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Theory of low Mach number compressible flow in a channel

Published online by Cambridge University Press:  26 April 2006

A. Shajii  and
J. P. Freidberg
A. Shajii
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
J. P. Freidberg
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 313 , 25 April 1996 , pp. 131 - 145
Copyright
© 1996 Cambridge University Press

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References

Berg, H. R. van den, Seldam, C. A. ten & Gulik, P. S. van der 1993 J. Fluid Mech. 246, 1–20.
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. John Wiley & Sons
Foumeny, E. A. & Ma, J. 1994 Chem. Engng Technol. 17, 50–60.
Kaviany, M. 1991 Principles of Heat Transfer in Porous Media. Springer
Prins, H. J. 1991 The optimal model for a non-Newtonian compressible gas. Rep. Fac. of Techn. Math. & Informatics. Delft Univ. of Technol.
Prud'homme, R. K., Chapman, T. W. & Bowen, J. R. 1986 Appl. Sci. Res. 43, 67.
Shajii, A., & Freidberg, J. P. 1994a J. Appl. Phys. 76, 3149.
Shajii, A., & Freidberg, J. P. 1994b J. Appl. Phys. 76, 3159.
Thome, R. J. 1994 IEEE Trans. Mag. 30, 1595–1601.
White, F. M. 1986 Fluid Mechanics. McGraw-Hill
White, F. M. 1991 Viscous Fluid Flow, pp. 173–190. McGraw-Hill.
Zanotti, F. & Carbonell, R. G. 1984 Chem. Engng Sci. 39, 299–311.