Improved lumped model for thermal analysis of high burn-up nuclear fuel rods

High burn-up nuclear fuel elements have been intensively studied for prolonged lifetime of existing reactors and for next-generation advanced reactors. This paper presents an improved lumped-differential formulation for one-dimensional transient heat conduction in a heat generating cylinder with temperature-dependent thermo-physical properties typical of high burn-up nuclear fuel rods. Two-points Hermite approximations for integrals (H1,1/H1,1) were used to obtain the average temperature and heat flux in the radial direction. As a testing case, transient heat conduction in a nuclear fuel rod was computed with the thermo-physical properties represented by the MATPRO correlations. The problem was formulated and solved by using the symbolic/numerical computation software system MATHEMATICA. The solutions of the proposed improved lumped model were validated by comparing with numerical solutions of the original distributed parameter formulation of the transient heat conduction problem, as well as by comparing with simulation results of a cold leg SBLOCA with RELAP5/MOD3.