Fractional-order modeling of neutron transport in a nuclear reactor

• Published in: Applied mathematical modelling 2013-12, Vol.37 (23), p.9747-9767
• Main Authors: Vyawahare, Vishwesh A., Nataraj, P.S.V.
• Format: Article
• Language: English
• Subjects: Absorption; Anomalous diffusion; Deviation; Diffusion; Fractional-order modeling; Mathematical analysis; Mathematical models; Microprocessors; Neutron telegraph equation model; Neutron transport; Nuclear reactor; Nuclear reactors; Random walk; Transport; Transport processes
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2013.05.023

This paper deals with fractional-order (FO) modeling of the neutron transport process inside the core of a nuclear reactor. Conventional integer-order diffusion model of neutron transport has serious shortcomings. Firstly, due to its parabolic nature, it predicts infinite neutron speed, which is very unphysical. Secondly, it has a very limited spatial applicability as it is not applicable everywhere (especially near the strong absorbing regions) in heterogeneous reactor core. The neutron–nuclei reactions like fission, radiative capture act as the traps for neutrons. Also, the deviation of neutron velocities from the Maxwellian distribution together suggest that neutron transport should be considered as an anomalous diffusion process, precisely a subdiffusion (fractal time random walk). For the case of one-dimensional, mono-energetic neutron transport, a fractional-order telegraph equation is developed using the continuous-time random walk technique. This model is a more faithful and realistic representation of neutron movements inside the core as it eliminates the above mentioned lacunae of the classical diffusion model. Being hyperbolic in nature, the proposed model predicts finite speed of neutron propagation. Also, it is applicable near moderate as well as strong absorbing regions in the core. The long-time and short-time behaviours of the developed FO model are also analyzed. An interesting feature of the model is that for long-times, it behaves as a sub-diffusion equation. Further, a comparative study of the mean-squared-displacement of the derived model with other conventional integer-order and fractional-order transport models is carried out.