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Open AccessArticle

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

1
Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan
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Fundamental and Applied Science Department, Universiti Teknologi Petronas, 32610 Perak, Malaysia
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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Department of Mathematics, University of Management and Technology Lahore, Punjab 54770, Pakistan
5
Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 962; https://doi.org/10.3390/sym11080962
Received: 4 April 2019 / Revised: 5 May 2019 / Accepted: 6 May 2019 / Published: 1 August 2019
(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)
The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations. View Full-Text
Keywords: Burgers’ fluid; velocity field; shear stress; Laplace transform; modified Bessel function; Stehfest’s algorithm; MATHCAD Burgers’ fluid; velocity field; shear stress; Laplace transform; modified Bessel function; Stehfest’s algorithm; MATHCAD
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Imran, M.; Ching, D.; Safdar, R.; Khan, I.; Imran, M.A.; Nisar, K.S. The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique. Symmetry 2019, 11, 962.

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