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Purpose. To investigate the peculiarities of distribution of a non­stationary temperature field over the thickness of a multilayer hollow cylinder under convective heat exchange conditions on its surfaces, taking into account the presence of internal (distrib­ uted) heat sources. Methodology. In order to achieve this goal, a direct method of solving boundary value problems of the theory of thermal con­ ductivity was applied, which includes the application of the method of reduction, the concept of quasi derivatives, the method of separation of variables, and the modified method of Fourier eigenfunctions. findings. The solution of the boundary value problem was obtained in a closed form, which allowed us to create an algorithm for calculating the propagation of a non­stationary temperature field in multilayer hollow cylindrical structures under convective heat exchange on its surfaces and the presence of internal heat sources. It should be noted that such algorithms include only: a) finding the roots of the characteristic equation; b) multiplication of finite number of known (2 × 2) matrices; c) calculation of defined integrals; d) summing the required number of members of the series to obtain the specified accuracy. Changing the third­ order boundary conditions to any other boundary conditions does not cause any significant difficulty in solving the problem. originality. A closed solution is obtained for the propagation of a non­stationary temperature field in a multilayer hollow cyl­ inder in the presence of internal sources of heat and convective heat exchange on its surfaces. Practical value. Implementation of the research results allows us to investigate the processes of heating or cooling multilayer hollow structures, taking into account the internal heat sources encountered in several applied problems. These are tasks that can be related to the processes of cooling of thermal elements of nuclear power plants, changes in the temperature field during microar­ ray oxidation, heating of electronic components during the passage of electric current.

Simulation of heat transfer process in a multilateral cylindrical shell taking into account the internal heat sources