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USE OF ATANGANA–BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE

KASHIF ALI ABRO

Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

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ILYAS KHAN

Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

E-mail Address: ilyaskhan@tdtu.edu.vn

Corresponding author.

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, and

KOTTAKKARAN SOOPPY NISAR

Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

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https://doi.org/10.1142/S0218348X20400496Cited by:9 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.

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Vol. 28, No. 08

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History

Received 28 December 2019

Accepted 8 February 2020

Published: August 10, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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USE OF ATANGANA–BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE

Abstract

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