Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer
The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathem...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/13/4713 |
| _version_ | 1797480230046138368 |
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| author | Yasir Nawaz Muhammad Shoaib Arif Kamaleldin Abodayeh Mairaj Bibi |
| author_facet | Yasir Nawaz Muhammad Shoaib Arif Kamaleldin Abodayeh Mairaj Bibi |
| author_sort | Yasir Nawaz |
| collection | DOAJ |
| description | The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering. |
| first_indexed | 2024-03-09T21:57:05Z |
| format | Article |
| id | doaj.art-d7340f0624ce42fe9f3ac3215e0269e6 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T21:57:05Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-d7340f0624ce42fe9f3ac3215e0269e62023-11-23T19:56:12ZengMDPI AGEnergies1996-10732022-06-011513471310.3390/en15134713Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass TransferYasir Nawaz0Muhammad Shoaib Arif1Kamaleldin Abodayeh2Mairaj Bibi3Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, PakistanDepartment of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, Comsats University Islamabad, Islamabad 44000, PakistanThe recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering.https://www.mdpi.com/1996-1073/15/13/4713non-Newtonian fluidthermal radiationsfinite element methodfinite difference methodMatlab solver bv4c |
| spellingShingle | Yasir Nawaz Muhammad Shoaib Arif Kamaleldin Abodayeh Mairaj Bibi Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer Energies non-Newtonian fluid thermal radiations finite element method finite difference method Matlab solver bv4c |
| title | Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer |
| title_full | Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer |
| title_fullStr | Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer |
| title_full_unstemmed | Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer |
| title_short | Finite Element Method for Non-Newtonian Radiative Maxwell Nanofluid Flow under the Influence of Heat and Mass Transfer |
| title_sort | finite element method for non newtonian radiative maxwell nanofluid flow under the influence of heat and mass transfer |
| topic | non-Newtonian fluid thermal radiations finite element method finite difference method Matlab solver bv4c |
| url | https://www.mdpi.com/1996-1073/15/13/4713 |
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