Analytical solution for three-dimensional heat conduction in a nuclear waste repository with adiabatic boundaries

Near-field temperature is a critical indicator in evaluating the safe operation of a nuclear waste repository. Analytical solutions are common methods for analyzing the thermal performance. The existing analytical solutions for temperatures from a single nuclear waste canister in a repository include compound line heat source solutions, semi-analytical solutions, and fully-analytical solutions. However, given that a repository contains thousands of canisters, existing analytical solutions are unable to accurately determine the temperature around the target canister, which is surrounded by numerous adjacent canisters. To this end, the thermal problem at the repository-scale is first transformed into an equivalent problem within a cuboid unit. This unit consists of an individual waste canister encapsulated in buffer material and wrapped in rock under specified boundary conditions. By applying Duhamel's theorem and finite Fourier sine transform, a fully-analytical solution for the temperature field of a single canister under adiabatic boundary conditions was derived. These solutions allow for a convenient and straightforward visualization of temperature evolutions and distributions at a repository-scale through explicit expressions. Furthermore, a formula for calculating the radius of the cylindrical calculation domain was developed, enabling an accurate transformation of the temperature field problem from a cuboid domain to a cylindrical domain.