Application of Duhamel's theorem in the thermal field analysis of a DC cable with two layers of insulation

In the paper we presented an asymptotic method of determination of the transient thermal field in a three-zone cable (i.e. in a core and in two layers of insulation). A basis of our method was decomposition of the system. We considered separately the region of the core, which we modelled by a concentrated element of the first order. In turn, we treated the two-zone region of insulation as the system of distributed parameters. In the analysis we applied Duhamel's theorem and the method of separation of variables. Eigenvalues of the boundary-initial problem and coefficients of eigenfunctions we determined numerically. In the result we obtained spatial-temporal heat-up curves of the investigated cable. Our results we presented in a graphic form.