Abstract
A one-dimensional generalized magnetothermoelastic problem of a thermoelastic rod with finite length is investigated in the context of the fractional order thermoelasticity. The rod with variable properties, which are temperature-dependent, is fixed at both ends and placed in an initial magnetic field, and the rod is subjected to a moving heat source along the axial direction. The governing equations of the problem in the fractional order thermoelasticity are formulated and solved by means of Laplace transform in tandem with its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress in the rod are obtained and illustrated graphically. The effects of the temperature-dependent properties, the velocity of the moving heat source, the fractional order parameter, and so forth on the considered variables are concerned and discussed in detail, and the results show that they significantly influence the variations of the considered variables.
Highlights
The classical coupled thermoelasticity proposed by Biot [1] predicts an infinite speed for heat propagation, which is physically impossible
The present paper is devoted to our investigation of a generalized magnetothermoelastic medium with temperature-dependent properties subjected to a moving heat source in the fractional order theory, as proposed by Sherief et al [31]
In Case 1, we investigate the nondimensional temperature, displacement, and stress varying with time as shown in Figures 1–3 with the moving heat source velocity, fractional order parameter, value of temperature-dependent properties, 0.0
Summary
The classical coupled thermoelasticity proposed by Biot [1] predicts an infinite speed for heat propagation, which is physically impossible. Sherief and Abd El-Latief [38] solved a one-dimensional problem with a spherical cavity subjected to a thermal shock with fractional order theory of thermoelasticity Ma and He [39] dealt with a generalized piezoelectric-thermoelastic problem subjected to a moving heat source in the context of the fractional order theory of thermoelasticity. The generalized magnetothermoelastic problem of an infinite homogeneous isotropic microstretch half-space with temperature-dependent material properties placed in a transverse magnetic field was investigated in the context of different generalized thermoelastic theories by Xiong and Tian [46]. The present paper is devoted to our investigation of a generalized magnetothermoelastic medium with temperature-dependent properties subjected to a moving heat source in the fractional order theory, as proposed by Sherief et al [31]
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