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

Author

Listed:
  • 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
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, United Arab Emirates)

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.

Suggested Citation

  • Mohammad Shqair & Emad A. M. Farrag & Mohammed Al-Smadi, 2022. "Solving Multi-Group Reflected Spherical Reactor System of Equations Using the Homotopy Perturbation Method," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1784-:d:822110
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    References listed on IDEAS

    as
    1. Mohammed Shqair & Ahmad El-Ajou & Mazen Nairat, 2019. "Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
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