The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique
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 i...
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| Format: | Article |
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MDPI AG
2019-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/962 |
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| author | M. Imran D.L.C. Ching Rabia Safdar Ilyas Khan M. A. Imran K. S. Nisar |
| author_facet | M. Imran D.L.C. Ching Rabia Safdar Ilyas Khan M. A. Imran K. S. Nisar |
| author_sort | M. Imran |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mi>R</mi> <msup> <mi>t</mi> <mi>p</mi> </msup> </mrow> </semantics> </math> </inline-formula> 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. |
| first_indexed | 2024-04-14T05:26:47Z |
| format | Article |
| id | doaj.art-f965ea04bfa8400c840d03b47122541f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T05:26:47Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f965ea04bfa8400c840d03b47122541f2022-12-22T02:09:58ZengMDPI AGSymmetry2073-89942019-08-0111896210.3390/sym11080962sym11080962The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical TechniqueM. Imran0D.L.C. Ching1Rabia Safdar2Ilyas Khan3M. A. Imran4K. S. Nisar5Department of Mathematics, Government College University, Faisalabad, Punjab 38000, PakistanFundamental and Applied Science Department, Universiti Teknologi Petronas, 32610 Perak, MalaysiaDepartment of Mathematics, Government College University, Faisalabad, Punjab 38000, PakistanFaculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, VietnamDepartment of Mathematics, University of Management and Technology Lahore, Punjab 54770, PakistanDepartment of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi ArabiaThe 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mi>R</mi> <msup> <mi>t</mi> <mi>p</mi> </msup> </mrow> </semantics> </math> </inline-formula> 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.https://www.mdpi.com/2073-8994/11/8/962Burgers’ fluidvelocity fieldshear stressLaplace transformmodified Bessel functionStehfest’s algorithmMATHCAD |
| spellingShingle | M. Imran D.L.C. Ching Rabia Safdar Ilyas Khan M. A. Imran K. S. Nisar The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique Symmetry Burgers’ fluid velocity field shear stress Laplace transform modified Bessel function Stehfest’s algorithm MATHCAD |
| title | The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique |
| title_full | The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique |
| title_fullStr | The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique |
| title_full_unstemmed | The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique |
| title_short | The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique |
| title_sort | solutions of non integer order burgers fluid flowing through a round channel with semi analytical technique |
| topic | Burgers’ fluid velocity field shear stress Laplace transform modified Bessel function Stehfest’s algorithm MATHCAD |
| url | https://www.mdpi.com/2073-8994/11/8/962 |
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