Two Energy groups Neutron Diffusion Model in Spherical Reactors


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Authors

  • Iqbal Batiha Al Zaytoonah University of Jordan
  • Mohammed Shqair
  • Mohammed H.E. Abu-Sei'leek
  • Shameseddin Alshorm
  • S.A. Abd El-Azeem
  • Shaher Momani

Abstract

This paper investigates the neutron diffusion model with two energy groups in spherical reactors. In particular, the integer-order two energy groups neutron diffusion model in spherical reactors is resolved using the Laplace transform method by regarding the spherical radius r as a time domain. Next, we transform the neutron diffusion model into fractional-order versions using the Caputo differentiator, resulting in what is referred to as the fractional-order two-energy-group neutron diffusion model. To address this fractional-order system, we introduce a novel approach to reduce a system of 2α-order to a duplicated system of α-order, where 0 < α ≤ 1. This converted system is then solved using one of the recent modifications of the fractional Euler method called the Modified Fractional Euler Method (MFEM). Several numerical simulations are depicted to verify our findings.

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Published

2024-06-03

How to Cite

Batiha, I., Shqair, M., Abu-Sei’leek, M. H., Alshorm, S., Abd El-Azeem, S., & Momani, S. (2024). Two Energy groups Neutron Diffusion Model in Spherical Reactors. Results in Nonlinear Analysis, 7(2), 160–173. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/379

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