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Two analytical solutions of thermal problems connected with the disposal of nuclear waste are presented. Non‐linear diffusion problems are analysed. The use of the Kirchhoff transformation and the transformation of coordinates are made along with a numerical solution. Also comparison is made for the exact and numerical solutions for temperature histories at a nuclear waste site. A time dependent heat source is considered.

The Kirchhoff transformation, in conjunction with the finite element method, is proposed as a tool in solving non‐linear heat conduction problems. A very simple way to obtain the inverse Kirchhoff transformation is shown, using the contour lines of the Kirchhoff variable obtained from a finite element analysis.