Analytical methods of heat transfer compared with numerical methods as related to nuclear waste repositories

Analytical methods were applied to the prediction of the far-field thermal impact of a nuclear waste repository. Specifically, the transformation of coordinates and the Kirchhoff transformation were used to solve one-dimensional nonlinear heat conduction problems. Calculations for the HLW and TRU nuclear waste with initial areal thermal loadings of 12 kW/acre and 0.7 kW/acre, respectively, are carried out for various models. Also, finite difference and finite element methods are applied. The last method is used to solve two-dimensional linear and nonlinear heat conduction problems. Results of the analysis are temperature distributions and temperature histories. Explicit analytical expressions of the maximum temperature rise as a function of the system parameters are presented. The theoretical approaches predict maximum temperature increases in the overburden with an error of 10%. When the finite solid one-dimensional NWR thermal problem is solved with generic salt and HLW thermal load as parameters, the maximum temperature rises predicted by the finite difference and finite element methods had maximum errors of 2.6 and 6.7%, respectively. In all the other cases the finite difference method also gave a smaller error than the finite element method