Short-time Analysis of Magnetothermoelastic Wave Under Fractional Order Heat Conduction Law

Abstract

This paper deals with the problem of magnetothermoelastic interactions in a perfectly conducting elastic medium in which the boundary is stress free and subjected to thermal loading in the context of the fractional-order, two-temperature generalized thermoelasticity theory (2TT). The two-temperature, three-phase-lag (2T3P) model and two-temperature Lord–Shulman (2TLS) model of thermoelasticity are combined into a unified formulation introducing unified parameters. The governing equations of generalized thermoelasticity of these models under the influence of a magnetic field are established. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace-transform domain, which is then solved by the state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier-series expansion techniques. Because of the short duration of the second sound effects, small time approximations of the solutions are studied. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. The effect of the fractional-order parameter and the two-temperature and magnetic field parameters on the solutions has been studied and the comparisons among different thermoelastic models are made.

Keywords:

• Fractional order
• Generalized magnetothermoelasticity
• LS model
• Three-phase-lag thermoealstic model
• Two-temperature
• Vector-matrix differential equation

ACKNOWLEDGMENT

We are grateful to Professor S. C. Bose of the Department of Applied Mathematics, University of Calcutta, for his kind help and guidance in preparation of the paper.