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On duct flow of a linear viscoelastic fluid

Published online by Cambridge University Press:  26 February 2010

M. Chen
Affiliation:
Department of Mathematics, Red Deer College, Red Deer, Alberta, Canada.
V. Madan
Affiliation:
Department of Mathematics, Red Deer College, Red Deer, Alberta, Canada.
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Extract

Viscoelastic and viscoinelastic flows through straight ducts of different cross-sectional shapes have engaged the attention of a number of workers. These results may be found in all standard texts on the subject. The viscoelastic flows present a more complex analysis than the viscous flows, and for this reason a viscoelastic solution can rarely be obtained in an explicit and usable form. In this note, we obtain a simple formula relating the drag per unit length of the duct, the pressure gradient, the cross-sectional area, and the rate of flux across the section for a duct of arbitrary cross-section without explicitly solving for the physical components of velocity. This result may be of interest to workers experimenting with the non-Newtonian fluids. The recent work of Nigam and Arunachalam [1], which gives a similar result for the drag in viscous flows, can be deduced very easily from the present analysis.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1972

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References

1.Nigam, S. D. and Arunachalam, P. V., “Viscous Flow in Ducts”, Jour. Math. Phys. Sci., 5 (1971).Google Scholar
2.Fredrickson, A. G., Principles and Applications of Rheology (Prentice-Hall, 1964).Google Scholar