Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles
This paper analyzes the system describing the absorption solar collector as an application of nanoparticles for the storage of solar energy. The system involves two fractional partial differential equations (FPDEs) utilizing the Caputo fractional definition (CFD). Explicit solutions are determined f...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-03-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016822008286 |
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| author | Abdulrahman F. Aljohani Abdelhalim Ebaid Emad H. Aly Ioan Pop Ahmed O.M. Abubaker Dalal J. Alanazi |
| author_facet | Abdulrahman F. Aljohani Abdelhalim Ebaid Emad H. Aly Ioan Pop Ahmed O.M. Abubaker Dalal J. Alanazi |
| author_sort | Abdulrahman F. Aljohani |
| collection | DOAJ |
| description | This paper analyzes the system describing the absorption solar collector as an application of nanoparticles for the storage of solar energy. The system involves two fractional partial differential equations (FPDEs) utilizing the Caputo fractional definition (CFD). Explicit solutions are determined for the temperature and velocity in terms of the Wright function (WrFn) via Laplace transform (LT). In addition, the solutions are expressed in terms of some well–known special functions at selected values of the fractional–order. Moreover, the behaviors of the temperature and velocity are investigated graphically using the thermo–physical data of the Cu/Al2O3–nanoparticles. Furthermore, some numerical results are conducted about the performance of the Cu and Al2O3. The results reveal the higher efficiency/performance of the Cu–nanoparticles over the Al2O3 and thus copper enjoys higher capability than alumina for the purpose of solar energy storage. In addition, it is found that 1.41% in the enhancement of heat transfer is achieved by adding 1% of the Cu–nanoparticles while the corresponding enhancement rate of the other three nanoparticles was less. Besides, the enhancement rate reaches 7.1% by increasing the volume fraction of the Cu–nanoparticles to 5%. Furthermore, the enhancement rates for the TiO2, Ag, and Al2O3 are 5.41%, 6.47%, and 6.53%, respectively when using 5% of these nanoparticles. Finally, the advantages/effectiveness of the current approach over a previous work in the literature are discussed in detail. |
| first_indexed | 2024-04-10T04:08:25Z |
| format | Article |
| id | doaj.art-803afe67ba7749289e97c01d48788c54 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-10T04:08:25Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-803afe67ba7749289e97c01d48788c542023-03-13T04:15:16ZengElsevierAlexandria Engineering Journal1110-01682023-03-0167447459Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticlesAbdulrahman F. Aljohani0Abdelhalim Ebaid1Emad H. Aly2Ioan Pop3Ahmed O.M. Abubaker4Dalal J. Alanazi5Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia; Corresponding author.Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, EgyptDepartment of Mathematics, Babeş–Bolyai University, 400084 Cluj–Napoca, RomaniaDepartment of Mathematics, University College of Umluj, University of Tabuk, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi ArabiaThis paper analyzes the system describing the absorption solar collector as an application of nanoparticles for the storage of solar energy. The system involves two fractional partial differential equations (FPDEs) utilizing the Caputo fractional definition (CFD). Explicit solutions are determined for the temperature and velocity in terms of the Wright function (WrFn) via Laplace transform (LT). In addition, the solutions are expressed in terms of some well–known special functions at selected values of the fractional–order. Moreover, the behaviors of the temperature and velocity are investigated graphically using the thermo–physical data of the Cu/Al2O3–nanoparticles. Furthermore, some numerical results are conducted about the performance of the Cu and Al2O3. The results reveal the higher efficiency/performance of the Cu–nanoparticles over the Al2O3 and thus copper enjoys higher capability than alumina for the purpose of solar energy storage. In addition, it is found that 1.41% in the enhancement of heat transfer is achieved by adding 1% of the Cu–nanoparticles while the corresponding enhancement rate of the other three nanoparticles was less. Besides, the enhancement rate reaches 7.1% by increasing the volume fraction of the Cu–nanoparticles to 5%. Furthermore, the enhancement rates for the TiO2, Ag, and Al2O3 are 5.41%, 6.47%, and 6.53%, respectively when using 5% of these nanoparticles. Finally, the advantages/effectiveness of the current approach over a previous work in the literature are discussed in detail.http://www.sciencedirect.com/science/article/pii/S1110016822008286Fractional PDEWright functionSolar collectorPhotovoltaicLaplace transformBoundary value problem |
| spellingShingle | Abdulrahman F. Aljohani Abdelhalim Ebaid Emad H. Aly Ioan Pop Ahmed O.M. Abubaker Dalal J. Alanazi Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles Alexandria Engineering Journal Fractional PDE Wright function Solar collector Photovoltaic Laplace transform Boundary value problem |
| title | Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles |
| title_full | Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles |
| title_fullStr | Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles |
| title_full_unstemmed | Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles |
| title_short | Explicit solution of a generalized mathematical model for the solar collector/photovoltaic applications using nanoparticles |
| title_sort | explicit solution of a generalized mathematical model for the solar collector photovoltaic applications using nanoparticles |
| topic | Fractional PDE Wright function Solar collector Photovoltaic Laplace transform Boundary value problem |
| url | http://www.sciencedirect.com/science/article/pii/S1110016822008286 |
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