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

Mohammed Shqair,Mazen Nairat,Ahmad El-Ajou

doi:10.3390/math7070633

Mohammed Shqair, Mazen Nairat + Show 1 more

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https://doi.org/10.3390/math7070633

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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.

Highlights

The nuclear reactor is a complex fuel system competition, with reflectors, coolants, control rods and other parts
The balance between neutron production from fission chain reaction and neutron loss due to radiative capture and neutron leakage must be always achieved. This balance is known as criticality, it can be mathematically represented by the steady-state neutron transport equation which can be simplified using Fick’s law [1] to neutron diffusion equations
The present study introduces sufficient analytical procedure based on residual power series method (RPSM) [3,4,5,6,7,8,9,10,11,12] to provide general solution to multi-energy groups of neutron diffusion equations in rectangular, cylindrical, and spherical geometries

Summary

Introduction

The nuclear reactor is a complex fuel system competition, with reflectors, coolants, control rods and other parts. Among the most important is the determination of neutron flux distribution within the reactor core and finding the critical dimension and mass. This issue has received considerable attention in the field of reactor physics in the past decades. The balance between neutron production from fission chain reaction and neutron loss due to radiative capture and neutron leakage must be always achieved. This balance is known as criticality, it can be mathematically represented by the steady-state neutron transport equation which can be simplified using Fick’s law [1] to neutron diffusion equations. Because neutrons in a reactor have different velocities it’s more convenient to represent their fluxes by multi-energy groups of neutron diffusion equations

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Conclusion