Unsteady one-dimensional problem of thermoelastic diffusion for homogeneous multicomponent medium with plane boundaries
A.V. Vestyaka*, S.A. Davydova**, A.V. Zemskova,b***, D.V. Tarlakovskiib,a****
a Moscow Aviation Institute (National Research University), Moscow, 125993 Russia
b Research Institute of Mechanics, Moscow State University, Moscow, 119192 Russia
E-mail: *v.a.vestyak@mail.ru, **xenon_93@inbox.ru, ***azemskov1975@mail.ru, ****tdvhome@mail.ru
Received December 14, 2017
Abstract
The paper deals with the problem of determining the stress-strain state of a thermoelastic multicomponent medium with plane boundaries (layer and half-space) taking into account the presence of diffusion fluxes in each medium component. The effect of changes in the concentration and temperature on the stress-strain state of the medium has been studied with the help of a locally equilibrium model of thermoelastic diffusion, which includes the coupled system of equations of motion, heat transfer, and mass transfer. The solution has been found using the Laplace transform, as well as using the Fourier expansion for the layer and the sine-cosine transform for the half-space. The surface Green's functions have been expressed and analyzed. Test calculation has been performed.
Keywords: mechanical diffusion, multicomponent media, thermoelastic diffusion, integral transforms, Fourier series, Green's functions
Figure Captions
Fig. 1. Change u in time τ and by layer depth x.
Fig. 2. Change υ in time τ and by layer depth x.
Fig. 3. Change η1 in time τ and by layer depth x.
Fig. 4. Change η2 in time τ and by layer depth x.
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For citation: Vestyak A.V., Davydov S.A., Zemskov A.V., Tarlakovskii D.V. Unsteady one-dimensional problem of thermoelastic diffusion for homogeneous multicomponent medium with plane boundaries. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 1, pp. 183–195. (In Russian)
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