Solution of different geometries reflected reactors neutron diffusion equation using the homotopy perturbation method

Abstract

The Homotopy Perturbation Method (HPM) proves continuous efficiency for a long time in solving linear and nonlinear mathematical differential equations and their applications in physical and engineering phenomena. In this work, HPM is applied to formulate new analytic solutions of time-independent neutron diffusion equation for different reflected reactor geometries, which is essential in describing the behaviour of the neutrons in the nuclear reactors. The reflector part is added to the core to minimize the critical dimensions and critical mass too. The results have been compared with canonical calculations, as well as to that taken from transport theory. This comparison has been achieved after computationally applying the developed theory and analytical formulas in numerical experiments. The methodology furnishes the ground for further future research in this field.