The problem on heat conduction of an infinite plate with a heat-transfer coefficient changing linearly with time for third-kind boundary conditions was solved analytically based on determination of the front of a temperature disturbance in this plate and introduction of additional boundary conditions. On the basis of the solution obtained, graphs of the distribution of isotherms in the indicated plate and the velocities of their movement along a spatial variable in it were constructed. As a result of the solution of the inverse problem on the heat conduction of the infinite plate with the use of the results of numerical calculation of the change in its temperature at any point on the indicated spatial coordinate, the Predvoditelev number was identified with an accuracy of 2%, which made it possible to determine the time dependence of the heat-transfer coefficient of the plate.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 88, No. 3, pp. 663–673, May–June, 2015.
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Kudinov, V.A., Eremin, A.V. & Stefanyuk, E.V. Analytical Solutions of Heat-Conduction Problems with Time-Varying Heat-Transfer Coefficients. J Eng Phys Thermophy 88, 688–698 (2015). https://doi.org/10.1007/s10891-015-1238-y
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DOI: https://doi.org/10.1007/s10891-015-1238-y