Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary

Muhammad Mansha Ghalib; Azhar Ali Zafar; Zakia Hammouch; Muhammad Bilal Riaz; Khurram Shabbir

doi:10.3934/dcdss.2020037

Article Contents

2020, Volume 13, Issue 3: 683-693. Doi: 10.3934/dcdss.2020037

This issue Previous Article Perturbations of Hindmarsh-Rose neuron dynamics by fractional operators: Bifurcation, firing and chaotic bursts Next Article Variational principles in the frame of certain generalized fractional derivatives

Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary

1.
Department of Mathematics and statistics, The University of Lahore, Lahore, Pakistan
2.
Department of Mathematics, Govt. College University, Lahore, Pakistan
3.
Faculty of Sciences and Techniques Errachidia, Moulay Ismail University, Morocco
4.
Department of Mathematics, University Of Management and Technology, Lahore, Pakistan

^* Corresponding author: Zakia Hammouch, email: hammouch.zakia@gmail.com
^* Corresponding author: Zakia Hammouch, email: hammouch.zakia@gmail.com

Received: April 30, 2018

Revised: October 31, 2018

Published: December 2019

Prof. Zakia Hammouch was supported by the Research Project UMI2016 financed by Moulay Ismail University allowed to team E3MI

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Abstract

The objective of this paper is to study the unsteady rotational flow of some non Newtonian fluids with Caputo fractional derivative through an infinite circular cylinder by means of the finite Hankel and Laplace transform. The novelty of the work is that motion is produced by applying tangential force not a specific but general function of time on the boundary. Initially the cylinder is at rest and after time $ t_{o} = 0^{+} $ it begins to rotate about its axis with an angular velocity $ \tau_{o} g(t) $. The obtained solutions of velocity field and shear stress have been presented under series form in terms of generalized $ G $-function, satisfying all imposed initial and boundary conditions. The corresponding solutions can be easily particularized to give similar solutions from existing literature for Oldroyd-B fluids, Maxwell fluids, Second grade fluids and Newtonian fluids with/without fractional derivatives performing similar motions.

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Mathematics Subject Classification: Primary: 26A33, 76F10; Secondary: 76A05, 65R10.

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