Neutrons diffusion variable coefficient advection in nuclear reactors

The analysis of nuclear reactors in dissimilar geometries is an important topic in sciences and engineering. Two approaches are used in literature for homogeneous systems: computational and analytical methods. In this study, an analytical solution based on a variable coefficient advection is introduced. Such a coefficient is analogous to the addition of a damping term in the static neutron diffusion equation due to dissipations which are important in nuclear reactors. This coefficient plays also an imperative role in wave theory and is of a particular interest to applied physicists. Both the parallelepiped and the homogeneous bare cylinder reactors geometries were analyzed in this work. It was observed that the higher advection gradient, the lower the maximum neutron flux occurring in the nuclear core, a result which is practical for different reactors shapes