Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations
We investigate the thermal flow of Maxwell fluid in a rotating frame using a numerical approach. The fluid has been considered a temperature-dependent thermal conductivity. A non-Fourier heat flux term that accurately reflects the effects of thermal relaxation is incorporated into the model that is...
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AIMS Press
2023-03-01
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| author | Afraz Hussain Majeed Sadia Irshad Bagh Ali Ahmed Kadhim Hussein Nehad Ali Shah Thongchai Botmart |
| author_facet | Afraz Hussain Majeed Sadia Irshad Bagh Ali Ahmed Kadhim Hussein Nehad Ali Shah Thongchai Botmart |
| author_sort | Afraz Hussain Majeed |
| collection | DOAJ |
| description | We investigate the thermal flow of Maxwell fluid in a rotating frame using a numerical approach. The fluid has been considered a temperature-dependent thermal conductivity. A non-Fourier heat flux term that accurately reflects the effects of thermal relaxation is incorporated into the model that is used to simulate the heat transfer process. In order to simplify the governing system of partial differential equations, boundary layer approximations are used. These approximations are then transformed into forms that are self-similar with the help of similarity transformations. The mathematical model includes notable quantities such as the rotation parameter $ \lambda $, Deborah number $ \beta $, Prandtl number <italic>Pr</italic>, parameter $ ϵ $ and the dimensionless thermal relaxation times $ \gamma $. These are approximately uniformly convergent. The Keller box method is used to find approximate solutions to ODEs. We observed due to the addition of elastic factors, the hydrodynamic boundary layer gets thinner. The thickness of the boundary layer can be reduced with the use of the k rotation parameter as well. When <italic>Pr</italic> increases, the wall slope of the temperature increases as well and approaches zero, which is an indication that <italic>Pr</italic> is decreasing. In addition, a comparison of the Cattaneo-Christov (CC) and Fourier models are provided and discussed. |
| first_indexed | 2024-04-09T18:50:01Z |
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| id | doaj.art-e25c04ae841d461f93c248f7ef30c150 |
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| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T18:50:01Z |
| publishDate | 2023-03-01 |
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| spelling | doaj.art-e25c04ae841d461f93c248f7ef30c1502023-04-10T01:10:20ZengAIMS PressAIMS Mathematics2473-69882023-03-0185125591257510.3934/math.2023631Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulationsAfraz Hussain Majeed0Sadia Irshad1Bagh Ali 2Ahmed Kadhim Hussein3Nehad Ali Shah 4Thongchai Botmart 51. Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan2. Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Punjab 64200, Pakistan3. Faculty of Computer Science and Information Technology, Superior University, Lahore 54000, Pakistan4. Mechanical Engineering Department, College of Engineering, University of Babylon, Hilla 00964, Iraq 5. College of Engineering, University of Warith Al-Anbiyaa, Karbala 56001, Iraq6. Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea7. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandWe investigate the thermal flow of Maxwell fluid in a rotating frame using a numerical approach. The fluid has been considered a temperature-dependent thermal conductivity. A non-Fourier heat flux term that accurately reflects the effects of thermal relaxation is incorporated into the model that is used to simulate the heat transfer process. In order to simplify the governing system of partial differential equations, boundary layer approximations are used. These approximations are then transformed into forms that are self-similar with the help of similarity transformations. The mathematical model includes notable quantities such as the rotation parameter $ \lambda $, Deborah number $ \beta $, Prandtl number <italic>Pr</italic>, parameter $ ϵ $ and the dimensionless thermal relaxation times $ \gamma $. These are approximately uniformly convergent. The Keller box method is used to find approximate solutions to ODEs. We observed due to the addition of elastic factors, the hydrodynamic boundary layer gets thinner. The thickness of the boundary layer can be reduced with the use of the k rotation parameter as well. When <italic>Pr</italic> increases, the wall slope of the temperature increases as well and approaches zero, which is an indication that <italic>Pr</italic> is decreasing. In addition, a comparison of the Cattaneo-Christov (CC) and Fourier models are provided and discussed.https://www.aimspress.com/article/doi/10.3934/math.2023631mail.aimscience.commaxwell fluidcc modelrotating surfaceheat fluxkeller box method |
| spellingShingle | Afraz Hussain Majeed Sadia Irshad Bagh Ali Ahmed Kadhim Hussein Nehad Ali Shah Thongchai Botmart Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations AIMS Mathematics maxwell fluid cc model rotating surface heat flux keller box method |
| title | Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations |
| title_full | Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations |
| title_fullStr | Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations |
| title_full_unstemmed | Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations |
| title_short | Numerical investigations of nonlinear Maxwell fluid flow in the presence of non-Fourier heat flux theory: Keller box-based simulations |
| title_sort | numerical investigations of nonlinear maxwell fluid flow in the presence of non fourier heat flux theory keller box based simulations |
| topic | maxwell fluid cc model rotating surface heat flux keller box method |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023631mail.aimscience.com |
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