Exact analytical solution of the nonstationary problem of calculation of temperature and mechanical-stress fields in a two-layer cylinder and its application for the verification of numerical models

The self-adjointness of the heat-conductunce operator in the space of piecewise differentiable functions defined in inhomogeneous regions with a discontinuous thermal conductivity, for which the condition of ideal thermal contact is formally satisfied on the boundary between the regions, is proved. This made it possible to apply the method of separation of variables and obtain, in the form of a functional series, an exact analytical solution of the nonstationary problem of calculating the temperature fields in a two-layer cylinder with a heat source. The resulting solution was used to calculate thermomechanical stresses. The solution can be used to estimate temperatures and stresses in objects that can be approximately represented as a two-layer cylinder, as well as to verify numerical models used to calculate thermomechanical processes in objects with discontinuous physical properties. The presented solution was created to satisfy the need to verify the FENIA code on the problem of cooling a canister with vitrified radioactive waste. Complete agreement between the numerical and analytical solutions is shown, including the vicinity of the discontinuity point at the media boundary.