Generalized magneto‐thermoelastic medium with variable material properties subjected to ramp‐type heating

Abstract

The equations of magneto-generalized thermoelasticity with one relaxation time with variable electrical and thermal conductivity for one-dimensional problems are cast into a matrix form using the statespace approach and Laplace transform techniques. The resulting formulation is applied to a problem of a half space where the bounded plane is subjected to a ramptype heating and a traction free. This takes place when a constant magnetic field permeates the medium in the absence of an external electric field. The inversion of the Laplace transform is carried out using a numerical approach. Numerical results for the temperature, the displacement, and the stress distributions are given and illustrated graphically.

Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory

“…For the numerical results, silicon (Si) has been taken as the thermoelastic semiconducting material, for which we take the following values of the different physical constants [7,[33][34][35]: 𝜇 = 5.46×10 10 kg m -1 s -2 , 𝜆 =3.64×10 10 kg m -1 s -2 , 𝜌 = 2330 kg m -3 , 𝐶 = 695 m 2 K -1 s -2 , 𝛼 = 3.0×10 -6 K -1 , 𝐾 = 150 kg m k -1 s -3 , 𝜑 = 1.0.…”

“…Now, we must determine the thermal loading function 𝑓 𝑡 , so we will consider that the thermal loading function is a ramp-type heating which takes the form [7,33,34]:…”

Magneto-Thermo-Viscoelastic Medium Associated with Wiedemann-Franz Law

“…A constant magnetic field with the components H = (0, H O , 0) is permeating the medium in the absence of an external electric field. Since no external electric field is applied, and the effect of polarization of the ionized medium can be neglected, it follows that the total electric field E vanished identically inside the medium [14]. Now for the one-dimensional problems, all of the considered functions will depend only on the space variable x and the time t. The governing equations for generalized magnetothermo-viscoelasticity (MTVE) (Eqs.…”

“…Ezzat and Youssef [13] established a new model for magnetothermoelastic medium with variable electrical and thermal conductivity and solved many problems in this field. Youssef and El Bary [14] solved a problem in the previous medium properties involving ramp-type heating.…”