Analytic solutions to heat transfer problems on a basis of determination of a front of heat disturbance. (English. Russian original) Zbl 1397.80006

Russ. Math. 60, No. 11, 22-34 (2016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 11, 27-41 (2016).
The authors study the nonstationary heat conductivity problem for the infinite plate. Their goal is to improve the accuracy of the approximation of the analytical solution which is represented as an infinite series at small time values. A technique for obtaining the analytical solution by using additional boundary conditions is presented. The method divides the heating process into two stages in time by introducing a time-dependent boundary (heat perturbation front) and this leads to two separate simpler problems (and additional boundary conditions). The effectiveness of the method is demonstrated through its application to the heat conductivity problem for the infinite plate with symmetric boundary conditions. The authors note that the convergence of approximate solutions is rapid since there is no need to fulfill initial conditions in each individual problem in the whole range of the spatial variable as well as that the accuracy of the approximate solution increases with the increase of additional boundary conditions.


80A20 Heat and mass transfer, heat flow (MSC2010)
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