Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method

Mohammad Shqair, Emad A. M. Farrag and Mohammed Al-Smadi
Additional contact information
Mohammad Shqair: Physics Department, Faculty of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Emad A. M. Farrag: Physics Department, Faculty of Sciences and Arts, Jouf University, Tabarjal 75764, Saudi Arabia
Mohammed Al-Smadi: College of Commerce and Business, Lusail University, Doha 122104, Qatar

Mathematics, 2022, vol. 10, issue 10, 1-17

Abstract: 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.

Keywords: neutron diffusion; homotopy perturbation method; flux calculation; critical system; reflected reactor; multi-group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/10/1784/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/10/1784/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:10:p:1784-:d:822110

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().