Analytic solutions and numerical method for a coupled thermo-neutronic problem

We consider in this contribution a simplified idealized one-dimensional coupled model for neutronics and thermo-hydraulics under the low Mach number approximation. We propose a numerical method treating globally the coupled problem for finding its unique solution. Simultaneously, we use incomplete elliptic integrals to represent analytically the neutron flux. Both methods match perfectly. Note that the multiplication factor, classical output of neutronics problems, depends considerably of the representation of the cross sections.