With the use of the integral heat balance method based on the introduction of the temperature perturbation field and additional boundary conditions, we consider a method for finding analytical solutions of boundary-value problems of nonstationary heat conduction that permits obtaining, for a series of problems, solutions with a given degree of accuracy throughout the range of variation of the Fourier number. Solutions have a simple form of exponential algebraic polynomials, which makes it possible to investigate the heat transfer in the fields of isothermal lines, as well as analyze the time distributions of velocities of motion of isotherms.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 3, pp. 540–558, May–June, 2009.
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Kudinov, V.A., Stefanyuk, E.V. Analytical solution method for heat conduction problems based on the introduction of the temperature perturbation front and additional boundary conditions. J Eng Phys Thermophy 82, 537–555 (2009). https://doi.org/10.1007/s10891-009-0223-8
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DOI: https://doi.org/10.1007/s10891-009-0223-8