An application of the nodal expansion method to the determination of the radial temperature distribution in a nuclear fuel rod

Within nuclear reactor simulation codes, the temperature distribution inside the fuel rod is computed with a mono-dimensional cylindrical heat conduction model. The main discretization methods applied to reduce the differential equation into an algebraic system are the finite difference or the finite volume method. These methods require a fine mesh to obtain accurate fuel temperature distributions. We explore here the applicability of the Nodal Expansion Method (NEM) limited to the second order. The results on some steady state examples show a good performance of the method. The development of the solver has been carried out with the Computer Algebra System Mathematica associated to the package MathCompile, which enables to follow the various development steps from the specification of the method to the FORTRAN programming and numerical verification.