Purpose. To develop a new generalized 3D mathematic model for calculating temperature fields in the solid finite cylinder with homogeneous layers in the form of the mathematical physics boundary problem for hyperbolic equations by the Dirichlet conditions (temperature on the cylinder surface is a continuous function of the coordinate axis), and to solve the obtained boundary problem. Methodology. Use of the known Laplace and Fourier integral transformations and application of the new integral transformation to the space with homogeneous layers. Findings. A nonstationary temperature field in the rotating double-layer solid finite cylinder in the cylindrical coordinate system with taking into account finite velocity of the heat conduction was defined. Heat-transfer properties of the cylinder in either layer are constant at an ideal heat contact between the layers while no internal sources of the heat are available. At the initial moment of time, the cylinder temperature is constant, and temperature on the outside surface of the cylinder is known. Originality. It is the first a mathematical 3D model for calculating temperature fields in the rotating double-layer solid finite cylinder has been created in the form of the physico-mathematical boundary problem for the heat conduction hyperbolic equations by the Dirichlet conditions and with taking into account finite velocity of the heat conduction. A new integral transformation was created for the space with homogeneous layers, with the help of which it became possible to present a temperature field in the finite cylinder with homogeneous layers in the form of convergence orthogonal series by Bessel and Fourier functions. Practical value. The obtained analytical solution of the generalized boundary problem of heat exchange in the rotating double-layer cylinder, which takes into account the known time period of the heat-conduction relaxation, can be used for detecting temperature fields, which occur in different technical systems (forming rolls, satellites, turbines, etc.).

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