Unsteady heat conduction in the soil layers above underground repository for spent nuclear fuel

Due to radioactivity of spent nuclear fuel, a repository is expected to act as a heat source of exponentially decreasing intensity over hundreds of years. In case of underground emplacement of such a heat source, the temperature changes in the soil layers surrounding the heat source may have important implications such as evaporation of the water contained in the soil and its subsequent condensation. Assuming a uniformly distributed power generation over a horizontal, relatively thin, circular zone of several thousand meters diameter located several hundred meters below the ground surface, the temperature variations along the vertical centerline of the heating zone was estimated analytically under simplifying assumptions. Unsteady one-dimensional heat conduction in a semi-infinite solid with an exponentially decreasing heat flux at the proximal end was considered. The corresponding solution of the Fourier equation for heat conduction contains Error Functions of complex arguments. The evaluation of the Error Functions for discrete space and time parameters was performed applying analytical procedures and using standard tables. The results show temperature distributions in the soil at various time points over thousands of years after underground emplacement of spent nuclear fuel. (orig.)