By using the straight-line method and conservative difference schemes, we reduce the nonlinear nonstationary boundary-value problem of heat conduction for a three-layer hollow cylinder to a Cauchy problem for a system of ordinary differential equations, which is solved numerically with the help of the formulas of backward differentiation. The conservative discretization of the heat conduction equation and the boundary conditions with respect to the space variable is performed by the integro-interpolation method. We also analyze the influence of temperature dependence of the thermal characteristics of the chosen materials on the temperature field formed in the layers of a three-layer cylinder.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 2, pp. 129–136, April–June, 2020.
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Harmatii, G.Y. Numerical Determination of the Nonsteady Thermal State of a Three-Layer Hollow Thermosensitive Cylinder Under the Conditions of Complex Heat Exchange. J Math Sci 272, 151–160 (2023). https://doi.org/10.1007/s10958-023-06406-0
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DOI: https://doi.org/10.1007/s10958-023-06406-0