Chapter 1 - Fractional-order modeling in nuclear reactors

Abstract

In this book, it is shown that the reduced order models of nuclear reactors based on the theory of neutron diffusion with a fractional constitutive law are obtained using all known theoretical arguments, that is, neutron transport theory. This book is intended for researchers and engineers interested in exploring new horizons in the modeling for nuclear reactors, focusing on nonclassical modeling with an approximation of the fractional calculus with the idea of incorporating trends in these disciplines. From a fundamental point of view, the phenomena of the neutron processes in nuclear reactors consider in a natural form a parameter that establishes that the phenomena are not instantaneous, that is, with memory effects in space and time. Another fundamental characteristic is that the nuclear reactor models based on fractional-order differential operators are by nature nonlocal. Combining these attributes in the neutronic processes general descriptions with anomalous diffusion are obtained, wherein the limit the classical description is recovered, that is, normal diffusion.