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

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.     

THERMAL STRESS PROBLEM FOR MIXED HEAT CONDUCTION BOUNDARY AROUND AN ARBITRARILY SHAPED HOLE WITH CRACK UNDER UNIFORM HEAT FLUX

This article deals with a thermal stress problem for thermal conduction around an arbitrarily shaped hole with a crack under uniform heat flux. Two cases for the hole edge and the crack faces are assumed: adiabatic and isothermal conditions or vice versa (isothermal and adiabatic). A closed-form solution is obtained using conformal mapping, dislocation functions, and the complex variable method. Results of temperature, heat flux, stress, and stress intensity factor are illustrated.     

SOLUTION OF AN ELLIPTICAL RIGID INCLUSION WITH DEBONDINGS IN AN INFINITE PLANE UNDER THE UNIFORM HEAT FLUX

A problem of an elliptical rigid inclusion in an infinite plane subjected to uniform heat flux in an arbitrary direction and with a number of debondings on the interface of the elliptical rigid inclusion and the elastic matrix is solved. The rotation of the inclusion under the uniform heat flux is considered. The complex variable method is used, and the closed-form solution is obtained. The stress intensity of debonding at the debonding tips is calculated and the extension of debonding is investigated. Examples of stress distributions and resultant moments on the inclusion are shown for the inclusion with two debondings.     

Elasto-Thermodiffusive Response in a Spherically Isotropic Hollow Sphere

The present work deals with the investigation of elasto-thermo diffusion interactions inside a spherically isotropic hollow sphere in the context of linear theory of generalized thermoelastic diffusion based on Green and Lindsay theory. The inner and outer boundaries of the body are free from stresses and are subjected to a time-dependent thermal shock and also the chemical shock. Laplace transform techniques are used to write the basic equations in the form of a vector matrix differential equations, which is then solved by the eigenvalue approach. The inversion of the transformed solution is carried out by applying the method of Bellman. The stress, temperature, mass concentration and chemical potential are computed and presented graphically. A comparative study of diffusive medium and thermoelastic medium is carried out, and it was seen that the effect of diffusion is significant on the stresses. A comparison of spherically isotropic body with isotropic body has also been presented, and a significant difference is observed.     

GREEN'S FUNCTION FOR THERMAL STRESS MIXED BOUNDARY VALUE PROBLEM OF AN INFINITE PLANE WITH AN ARBITRARY HOLE UNDER A POINT HEAT SOURCE

Green's function of a point heat source is derived for a mechanical mixed boundary value problem of an infinite plane with an arbitrary hole, for which zero-displacement and traction-free boundary conditions are prescribed to its boundary. As the thermal boundary condition on the hole, either an adiabatic or isothermal condition is considered. By employing the mapping technique and complex variable method, an explicit solution including a hypergeometrical function is obtained. Stress distributions are shown in illustrative examples for a square hole.