Physics

Pure mathematics

Dimension (graph theory)

Mathematics

Diffusion

Neutron flux

Slab

Algorithm

Criticality

Residual

Mathematical analysis

Neutron

Cylinder

Nuclear physics

Geometry

Neutron transport

Geophysics

Thermodynamics

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.

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