Abstract
We solve a nonstationary problem of heat conduction for a thermosensitive half space in contact with a thermosensitive layer under the conditions of complex heat exchange with the medium of constant temperature. To construct the solution, we use a numerical-analytic approach characterized by the application of a version of the method of successive approximations, linearizing parameters, the Laplace integral transformation, and its numerical inversion with the help of the Prudnikov formula adapted to the problems of heat conduction. The thermoelastic state of the outlined thermosensitive piecewise homogeneous structure is analyzed by applying the proposed algorithm.
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