We propose a method for the determination of temperature fields formed in a plate with regard for the thermal radiation, temperature dependence of thermal characteristics, and densities of surface and volumetric heat sources for a nonuniform distribution of the initial temperature. By using the Kirchhoff transformation, Green’s function, generalized functions, and linear splines, we reduce the problems of heat conduction to the solution of a recurrence nonlinear algebraic equation for the values of the Kirchhoff variable at the spline nodes on the corresponding boundary surface. The results of numerical analysis are presented.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 2, pp. 117–128, April–June, 2020.
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Protsiuk, B.V. Nonstationary Problems of Heat Conduction for a Thermosensitive Plate with Nonlinear Boundary Condition on One Surface. J Math Sci 272, 135–150 (2023). https://doi.org/10.1007/s10958-023-06405-1
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DOI: https://doi.org/10.1007/s10958-023-06405-1