The general idea of the combined method of separation of variables, as applied to the solution of problems on the nonstationary heat conduction in solid bodies canonical in shape (plate, cylinder, sphere) with the first-kind boundary condition, is elucidated. Four efficient schemes of calculating the eigenvalues of the Sturm–Liouville boundary-value problem are presented. An original method is proposed for determining initial amplitudes with a relatively high accuracy. Using the example of approximate solution of the heat-conduction problem for a solid cylinder with the first-kind boundary condition, the significant simplicity and, at the same time, the high efficiency of the combined method of separation of variables is graphically demonstrated.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 94, No. 2, pp. 326–359, March–April, 2021.
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Kot, V.A. Combined Method of Separation of Variables. 3. Nonstationary Heat Conduction in Solids with the First-Kind Boundary Condition. J Eng Phys Thermophy 94, 311–344 (2021). https://doi.org/10.1007/s10891-021-02303-y
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DOI: https://doi.org/10.1007/s10891-021-02303-y