Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach
Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scien...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/242 |
| _version_ | 1797504526376239104 |
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| author | Arfan Ali Muhammad Imran Asjad Muhammad Usman Mustafa Inc |
| author_facet | Arfan Ali Muhammad Imran Asjad Muhammad Usman Mustafa Inc |
| author_sort | Arfan Ali |
| collection | DOAJ |
| description | Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scientists. This paper presents a study of unsteady free convection fluid flow and heat transfer of Maxwell fluids with the presence of Clay nanoparticle modelling using fractional calculus. The obtained model was transformed into a set of linear nondimensional, partial differential equations (PDEs). The finite difference scheme is proposed to discretize the obtained set of nondimensional PDEs. The Maple code was developed and executed against the physical parameters and fractional-order parameter to explain the behavior of the velocity and temperature profiles. Some limiting solutions were obtained and compared with the latest existing ones in literature. The comparative study witnesses that the proposed scheme is a very efficient tool to handle such a physical model and can be extended to other diversified problems of a complex nature. |
| first_indexed | 2024-03-10T04:05:50Z |
| format | Article |
| id | doaj.art-f6049aefea104718a2ed0f79c5d1b65f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:50Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f6049aefea104718a2ed0f79c5d1b65f2023-11-23T08:24:14ZengMDPI AGFractal and Fractional2504-31102021-11-015424210.3390/fractalfract5040242Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference ApproachArfan Ali0Muhammad Imran Asjad1Muhammad Usman2Mustafa Inc3Department of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, National University of Modern Languages (NUML), Islamabad 44000, PakistanDepartment of Computer Engineering, Biruni University, Istanbul 34025, TurkeyFractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scientists. This paper presents a study of unsteady free convection fluid flow and heat transfer of Maxwell fluids with the presence of Clay nanoparticle modelling using fractional calculus. The obtained model was transformed into a set of linear nondimensional, partial differential equations (PDEs). The finite difference scheme is proposed to discretize the obtained set of nondimensional PDEs. The Maple code was developed and executed against the physical parameters and fractional-order parameter to explain the behavior of the velocity and temperature profiles. Some limiting solutions were obtained and compared with the latest existing ones in literature. The comparative study witnesses that the proposed scheme is a very efficient tool to handle such a physical model and can be extended to other diversified problems of a complex nature.https://www.mdpi.com/2504-3110/5/4/242numerical methodfractional calculusnanoparticlesMaxwell fluidheat transfer |
| spellingShingle | Arfan Ali Muhammad Imran Asjad Muhammad Usman Mustafa Inc Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach Fractal and Fractional numerical method fractional calculus nanoparticles Maxwell fluid heat transfer |
| title | Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach |
| title_full | Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach |
| title_fullStr | Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach |
| title_full_unstemmed | Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach |
| title_short | Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach |
| title_sort | numerical solutions of a heat transfer for fractional maxwell fluid flow with water based clay nanoparticles a finite difference approach |
| topic | numerical method fractional calculus nanoparticles Maxwell fluid heat transfer |
| url | https://www.mdpi.com/2504-3110/5/4/242 |
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