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Abstract
In this paper, a semi-analytical solution of the time-dependent heat conduction equation is presented for laterally infinite, multi-layered media with anisotropic thermal conductivities, convective outer boundaries and perfect thermal contact between the layers. Space and time-dependent moving heat sources on the boundary as well as inside the medium are considered. In addition, the outer fluid temperature may also depend on space and time. The derived solutions are successfully compared to numerical solutions. A Python implementation of the solution is made freely available.
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