Numerical-Asymptotic Method for Determining Nonlinear Thermal Conductivity Coefficients and Heat Fluxes and Applications in the Assessing the Thermophysical Characteristics of High-Temperature Fuel Compositions and Alloys

A new method for determining thermal conductivity coefficients and estimating heat flux densities in nonlinear media using the simulation data has been developed and justified. The method is based on a stable numerical algorithm for solving the inverse problem of reconstructing the unknown parameters of a singularly perturbed model for a stationary nonlinear heat equation with a flux term linearly dependent on the temperature (as an example). This algorithm uses either an asymptotic small-parameter approximation of a stable solution to the direct problem or an information on the position of the internal layer of the thermal structure obtained using an asymptotic analysis in combination with experimental data. Numerical calculations were performed for several innovative and promising types of fuel alloys and mixed nitride nuclear fuel using the parameters of real fuel cores for fast neutron reactors.