Applied Mathematics and Mechanics

, Volume 18, Issue 6, pp 535–541

# An analytical solution and analysis of characters for viscoelastic fluid flow in annular pipe

• Huang Junqi
• Liu Ciqun
Article

## Abstract

In this paper an analytical solution to flow of second order and Maxwell fluids in annular pipe by using Hankel integral transform is presented. A derived formula can be used to analyze the behavior of rotatory velocity and shear stress; since the parameters of material and the gap size of annular pipe explicitly appear in the analytical formula one can easily analyze their effection on the flow behavior. This solution can provide a theoretical base to drilling engineering and polymer shaping techniques. In addition, it can be used to analyze the flow characters in concentric cylinder rheometer and obtain material constants with curve fitting procedure. By investigation it is found that when outer cylinder makes uniform rotatory the history curve of velocity and stress of Maxwell fluid exhibit obliquerectangle wave and raw-wave oscillation respectively. The wave period and amplitude increase with material constant Ha. This conclusion may be of significance in practice.

### Key words

viscoelastic fluid annular pipe analytical solution

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### References

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Liu Ciqun and Huang Junqi, Analytical solution for equations of unsteady flow of non-Newtonian fluids in tube,Applied Mathematics and Mechanicsd (English Ed.),10, 11 (1989), 989–996.Google Scholar
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Zhu Wenhui and Liu Ciqun, Analytical solution for unsteady flow of Maxwell fluid in annular pipe,Acta Mechanica Sinica,24, 1 (1992). (in Chinese)Google Scholar
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M. N. Auchisic,Heat Conduction, Chinese Trans. by Yu Changming, High Education Press (1989). (Chinese version)Google Scholar

## Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

## Authors and Affiliations

• Huang Junqi
• 1
• Liu Ciqun
• 2
1. 1.Department of Resources and Environmental SciencesPeking Normal UniversityBeijingP. R. China
2. 2.Institute of Porous Flow and Fluid MechanicsAcademia SinicaLangfangP. R. China