Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

1.
Chapman
D. R.
, and
Rubesin
M. N.
,
1949
, “
Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature
,”
Journal of the Aeronautical Sciences
, Vol.
16
, No.
9
, pp.
547
565
.
2.
Gross, W. A., 1968, Gas Film Lubrication, Wiley, New York.
3.
Harley
C. J.
,
Huang
Y.
,
Bau
H. H.
, and
Zemel
N. J.
,
1995
, “
Gas Flow in Micros-Channels
,”
Journal of Fluid Mechanics
, Vol.
284
, pp.
257
274
.
4.
Joyce, J. W., 1983, “Fluidics: Basic Components and Applications,” US Army Electronics Development Command, Harry Diamond Labs Special Report HDL-SR-83-9.
5.
Schlichting, H., 1979, Boundary Layer Theory, McGraw-Hill.
6.
Schwartz
L. W.
,
1987
, “
A Perturbation Solution for Compressible Viscous Channel Flows
,”
Journal of Engineering Mathematics
, Vol.
21
, pp.
69
86
.
7.
Stewartson
K.
,
1949
, “
Correlated Compressible and Incompressible Boundary Layers
,”
Proceedings Royal Society
, (London), Series
A20
, pp.
84
100
.
8.
Stewartson, K., 1964, “The Theory of Laminar Boundary Layers in Compressible Fluids,” Oxford University Press.
9.
Tuckerman, D. B., 1984, “Heat Transfer Microstructures for Integrated Circuits,” PhD thesis, Department of Electrical Engineering, Stanford University.
10.
Williams
J. C.
,
1963
, “
Viscous Compressible and Incompressible Flow in Slender Channels
,”
AIAA Journal
, Vol.
1
, pp.
186
195
.
11.
Woo, P., and Little, W. A., 1983, “Measurement of Friction Factors for the Flow of Gases in Very Fine Channels Used for Microminiature Joule-Thomson Refrigerators,” Cryogenics, May, pp. 273–278.
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