Laminar forced convection in thermally developing slip flow through isoflux rectangular microchannels is analytically investigated. Local and fully developed Nusselt numbers, fluid temperatures, and wall temperatures are obtained by solving the continuum energy equation for hydrodynamically fully developed slip flow with the velocity slip and temperature jump condition at the walls. It is found that heat transfer may increase, decrease, or remain unchanged, compared to nonslip flow conditions, depending on aspect ratios and two-dimensionless variables that include effects of the microchannel size or rarefaction and the fluid/wall interaction. The transition points that separate heat transfer enhancement from reduction are acquired for different aspect ratios.

1.
Eckert, E. G. R., and Drake, R. M., Jr., 1972, Analysis of Heat and Mass Transfer, McGraw-Hill, pp. 467–486.
2.
Liu, J. Q., Tai, Y. C., and Ho, C. M., 1995, “MEMS for Pressure Distribution Studies of Gaseous Flows in Microchannels,” Proceedings, IEEE Micro Electro Mechanical Systems, pp. 209–215.
3.
Arkilic, E. B., Breuer, K. S., and Schmidt, M. A., 1994, “Gaseous Flow in Microchannels, Application of Micro-Fabrication to Fluid Mechanics,” ASME FED-Vol. 197, pp. 57–66.
4.
Ameel
,
T. A.
,
Barron
,
R. F.
,
Wang
,
X. M.
, and
Warrington
,
R. O.
,
1997
, “
Laminar Forced Convection in a Circular Tube with Constant Heat Flux and Slip Flow
,”
Microscale Thermophysical Engineering
,
1
, No.
4
, pp.
303
320
.
5.
Shih
,
Y. P.
,
Huang
,
C. C.
, and
Tsay
,
S. Y.
,
1995
, “
Extended Leveque Solution for Laminar Heat Transfer to Power-law Fluids in Pipes with Wall Slip
,”
Int. J. Heat Mass Transf.
,
38
, No.
3
, pp.
403
408
.
6.
Barron
,
R. F.
,
Wang
,
X. M.
,
Warrington
,
R. O.
, and
Ameel
,
T. A.
,
1996
, “
Evaluation of the Eigenvalues for the Graetz Problem in Slip-Flow
,”
Int. J. Heat Mass Transf.
,
23
, No.
4
, pp.
563
574
.
7.
Barron
,
R. F.
,
Wang
,
X. M.
,
Ameel
,
T. A.
, and
Warrington
,
R. O.
,
1997
, “
The Graetz Problem Extended to Slip Flow
,”
Int. J. Heat Mass Transf.
,
40
, No.
8
, pp.
1817
1823
.
8.
Wang, X. M., 1996, “Evaluation of the Eigenvalues of the Graetz Problem in Slip-Flow,” M.S. thesis. Louisiana Tech University, Ruston, LA.
9.
Wang, M. L., Ameel, T. A., Frazier, A. B., and Warrington, R. O., 1998, “Microtube Convection Heat Transfer For a Power-Law Fluid in Laminar Slip Flow with an Isoflux Boundary Condition,” International Mechanical Engineering Congress and Exposition, CA., ASME HTD-Vol.361-3/PID-Vol.3, pp. 157–164.
10.
Larrode
,
F. E.
,
Housiadas
,
C.
, and
Drossinos
,
Y.
,
2000
, “
Slip-Flow Heat Transfer in Circular Tubes
,”
Int. J. Heat Mass Transf.
,
43
, pp.
2669
2680
.
11.
Yu, S. P., and Ameel, T. A., 2000, “Slip-Flow Low Peclet Number Thermal Entry Problem Within a Flat Microchannel Subject to Constant Wall Temperature,” Proceedings, Heat Transfer and Transport Phenomena in Microsystems, Banff, Alberta, Canada, October.
12.
Yu
,
S. P.
, and
Ameel
,
T. A.
,
2001
, “
Slip Flow Heat Transfer in Rectangular Microchannels
,”
Int. J. Heat Mass Transf.
,
44
, No.
22
, pp.
4225
4234
.
13.
Aparecido
,
J. B.
, and
Cotta
,
R. M.
,
1990
, “
Thermally Developing Laminar Flow Inside Rectangular Ducts
,”
Int. J. Heat Mass Transf.
,
33
, No.
2
, pp.
341
347
.
14.
Cotta, R. M., 1993, Integral Transforms in Computational Heat and Fluid Flow, CRC Press, FL, pp. 180–188.
15.
Yu
,
S. P.
, and
Ameel
,
T. A.
,
2001
, “
A Universal Entrance Nusselt Number for Internal Slip Flow
,”
Int. Commun. Heat Mass Transfer
,
28
, No.
7
, pp.
905
910
.
16.
Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Advances in Heat Transfer, Supplement 1, Academic Press, New York, pp. 196–222.
17.
Rohsenow, W. M., and Hartnett, J. P., 1973, Handbook of Heat Transfer, McGraw-Hill, pp. 9.1–9.8.
18.
Goniak
,
R.
, and
Duffa
,
G.
,
1995
, “
Corrective Term in Wall Slip Equations for Knudsen Layer
,”
J. Thermophys. Heat Transfer
,
9
, No.
2
, pp.
383
384
.
19.
Ebert, W. A., and Sparrow, E. M., 1965, “Slip Flow in Rectangular and Annular Ducts,” Journal of Basic Engineering, Transactions of the ASME, pp. 1018–1024.
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