EXACT ANALYTICAL SOLUTIONS FOR NON-STEADY HEAT TRANSFER PROBLEMS AND THEIR ROLE IN VERIFICATION OF MODELS FOR THERMO-HYDRO-MECHANICAL PROCESSES IN DEEP GEOLOGICAL RADIOACTIVE WASTE REPOSITORIES

Numerical simulation of complex underground facilities, such as deep geological radioactive waste repositories, requires coupled assessment of thermo-hydro-mechanical and, possibly, other processes. Therefore, a robust estimate of the temperature field is one of the crucial tasks. Computer codes used for modelling require verification on the problems that have exact analytical solution. Furthermore, these problems should reflect characteristic features of modelled objects. For heat transfer problems, these features are primarily spatial and temporal distribution of heat sources. In this paper, the exact analytical solutions for non-steady 3D heat transfer equation are obtained for the medium with constant thermal properties and exponentially decreasing point, linear and planar heat sources. These configurations are sufficiently well related for verification purposes to actual problems solved in safety analysis of deep geological radioactive waste repositories. Presented solutions can be used for verification of computer codes that implement the numerical solution of heat transfer equation or similar numerical models, such as diffusion, Brownian movement, etc.

Keywords: radioactive waste, deep geological repository, computer code verification, non-steady heat transfer equation, exact analytical solutions.

Tokarev Y. N., Moiseenko E. V., Drobyshevsky N. I., Butov R. A. Exact analytical solutions for non-steady heat transfer problems and their role in verification of models for thermo-hydro-mechanical processes in deep geological radioactive waste repositories. Radioactive Waste, 2018, no. 4 (5), pp. 90—98. (In Russian).