A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series - El-Ajou, Ahmad; Shqair, Mohammed; Ghabar, Ibrahim; Burqan, Aliaa; Saadeh, Rania (Frontiers in Physics, 2023)
This research develops a novel analytical solution to the neutron diffusion equation using the residual power series approach for both spherical and hemispherical fissile material reactors. Various boundary conditions are investigated, including zero flux on the boundary, zero flux on the extrapolated boundary distance, and the radiation boundary condition. It also shows how two hemispheres with opposing flat faces interact. We give numerical results for the same energy neutrons diffused in pure 𝑃 239 𝑢. By qualitative comparison with the homotopy perturbation method andBessel function-based solutions, the residual power series method presents accurate series solutions that converge to the exact ones, as shown in this study. Moreover, numerical results were shown to be improved by the computer implementation of the analytic solutions.