**Investigation on Magneto-thermoelastic Disturbances Induced by Thermal Shock in an Elastic Half Space Having Finite Conductivity under Dual Phase-lag Heat Conduction**

Tiwari Rakhi *, Kumar Anil, Mukhopadhyay Santwana

Department of Mathematical Sciences, Indian Institute of Technology

(Banaras Hindu University), Varanasi 221 005, India

∗E-mail: rakhibhu2117@gmail.com

### Received:

Received: 20 April 2016; revised: 19 October 2016; accepted: 24 October 2016; published online: 16 November 2016

### DOI: 10.12921/cmst.2016.0000019

### Abstract:

The present work seeks to investigate the propagation of magneto-thermoelastic disturbances produced by a thermal shock in a finitely conducting elastic half-space in contact with vacuum. Normal load has been applied on the boundary of the existing media that is supposed to be permeated by a primary uniform magnetic field. We employ both the parabolic type (dual phase-lag magneto-thermoelasticity of type I (MTDPL-I)) and hyperbolic type (dual phase-lag magneto-thermoelasticity of type II (MTDPL-II)) dual phase-lag heat conduction models to account for the interactions among the magnetic, elastic and thermal fields. The integral transform technique is applied to solve the present problem and the analytical results of both cases have been obtained separately. A detailed analysis of results has been made in order to understand the nature of waves propagating inside the medium and the effects of the phase-lag parameters. The effect of the presence of magnetic field has been highlighted. Numerical results have also been obtained to analyze the effect of magnetic field on the behavior of the solution more clearly and a detailed analysis of the results predicted by two models has been presented. It has been noted that in some cases there are significant differences in the solution obtained in the contexts of MTDPL-I and MTDPL-II theory of magneto-thermoelasticity.

### Key words:

dual phase-lag heat conduction theory-I, dual phase-lag heat conduction theory-II, finite conductivity, magneto-thermoelastic waves, thermal shock

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