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Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

Author

Listed:
  • Mohammed Shqair

    (Physics Department, Faculty of Science and Humanities, Prince Sattam bin Abdulaziz University, 11942 Al-kharj, Saudi Arabia)

  • Ahmad El-Ajou

    (Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan)

  • Mazen Nairat

    (Department of Physics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan)

Abstract

In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:633-:d:249206
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    References listed on IDEAS

    as
    1. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    2. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    3. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
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    Cited by:

    1. 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.

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