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Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

1
Moscow Aviation Institute, National Research University, Moscow 125993, Russia
2
Research Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 26; https://doi.org/10.3390/mca24010026
Received: 2 January 2019 / Revised: 7 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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Abstract

This article presents an algorithm for solving the unsteady problem of one-dimensional coupled thermoelastic diffusion perturbations propagation in a multicomponent isotropic half-space, as a result of surface and bulk external effects. One-dimensional physico-mechanical processes, in a continuum, have been described by a local-equilibrium model, which included the coupled linear equations of an elastic medium motion, heat transfer, and mass transfer. The unknown functions of displacement, temperature, and concentration increments were sought in the integral form, which was a convolution of the surface and bulk Green’s functions and external effects functions. The Laplace transform on time and the Fourier sine and cosine transforms on the coordinate were used to find the Green’s functions. The obtained Green’s functions was analyzed. Test calculations were performed on the examples of some technological processes. View Full-Text
Keywords: thermoelastic diffusion; Green’s function; Laplace transform; Fourier transform; multi-component medium; bulk effect; surface perturbations; unsteady problem; modelling of technological processes thermoelastic diffusion; Green’s function; Laplace transform; Fourier transform; multi-component medium; bulk effect; surface perturbations; unsteady problem; modelling of technological processes
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Davydov, S.A.; Zemskov, A.V.; Akhmetova, E.R. Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations. Math. Comput. Appl. 2019, 24, 26.

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