An analytic and symbolic analysis of a coupled thermo-neutronic problem

Abstract : In this paper, we seek analytical approximate solutions of a problem coupling the neutronics equation and the thermal equation (using incomplete Elliptic integrals), and we compare these analytical approximate solutions to a numerical method for the coupled problem, using a Crank-Nicolson scheme for the thermal equation and an generalized eigenvalue problem for the neutronics equation. Both the approximate analytical methods and the numerical method amount to finding the multiplication factor keff (k−1eff is the generalized eigenvalue) as the unique solution of an equation. All methods yield values of keff close to each other with a difference of magnitude 10−7, which is much better than what is generally needed in neutronics.