Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell
The aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring–Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring–Powell equation was transformed in...
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MDPI AG
2022-02-01
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| author | José Luis Díaz Saeed Ur Rahman Juan Carlos Sánchez Rodríguez María Antonia Simón Rodríguez Guillermo Filippone Capllonch Antonio Herrero Hernández |
| author_facet | José Luis Díaz Saeed Ur Rahman Juan Carlos Sánchez Rodríguez María Antonia Simón Rodríguez Guillermo Filippone Capllonch Antonio Herrero Hernández |
| author_sort | José Luis Díaz |
| collection | DOAJ |
| description | The aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring–Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring–Powell equation was transformed into the travelling wave domain, where analytical solutions were obtained supported by the geometric perturbation theory. Such analytical solutions were validated with a numerical exercise. The main finding reported is the existence of a particular travelling wave speed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>=</mo><mn>1.212</mn></mrow></semantics></math></inline-formula> for which the analytical solution is close to the actual numerical solution with an accumulative error of <<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T21:30:09Z |
| format | Article |
| id | doaj.art-10b94a30e46e4e05a9448ae00bf4c6ee |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:09Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-10b94a30e46e4e05a9448ae00bf4c6ee2023-11-23T20:58:12ZengMDPI AGMathematics2227-73902022-02-0110466010.3390/math10040660Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid ModellJosé Luis Díaz0Saeed Ur Rahman1Juan Carlos Sánchez Rodríguez2María Antonia Simón Rodríguez3Guillermo Filippone Capllonch4Antonio Herrero Hernández5Escuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainDepartment of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, PakistanEscuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainEscuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainEscuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainEscuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainThe aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring–Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring–Powell equation was transformed into the travelling wave domain, where analytical solutions were obtained supported by the geometric perturbation theory. Such analytical solutions were validated with a numerical exercise. The main finding reported is the existence of a particular travelling wave speed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>=</mo><mn>1.212</mn></mrow></semantics></math></inline-formula> for which the analytical solution is close to the actual numerical solution with an accumulative error of <<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/10/4/660travelling wavesEyring–Powellgeometric perturbationnonlinear reaction–diffusionunsteady flow |
| spellingShingle | José Luis Díaz Saeed Ur Rahman Juan Carlos Sánchez Rodríguez María Antonia Simón Rodríguez Guillermo Filippone Capllonch Antonio Herrero Hernández Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell Mathematics travelling waves Eyring–Powell geometric perturbation nonlinear reaction–diffusion unsteady flow |
| title | Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell |
| title_full | Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell |
| title_fullStr | Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell |
| title_full_unstemmed | Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell |
| title_short | Analysis of Solutions, Asymptotic and Exact Profiles to an Eyring–Powell Fluid Modell |
| title_sort | analysis of solutions asymptotic and exact profiles to an eyring powell fluid modell |
| topic | travelling waves Eyring–Powell geometric perturbation nonlinear reaction–diffusion unsteady flow |
| url | https://www.mdpi.com/2227-7390/10/4/660 |
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