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On the unsteady squeezing of a viscous fluid from a tube

Published online by Cambridge University Press:  17 February 2009

F. M. Skalak  and
C. Y. Wang
F. M. Skalak
Affiliation:
Nuclear Eng. Division, Babcock and Wilcox Co., Barberton, Ohio, USA
C. Y. Wang
Affiliation:
Departments of Mathematics and Physiology, Michigan State University, East Lansing, MI, USA
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Abstract

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Viscous fluid is squeezed out from a shrinking (or expanding) tube whose radius varies with time as (1 – βt)½. The full Navier–Stokes equations reduce to a non-linear ordinary differential equation governed by a non-dimensional parameter S representing the relative importance of unsteadiness to viscosity. This paper studies the analytic solutions for large | S | through the method of matched asymptotic expansions. A simple numerical scheme for integration is presented. It is found that boundary layers exist near the walls for large | S |. In addition, flow reversals and oscillations of the velocity profile occur for large negative S (fast expansion of the tube).

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 1 , April 1979 , pp. 65 - 74
Copyright
Copyright © Australian Mathematical Society 1979

References

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