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A method for the study of fully developed parallel flow in straight ducts of arbitrary cross section

Published online by Cambridge University Press:  17 February 2009

J. Mazumdar  and
R. N. Dubey
J. Mazumdar
Affiliation:
Department of Applied Mathematics, University of Adelaide, Australia, 5001.
R. N. Dubey
Affiliation:
Department of Mechanical Engineering, University of Waterloo, Waterloo, CanadaN2L 3G1
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Abstract

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A method is presented for the study of fully developed parallel flow of Newtonian viscous fluid in uniform straight ducts of very general cross-section. The method is based upon the concept of contour lines of constant velocity in a typical cross section of the duct, and uses the function which describes the contour lines as an independent variable to derive the integral momentum equation. The resulting ordinary integro-differential equation is, in principle, much easier to solve than the original momentum equation in partial differential equation form. Several illustrative examples of practical interest are included to explain the method of solution. Some of these solutions are compared with available solutions in the literature. All details are explained by graphs and tables. The method has several interesting features. The study has relevance to biomedical engineering research for blood and urinary tract flow.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 2 , October 1991 , pp. 211 - 239
Copyright
Copyright © Australian Mathematical Society 1991

References

[1] Berker, R., “Intégration des équations du mouvement d'un fluide visqueux incompressible”, In Encyclopedia of Physics, (ed. by Flügge, S.) Vol. 8 /2, (Springer-Verlag, 1963) 71.Google Scholar
[2] Grace, S. F., “Oscillatory motion of a viscous liquid in a long straight tube”, Philosphical Magazine 5 (1928) 933–939.Google Scholar
[3] Jones, R. and Mazumdar, J., “Transverse vibrations of shallow shells by the method of constant-deflection contours”, Journal Acoust. Soc. Am. 56 (1974) 1487–1492.CrossRefGoogle Scholar
[4] Khamrui, S. R., “On the flow of a viscous liquid through a tube of elliptical section under the influence of a periodic pressure gradient”, Bull. Calcutta Math. Society 49 (1957) 57–60.Google Scholar
[5] Laura, P. A. A. and Faulstich, A. J. Jr, “An application of conformal mapping to the determination of the natural frequencies of membranes of regular polygonal shape”, 9th Midwestern Conference, Madison, Wisconsin (1965) 155–160.Google Scholar
[6] Laura, P. A. A., Nagaya, K. and Sarmiento, G. S., “Numerical experiments on the determination of cut off frequencies of waveguides of arbitrary cross-section”, IEEE trans. Microwave Theory Tech. MTT-28 (1980) 568–72.CrossRefGoogle Scholar
[7] Mazumdar, J., “A method for solving problems of elastic plates of arbitrary shape”, J. Aust. Math. Soc. 11 (1970) 95–112.CrossRefGoogle Scholar
[8] Mazumdar, J., “Transverse vibration of membranes of arbitrary shape by the method of constant deflection contours”, J. Sound and Vibration 27 (1973) 47–57.CrossRefGoogle Scholar
[9] Mazumdar, J. and Jones, R., “A simplified approach to the analysis of large deflection of plates”, Journal of Applied Mech. Trans. ASME 41 (1974) 523–524.CrossRefGoogle Scholar
[10] Mazumdar, J., “A method for the study of transient heat conduction in plates of arbitrary cross section”, Nuclear Engng. Design 31 (1974) 383–390.CrossRefGoogle Scholar
[11] Mazumdar, J., “A method for the study of TE and TM modes in waveguides of very general cross section”, IEEE Transactions on MTT 28 (1980) 991–995.CrossRefGoogle Scholar
[12] Mazumdar, J. and Hill, D., “A note on the determination of cut off frequencies of hollow waveguides by a contour line conformal mapping technique”, Applied Acoustics 21 (1987) 23–37.CrossRefGoogle Scholar
[13] O'Brien, V., “Pulsatile fully developed flow in rectangular channels”, Journal of Franklin Institute 300 (1975) 57–60.CrossRefGoogle Scholar
[14] O'Brien, V., “Steady and unsteady flow in noncircular straight ducts”, Journal of Applied Mechanics, Trans. ASME 44 (1977) 1–6.CrossRefGoogle Scholar
[15] Reynolds, O., “On the dynamical motion of viscous liquid in a long straight tube”, Philosophical Transaction of the Royal Society, Series A 186 (1895) 123–164.Google Scholar
[16] Sexl, T., “Uber den von E. G. Richardson's entdeckten Annulareffekt”, Zeitschrift für Physics 61 (1930) 349–356.CrossRefGoogle Scholar
[17] White, F., Viscous Fluid Flow (McGraw Hill, New York, 1974).Google Scholar