| Autor: |
Itrat Abbas Mirza, Muhammad Saeed Akram, Nehad Ali Shah, Waqas Imtiaz, Jae Dong Chung |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Alexandria Engineering Journal, Vol 60, Iss 1, Pp 1199-1208 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
1110-0168 |
| DOI: |
10.1016/j.aej.2020.10.043 |
| Popis: |
In this communication we have studied well known physical process of two-dimensional advection–diffusion phenomena. The advection–diffusion equation is time-fractionalized by exploiting Atangana-Baleanu fractional derivative operator. This fractionalization is achieved in the generalized constitutive equation of the mass flux density vector. The fractionalized two-dimensional advection–diffusion equation turns out to be a two-dimensional nonlinear fractional partial differential equation. This partial differential equation is considered under the hypothesis of an initial concentrated loading and Robin type boundary conditions. The analytical expression of the solution is determined for this boundary value problem by employing the integral transforms method, namely, the Laplace transform, sine-Fourier transform and finite sine–cosine Fourier transform. The effects of fractional parameter α on the concentration obtained from the analytical solution, for various parameters of interest, are illustrated graphically with the help of software Mathcad. The graphs illustrate that the memory effects are remarkable for small values of time and ordinary for large values of the time. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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