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Volume 8, Issue 5
Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

Vatsala Mathur & Kavita Khandelwal

DOI: 10.4208/aamm.2014.m588

Adv. Appl. Math. Mech., 8 (2016), pp. 784-794.

Published online: 2018-05

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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 is 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 fluid, velocity field, shear stress, fractional calculus, Hankel transform, Laplace transform.

  • AMS Subject Headings

76A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-784, author = {Mathur , Vatsala and Khandelwal , Kavita}, title = {Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {784--794}, 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 is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m588}, url = {http://global-sci.org/intro/article_detail/aamm/12116.html} }
TY - JOUR T1 - Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains AU - Mathur , Vatsala AU - Khandelwal , Kavita JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 784 EP - 794 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m588 UR - https://global-sci.org/intro/article_detail/aamm/12116.html KW - Fractional Maxwell fluid, velocity field, shear stress, fractional calculus, Hankel transform, Laplace transform. AB -

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 is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Mathur , Vatsala and Khandelwal , Kavita. (2018). Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains. Advances in Applied Mathematics and Mechanics. 8 (5). 784-794. doi:10.4208/aamm.2014.m588
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