Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method
The solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, the...
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| Format: | Article |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1784 |
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| author | Mohammad Shqair Emad A. M. Farrag Mohammed Al-Smadi |
| author_facet | Mohammad Shqair Emad A. M. Farrag Mohammed Al-Smadi |
| author_sort | Mohammad Shqair |
| collection | DOAJ |
| description | The solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, the system is solved for the first time using the approximation method. The considered system of neutron diffusion equations consists of two consistent subsystems, where the first studies the reactor and the multi-group subsystem of equations in the reactor core, and the other studies the multi-group subsystem of equations in the reactor reflector; each subsystem can deal with any finite number of neutron energy groups. The system is simplified numerically to a one-group bare and reflected reactor, which is compared with the modified differential transform method; a two-group bare reactor, which is compared with the residual power series method; a two-group reflected reactor, which is compared with the classical method; and a four-group bare reactor compared with the residual power series. |
| first_indexed | 2024-03-10T03:27:55Z |
| format | Article |
| id | doaj.art-5fd2ac84265b430086f22143a33dd647 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:27:55Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5fd2ac84265b430086f22143a33dd6472023-11-23T12:02:24ZengMDPI AGMathematics2227-73902022-05-011010178410.3390/math10101784Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation MethodMohammad Shqair0Emad A. M. Farrag1Mohammed Al-Smadi2Physics Department, Faculty of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaPhysics Department, Faculty of Sciences and Arts, Jouf University, Tabarjal 75764, Saudi ArabiaCollege of Commerce and Business, Lusail University, Doha 122104, QatarThe solution of the complex neutron diffusion equations system of equations in a spherical nuclear reactor is presented using the homotopy perturbation method (HPM); the HPM is a remarkable approximation method that successfully solves different systems of diffusion equations, and in this work, the system is solved for the first time using the approximation method. The considered system of neutron diffusion equations consists of two consistent subsystems, where the first studies the reactor and the multi-group subsystem of equations in the reactor core, and the other studies the multi-group subsystem of equations in the reactor reflector; each subsystem can deal with any finite number of neutron energy groups. The system is simplified numerically to a one-group bare and reflected reactor, which is compared with the modified differential transform method; a two-group bare reactor, which is compared with the residual power series method; a two-group reflected reactor, which is compared with the classical method; and a four-group bare reactor compared with the residual power series.https://www.mdpi.com/2227-7390/10/10/1784neutron diffusionhomotopy perturbation methodflux calculationcritical systemreflected reactormulti-group |
| spellingShingle | Mohammad Shqair Emad A. M. Farrag Mohammed Al-Smadi Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method Mathematics neutron diffusion homotopy perturbation method flux calculation critical system reflected reactor multi-group |
| title | Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method |
| title_full | Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method |
| title_fullStr | Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method |
| title_full_unstemmed | Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method |
| title_short | Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method |
| title_sort | solving multi group reflected spherical reactor system of equations using the homotopy perturbation method |
| topic | neutron diffusion homotopy perturbation method flux calculation critical system reflected reactor multi-group |
| url | https://www.mdpi.com/2227-7390/10/10/1784 |
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