Magneto-thermo-elastic response in a perfectly conducting medium with three-phase-lag effect

Abstract

This paper deals with the problem of magneto-thermo-elastic interactions in an unbounded, perfectly conducting elastic medium due to the presence of periodically varying heat sources in the context of linear theory of generalized thermo-elasticity with energy dissipation (TEWED or GN-III model), without energy dissipation (TEWOED or GN-II model) and three-phase-lag model (3P model). The governing equations of generalized thermo-elasticity of the above models under the influence of a magnetic field are established. The Laplace-Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Laguerre's method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. Displacement, temperature, stress and strain distributions have been computed numerically and presented graphically in numbers of figures. A comparison of the results for different theories (GN-II, GN-III and 3P model) and the effect of magnetic field and damping coefficient on the physical quantities has been discussed. List of symbols uDisplacement vector λ, μ Lamé's constants ρ Constant mass density of the medium γ Thermal modulus α t Coefficient of linear thermal expansion T 0 Uniform reference temperature T Small temperature increase above the reference temperature T 0 J Electric current density vector BMagnetic induction vector c v

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

“…In the context of a linearized version of this theory (Green and Naghdi [6,7]), a theorem on uniqueness of solutions has been established by Chandrasekhariah [8,9]. Applying the above theories of generalized thermoelasticity, several problems have been solved by Das and Kanoria [10,11], Roychoudhuri and Dutta [12], Kar and Kanoria [13,14].…”

A two-dimensional problem in magnetothermoelasticity with laser pulse under different boundary conditions

“…(5) If the laser pulse effect is neglected, then the results are in agreement with [Das and Kanoria 2012] with appropriate modification in the boundary conditions.…”

A laser pulse impactful on a half-space using the modified TPL G–N models

“…It is to be noted that Eqs. (6) and 7represent two forms of the simple G-N II model, the first is in terms of the rate of thermal conductivity k * while the second is in terms of the heat conductivity coefficient k. A lot of investigators have dealt with the simple G-N II and III models while other investigators have dealt with the TPL G-N III model (N = 1) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] . All these models are presented without the higher-order time derivatives as those presented in this study.…”