Closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections. To achieve this goal, starting from the general solution of the Poisson’s equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall. Then the application of boundary conditions for three different types of cross sections is examined. While the model is general enough to be extended to almost any arbitrary cross section, microchannels of polygonal (with circular as a limiting case), rectangular, and rhombic cross sections are analyzed in this study. The results are then successfully compared to the existing data in the literature.
References
1.
Antohe
, B. V.
, Lage
, J. L.
, Price
, D. C.
, and Weber
, R. M.
, 1996, “Numerical Characterization of Micro Heat Exchangers Using Experimentally Tested Porous Aluminum Layers
,” Int. J. Heat Fluid Flow
, 17
(6
), pp. 594
–603
.2.
Ho
, C. M.
, and Tai
, Y. C.
, 1998, “Micro-Electro-Mechanical–Systems (MEMS) and Fluid Flows
,” Annu. Rev. Fluid Mech.
, 30
, pp. 579
–612
.3.
Cha
, S. W.
, O’Hayre
, S.
, and Prinz
, F. B.
, 2004, “The Influence of Size Scale on the Performance of Fuel Cells
,” Solid State Ionics
, 175
, pp. 789
–795
.4.
Morini
, G. L.
, 2006, “Scaling Effects for Liquid Flows in Microchannels
,” Heat Transfer Eng.
, 27
(4
), pp. 64
–73
.5.
Merrikh
, A. A.
, and Lage
, J. L.
, 2005, “The Role of Red Cell Movement on Alveolar Gas Diffusion
,” Materialwiss. Werkstofftech.
, 36
(10
), pp. 497
–504
.6.
Morini
, G. L.
, 2004, “Viscous Heating in Liquid Flows in Micro-Channels
,” Int. J. Heat Mass Transfer
, 48
(17
), pp. 3637
–3647
.7.
Herwig
, H.
, and Hausner
, O.
, 2003, “Critical View on “New Results in Micro-Fluid Mechanics”: An Example
,” Int. J. Heat Mass Transfer
, 46
(5
), pp. 935
–937
.8.
Hooman
, K.
, Hooman
, F.
and Famouri
, M.
, 2009, “Scaling Effects for Flow in Micro-Channels: Variable Property, Viscous Heating, Velocity Slip, and Temperature Jump
,” Int. Commun. Heat Mass Transfer
, 36
(2
), pp. 192
–196
.9.
Gad-El-Hak
, M.
, 2006, “Gas and Liquid Transport at the Microscale
,” Heat Transfer Eng.
, 27
(4
), pp. 13
–29
.10.
Pfahler
, J.
, Harley
, J.
, Bau
, H.
, and Zemel
, J.
, 1991, “Liquid Transport in Micron and Submicron Channels
,” Sens. Actuators, A
, 22
, pp. 431
–434
.11.
Ebert
, W. A.
, and Sparrow
, E. M.
, 1965, “Slip Flow in Rectangular and Annular Ducts
,” J. Basic Eng.
, 87
, pp. 1018
–1024
.12.
Harley
, J. C.
, Huang
, Y. F.
, Bau
, H. H.
, and Zemel
, J. N.
, 1995, “Gas-Flow in Microchannels
,” J. Fluid Mech.
, 284
, pp. 257
–274
.13.
Morini
, G. L.
, Lorenzini
, M.
, and Salvigni
, S.
, 2006, “Friction Characteristics of Compressible Gas Flows in Microtubes
,” Exp. Therm. Fluid Sci.
, 30
(8
), pp. 733
–744
.14.
Hooman
, K.
, 2008, “A Superposition Approach to Study Slip-Flow Forced Convection in Microchannels of Arbitrary Cross–Section
,” Int. J. Heat Mass Transfer
, 51
, pp. 3753
–3762
.15.
Hooman
, K.
, 2009, “Slip Flow Forced Convection in a Microporous Duct of Rectangular Cross-Section
,” Appl. Therm. Eng.
, 29
, pp. 1012
–1019
.16.
Hooman
, K.
, 2007, “Entropy Generation for Microscale Forced Convection: Effects of different Thermal Boundary Conditions, Velocity Slip, Temperature Jump Viscous Dissipation, and Duct Geometry
,” Int. Commun. Heat Mass Transfer
, 34
(8
), pp. 945
–957
.17.
Hooman
, K.
, and Ejlali
, A.
, 2010, “Effects of Viscous Heating, Fluid Property Variation, Velocity Slip, and Temperature Jump on Convection Through Parallel Plate and Circular Microchannels
,” Int. Commun. Heat Mass Transfer
, 37
(1
), pp. 34
–38
.18.
Duan
, Z.
, and Musychka
, Y. S.
, 2007, “Slip Flow in Non-Circular Microchannels
,” Microfluids Nanofluids
, 3
, pp. 473
–484
.19.
Bahrami
, M.
, Tamayol
, A.
, and Taheri
, P.
, 2009, “Slip-Flow Pressure Drop in Microchannels of General Cross Section
,” ASME J. Fluids Eng.
, 131
, pp. 1036
–1044
.20.
Arkilic
, E. B.
, Schmidt
, M. A.
, and Breuer
, K. S.
, 1997, “Gaseous Slip Flow in Long Microchannels
,” J. Microelectromech. Syst.
, 6
(2
), pp. 167
–178
.21.
Araki
, T.
, Kim
, M. S.
, and Iwai
, H.
, 2002, “An Experimental Investigation of Gaseous Flow Characteristics in Microchannels
,” Microscale Thermophys. Eng.
, 6
(2
), pp. 17
–30
.22.
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
.23.
Delgado
, M. A.
, Franco
, J. M.
, Partal
, P.
, and Gallegos
, C.
, 2005, “Experimental Study of Grease Flow in Pipelines: Wall Slip and Air Entrainment Effects
,” Chem. Eng. Process.
, 44
(7
), pp. 805
–817
.24.
Kim
, M. S.
, Araki
, T.
, Inaoka
, K.
, and Suzuki
, K.
, 2000, “Gas Flow Characteristics in Microtubes
,” JSME Int. J., Ser. B
, 43
(4
), pp. 634
–639
.25.
Taheri
, P.
, and Struchtrup
, H.
, 2010, “An Extended Macroscopic Transport Model for Rarefied Gas Flows in Long Capillaries With Circular Cross Section,”
Phys. Fluids
, 22
, p. 112004
.26.
Hadjiconstantinou
, N. G.
, and Simek
, O.
, 2002, “Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels
,” ASME J. Heat Transfer
, 124
(2
), pp. 356
–364
.27.
Bird
, G. A.
, 1983, “Definition of Mean Free Path for Ideal Gases
,” Phys. Fluids
, 26
, pp. 3222
–3223
.28.
Morini
, G. L.
, Spiga
, M.
, and Tartarini
, P.
, 2004, “The Rarefaction Effect on the Friction Factor of Gas Flow in Microchannels
,” Superlattices Microstruct.
, 35
, pp. 587
–599
.29.
Sparrow
, E. M.
, and Hajisheikh
, A.
, 1966, “Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions
,” ASME J. Heat Transfer
, 88
(4
), pp. 351
–358
.30.
Tamayol
, A.
, and Bahrami
, M.
, 2010, “Parallel Flow Through Ordered Fibers: An Analytical Approach
,” ASME J. Fluids Eng.
, 132
(11
), p. 114502
.31.
Tamayol
, A.
, and Bahrami
, M.
, 2010, “Laminar Flow in Microchannels With Non-Circular Cross-Section
,” ASME J. Fluids Eng.
, 132
(11
), p. 111201
.32.
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
(10
), pp. 1075
–1081
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
