Plane wave propagation in an anisotropic dual-phase-lag thermoelastic diffusion medium

Rajneesh Kumar (Department of Mathematics, Kurukshetra University, Kurukshetra, India)
Vandana Gupta (Department of Mathematics, Indira Gandhi National College, Ladwa, India)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Publication date: 4 November 2014

Abstract

Purpose

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

Design/methodology/approach

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

Findings

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Originality/value

Introduction of a new model of DPLD in the equation of mass diffusion.

Keywords

Acknowledgements

One of the authors Ms Vandana Gupta is thankful to Council of Scientific and Industrial Research (CSIR) for the financial support.

Citation

Kumar, R. and Gupta, V. (2014), "Plane wave propagation in an anisotropic dual-phase-lag thermoelastic diffusion medium", Multidiscipline Modeling in Materials and Structures, Vol. 10 No. 4, pp. 562-592. https://doi.org/10.1108/MMMS-01-2014-0004

Publisher

:

Emerald Group Publishing Limited

Copyright © 2014, Emerald Group Publishing Limited

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