Analysis of fractional-order telegraph model for neutron transport in nuclear reactor with slab geometry

Abstract

This paper deals with the analysis of fractionalorder (FO) telegraph equation which models the transport of thermal neutrons inside a nuclear reactor with slab geometry. The FO model, previously developed by the authors, models the neutron transport as anomalous diffusion, precisely a subdiffusion. This model removes the lacunae of the conventional integer-order model of neutron movements. Here, the FO model is solved using the well known technique of separation of variables and the spatial distribution and time evolution of the neutron flux in the slab reactor are computed. This exercise is probably being performed for the first time for the fractionalorder model of neutron transport. It clearly depicts the wavelike nature of the neutron flux. Also, the convergence of neutron flux for FO telegraph and subdiffusion models for asymptotic time establishes the long-time subdiffusive behaviour of the FO telegraph equation. The analysis carried out in this paper is thus forms a crucial step in the process of development of fractional-order model for a nuclear reactor.

Solución de algunas ecuaciones telegráficas de orden fraccional

“…They are also used in modeling of many chemical processed, mathematical biology and many other problems in engineering [16,20,21]. In particular, fractional order telegraph equation models the transport of thermal neutrons inside a nuclear reactor with slab geometry [33].…”