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Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

Part of: Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  08 July 2016

Vatsala Mathur  and
Kavita Khandelwal
Vatsala Mathur*
Affiliation:
Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India
Kavita Khandelwal*
Affiliation:
Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India
*
*Corresponding author. Email:vatsalamathurmnit@gmail.com (V. Mathur), kavitakh21@gmail.com (K. Khandelwal)
*Corresponding author. Email:vatsalamathurmnit@gmail.com (V. Mathur), kavitakh21@gmail.com (K. Khandelwal)
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Abstract

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Keywords

Fractional Maxwell fluidvelocity fieldshear stressfractional calculusHankel transformLaplace transform

MSC classification

Secondary: 76A05: Non-Newtonian fluids
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 784 - 794
Copyright
Copyright © Global-Science Press 2016 

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