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EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

Part of: Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  21 February 2011

W. AKHTAR ,
CORINA FETECAU  and
A. U. AWAN
W. AKHTAR*
Affiliation:
Institute of Space Technology, P. O. Box 2750, Islamabad, Pakistan (email: [email protected])
CORINA FETECAU
Affiliation:
Department of Theoretical Mechanics, Technical University of Iasi, Iasi 700506, Romania (email: [email protected])
A. U. AWAN
Affiliation:
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan (email: [email protected])
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Abstract

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The Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

Keywords

generalized Maxwell fluidexact solutionstime-dependent shear stress

MSC classification

Secondary: 76A05: Non-Newtonian fluids
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 416 - 429
Copyright
Copyright © Australian Mathematical Society 2011

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