Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative
This paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions usi...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-06-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722002820 |
| _version_ | 1818201724195700736 |
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| author | Ndolane Sene |
| author_facet | Ndolane Sene |
| author_sort | Ndolane Sene |
| collection | DOAJ |
| description | This paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions using the Laplace transformation and its inverse method. After the determination of the exact solutions, the Prandtl (Pr), the Grashof parameters (Gr)and (Gm), the Schmidt parameter (Sc), the Brinkman number for fluid, and the chemical reaction parameter will attract our attention, and their impacts on the modeling will be provided and explained in term of physical viewpoints. Due to the heredity and the memory, the Caputo derivative will impact the mass diffusivity of the considered fluid. Therefore, the velocity and the temperature distributions can increase or decrease depending on the value of the order of the fractional operator. The findings of the paper will be illustrated by graphical representations. Note that in the expression of the exact solutions some well-known functions will be used as the Gaussian error function, the convolution rule, the exponential functions, and many others. |
| first_indexed | 2024-12-12T02:58:06Z |
| format | Article |
| id | doaj.art-b2ea2b80d3984be2a1c283a4ded9626f |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-12T02:58:06Z |
| publishDate | 2022-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-b2ea2b80d3984be2a1c283a4ded9626f2022-12-22T00:40:41ZengElsevierResults in Physics2211-37972022-06-0137105555Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivativeNdolane Sene0Department of Mathematics, Institut des Politiques Publiques, Dakar Fann, SenegalThis paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions using the Laplace transformation and its inverse method. After the determination of the exact solutions, the Prandtl (Pr), the Grashof parameters (Gr)and (Gm), the Schmidt parameter (Sc), the Brinkman number for fluid, and the chemical reaction parameter will attract our attention, and their impacts on the modeling will be provided and explained in term of physical viewpoints. Due to the heredity and the memory, the Caputo derivative will impact the mass diffusivity of the considered fluid. Therefore, the velocity and the temperature distributions can increase or decrease depending on the value of the order of the fractional operator. The findings of the paper will be illustrated by graphical representations. Note that in the expression of the exact solutions some well-known functions will be used as the Gaussian error function, the convolution rule, the exponential functions, and many others.http://www.sciencedirect.com/science/article/pii/S2211379722002820DiffusivityCaputo fractional operatorBrinkman numberGaussian functionLaplace transform method |
| spellingShingle | Ndolane Sene Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative Results in Physics Diffusivity Caputo fractional operator Brinkman number Gaussian function Laplace transform method |
| title | Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative |
| title_full | Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative |
| title_fullStr | Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative |
| title_full_unstemmed | Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative |
| title_short | Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative |
| title_sort | analytical investigations of the fractional free convection flow of brinkman type fluid described by the caputo fractional derivative |
| topic | Diffusivity Caputo fractional operator Brinkman number Gaussian function Laplace transform method |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722002820 |
| work_keys_str_mv | AT ndolanesene analyticalinvestigationsofthefractionalfreeconvectionflowofbrinkmantypefluiddescribedbythecaputofractionalderivative |