The nonlinear boundary axially symmetric problem of heat conduction for the thermosensitive piecewise homogeneous layer with reach-through cylindrical inclusion that generates heat has been considered. Using the introduced function, the partial linearization of the original problem has been carried out. With the proposed piecewise-linear approximation of temperature at the boundary surface of the foreign inclusion and on the contact surface of the homogeneous elements of the layer, the problem has been completely linearized. The analytical solution of this problem of finding the introduced function using Hankel integral transform has been formed. The formulae for calculating the desired temperature have been derived.

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