By the fast expansion method, the authors have obtained the approximate solution of the problem in analytical form, which holds true at all points of the cylinder up to the boundary. From an analysis of the solution, it follows that the broken thermal contact between annular regions gives rise to a weak thermal resistance. Beginning with four annular regions, the thermal resistance remains constant, in practice. This result was obtained for the first time. When no more than three terms in a Fourier series are used, the maximum residual of the differential heat-conduction equation is 10–2.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 90, No. 5, pp. 1288–1297, September–October, 2017.
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Chernyshov, A.D., Popov, V.M., Goryainov, V.V. et al. Investigation of Contact Thermal Resistance in a Finite Cylinder with an Internal Source by the Fast Expansion Method and the Problem of Consistency of Boundary Conditions. J Eng Phys Thermophy 90, 1225–1233 (2017). https://doi.org/10.1007/s10891-017-1678-7
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DOI: https://doi.org/10.1007/s10891-017-1678-7