Fuzzy finite element solution of uncertain neutron diffusion equation for imprecisely defined homogeneous triangular bare reactor

TL;DR

This paper introduces a fuzzy finite element approach with interval arithmetic to solve uncertain neutron diffusion equations in a homogeneous triangular reactor, providing a way to handle imprecise parameters.

Contribution

It develops a modified fuzzy finite element method with new interval arithmetic for solving uncertain neutron diffusion equations in reactors.

Findings

Eigenvalues obtained are analyzed in detail.

Comparison with classical finite element method shows differences.

Uncertain results are discussed thoroughly.

Abstract

Scattering of neutron collision inside a reactor depends upon geometry of the reactor, diffusion coefficient and absorption coefficient etc. In general these parameters are not crisp and hence we may get uncertain neutron diffusion equation. In this paper we have investigated the above problem for a bare triangular homogeneous reactor. Here the uncertain governing differential equation is modelled by a modified fuzzy finite element method using newly proposed interval arithmetic. Obtained eigenvalues by the proposed method are studied in detail. Further the eigenvalues are compared with the classical finite element method in special cases and various uncertain results have been discussed.