Microchannel convective heat transfer characteristics in the slip flow regime are numerically evaluated for two-dimensional, steady state, laminar, constant wall heat flux and constant wall temperature flows. The effects of Knudsen number, accommodation coefficients, viscous dissipation, pressure work, second-order slip boundary conditions, axial conduction, and thermally/hydrodynamically developing flow are considered. The effects of these parameters on microchannel convective heat transfer are compared through the Nusselt number. Numerical values for the Nusselt number are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. Numerical results are verified using analytic solutions for thermally and hydrodynamically fully developed flows. The resulting analytical and numerical Nusselt numbers are given as a function of Knudsen number, the first- and second-order velocity slip and temperature jump coefficients, the Peclet number, and the Brinkman number. Excellent agreement between numerical and analytical data is demonstrated. Viscous dissipation, pressure work, second-order slip terms, and axial conduction are all shown to have significant effects on Nusselt numbers in the slip flow regime.

1.
Karniadakis, G.E. and Beskok, A., 2002, “Micro Flows: Fundamentals and Simulation,” Springer-Verlag New York, Inc.
2.
Maxwell
J. C.
,
1879
, “
On Stresses in Rarified Gases Arising from Inequalities of Temperature
,”
Phil. Trans. R. Soc. London
,
170
, pp.
231
256
.
3.
Smoluchowski
M.
,
1898
, “
Ueber Wa¨rmeleitung in Verdu¨nnten Gasen
,”
Annalen der Physik und Chemie
,
64
, pp.
101
130
.
4.
Deissler
R. G.
, “
An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases
,”
1964
,
International Journal of Heat and Mass Transfer
,
7
, pp.
681
694
.
5.
Maurer
J.
,
Tabeling
P.
,
Joseph
P.
, and
Willaime
H.
,
2003
, “
Second-Order Slip Laws in Microchannels for Helium and Nitrogen
,”
Physics of Fluids
,
15
(
9)
, pp.
2613
2621
.
6.
Colin
S.
,
Lalonde
P.
, and
Caen
R.
,
2004
, “
Validation of a Second-Order Slip Flow Model in Rectangular Microchannels
,”
Heat Transfer Engineering
,
25
(
3)
, pp.
23
30
.
7.
Sparrow
E. M.
and
Lin
S. H.
,
1962
, “
Laminar Heat Transfer in Tubes Under Slip-Flow Conditions
,”
Journal of Heat Transfer
,
84
, pp.
363
369
.
8.
Inman, R.M., 1964, “Laminar Slip Flow Heat Transfer in a Parallel-Plate Channel or a Round Tube with Uniform Wall Heating,” NASA TN D-2393.
9.
Inman, R.M., 1964, “Heat Transfer for Laminar Slip Flow of a Rarefied Gas in a Parallel-Plate Channel or a Circular Tube with Uniform Wall Temperature,” NASA TN D–2213.
10.
Ameel
T. A.
,
Wang
X.
,
Barron
R. F.
, and
Warrington
R. O.
,
1997
, “
Laminar Forced Convection in a Circular Tube with Constant Heat Flux and Slip Flow
,”
Microscale Thermophysical Engineering
,
1
, pp.
303
320
.
11.
Barron
R. F.
,
Wang
X.
,
Ameel
T. A.
, and
Warrington
R. O.
,
1997
, “
Graetz Problem Extended to Slip-Flow
,”
International Journal of Heat and Mass Transfer
,
40
(
8)
, pp.
1817
1823
.
12.
Larrode
F. E.
,
Housiadas
C.
, and
Drossinos
Y.
,
2000
, “
Slip-Flow Heat Transfer in Circular Tubes
,”
Int. J. Heat Mass Transfer
,
43
, pp.
2669
2680
.
13.
Tunc
G.
and
Bayazitoglu
Y.
,
2000
, “
Heat Transfer for Gaseous Flow in Microtubes with Viscous Heating
,”,
ASME Heat Transfer Division Publication
,
366
, pp.
299
306
.
14.
Tunc, G. and Bayazitoglu, Y., 2002, “Convection at the Entrance of Micropipes with Sudden Wall Temperature Change,” ASME International Mechanical Engineering Congress and Exposition, pp. 265–270.
15.
Yu, S., 2002, “Slip Flow Heat Transfer in Rectangular Microchannels,” Ph.D. Dissertation, University of Utah.
16.
Aydin
O.
and
Avci
M.
,
2006
Heat and Fluid Flow Characteristics of Gases in Micropipes
,”
International Journal of Heat and Mass Transfer
,
49
, pp.
1723
1730
.
17.
Chen
C.
,
2006
, “
Slip-Flow Heat Transfer in a Microchannel With Viscous Dissipation
,”
International Journal of Heat and Mass Transfer
,
42
, pp.
853
860
.
18.
Jeong
H.
and
Jeong
J
,
2006
, “
Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation in Microchannel
,”
International Journal of Heat and Mass Transfer
,
49
, pp.
2151
2157
.
19.
Kavehpour
H. P.
,
Faghri
M.
, and
Asako
Y.
,
1997
, “
Effects of Compressibility and Rarefaction on Gaseous Flows in Microchannels
,”
Numerical Heat Transfer, Part A
,
32
, pp.
677
696
.
20.
Hadjiconstantinou
N. G.
,
2000
, “
Convective Heat Transfer in Micro and Nano Channels: Nusselt Number Beyond Slip Flow
,”
ASME Heat Transfer Division Publication
,
2
, pp.
13
22
.
21.
Hadjiconstantinou
N. G.
and
Simek
O.
,
2002
, “
Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels
,”
Journal of Heat Transfer
,
124
, pp.
356
364
.
22.
Hadjiconstantinou, N.G., 2003, “The Effect of Viscous Heat Dissipation on Convective Heat Transfer in Small-Scale Slipping Gaseous Flows,” First International Conference on Microchannels and Minichannels, Rochester, NY, pp. 269-273.
23.
Chen
C. S.
and
Kuo
W. J.
,
2004
, “
Heat Transfer Characteristics of Gaseous Flow in Long Mini- and Microtubes
,”
Numerical Heat Transfer: Part A - Applications
,
46
, pp.
497
514
.
24.
van Rij, J., Harman, T., and Ameel, T., 2006, “The Effect of Creep Flow on Two-Dimensional Isoflux Microchannels,” Fourth International Conference on Nanochannels, Microchannels and Minichannels, Limerick, Ireland.
25.
Shah, R.K. and London, A.L., 1978, “Laminar Flow Forced Convection in Ducts,” Academic Press, Inc., New York.
26.
Ou
J. W.
and
Cheng
K. C.
,
1973
, “
Effects of Pressure Work and Viscous Dissipation on Graetz Problem for Gas Flows in Parallel-Plate Channels
,”
Waerme-Stoffuebertrag.
,
6
, pp.
191
198
.
27.
Guilkey, J.E., Harman, T., Xia, A., Kashiwa, B., and McMurtry, P., 2003, “An Eulerian-Lagrangian Approach for Large Deformation Fluid Structure Interaction Problems, Part 1: Algorithm Development,” Second International Conference on Fluid Structure Interaction, pp. 143–156.
28.
Harman, T., Guilkey, J.E., Kashiwa, B., Schmidt, J., and McMurtry, P., 2003, “An Eulerian-Lagrangian Approach for Large Deformation Fluid Structure Interaction Problems, Part 2: Multi-Physics Simulations within a Modern Computational Framework,” Second International Conference on Fluid Structure Interaction, pp. 157–166.
This content is only available via PDF.
You do not currently have access to this content.