.
7.
Wu
,
H. Y.
, and
Cheng
,
P.
, 2003, “
Friction Factors in Smooth Trapezoidal Silicon Microchannels With Different Aspect Ratios
,”
Int. J. Heat Mass Transfer
0017-9310,
46
, pp.
2519
2525
.
8.
Shah
,
R. K.
, and
London
,
A. L.
, 1978,
Laminar Flow Forced Convection In Ducts
,
Academic
, New York.
9.
White
,
F. M.
, 1974,
Viscous Fluid Flow
,
McGraw-Hill
, New York.
10.
Yovanovich
,
M. M.
, Advanced Heat Conduction, Chap. 12 (in preparation).
11.
Muzychka
,
Y. S.
, and
Yovanovich
,
M. M.
, 1998, “
Modeling Friction Factors in Non-Circular Ducts For Developing Laminar Flow
,”
2nd AIAA Theoretical Fluid Mechanics Meeting
, June 15–18, Albuquerque, NM.
12.
Muzychka
,
Y. S.
, and
Yovanovich
,
M. M.
, 2002, “
Laminar Flow Friction and Heat Transfer in Non-Circular Ducts and Channels Part 1: Hydrodynamic Problem
,”
Proceedings of Compact Heat Exchangers, A Festschrift on the 60th Birthday of Ramesh K. Shah
, Grenoble, France, pp.
123
130
.
13.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
, 1970,
Theory of Elasticity
,
McGraw-Hill
, New York, Chap. 10.
14.
Gao
,
P.
,
Person
,
S. L.
, and
Favre-Marinet
,
M.
, 2002, “
Scale Effects on Hydrodynamics and Heat Transfer in Two Dimensional Mini and Microchannels
,”
Int. J. Therm. Sci.
1290-0729,
41
, pp.
1017
1027
.
15.
Churchill
,
S. W.
, and
Usagi
,
R.
, 1972, “
A General Expression For the Correlation of Rates of Transfer and Other Phenomena
,”
AIChE J.
0001-1541,
18
, pp.
1121
1128
.
You do not currently have access to this content.