Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity

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.

Thermoelastic Interactions in a Rotating Infinite Orthotropic Elastic Body with a Cylindrical Hole and Variable Thermal Conductivity

“…For linearity and by means of the binomial theorem for fractional powers and the assumption |θ/T 0 | 1, the radial equation of motion (19) and constitutive relations (8) will be in the forms…”

“…Singh and Kumar [18] explained the rotation effect on micropolar magneto-thermoelastic body. Xiong and Guo [19] investigated the effect of heat source moving with constant speed, and variable properties of a magneto-thermoelastic medium, under the fractional order theory of thermoelasticity. Kumar et al [20] analyzed the interactions subjected to the effect of rotation and hall current in a magneto-thermoelastic micropolar half-space under the fractional order thermoelasticity.…”

Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses

“…Sherief and Latief [43] found the application of one dimensional thermoelastic problem using the fractional calculus methodology in a half space. Xiong and Guo [59] investigated fractional order thermoelasticity for a one-dimensional finite length generalized magnetothermoelastic problem of a thermoelastic rod. In [35, 40, 41, 44, 56, 57 and 58], various thermoelastic problems studied which based on the theory of fractional-order thermoelastic model.…”

Effect of Variable Thermal Conductivity on the Generalized Thermoelasticity Problems in a Fiber-Reinforced Anisotropic Half-Space

“…However, several experimental and theoretical studies have indicated that thermal conductivity is closely related to temperature change [16][17][18][19][20][21][22]. Xiong and Guo [23] validated the effects of variable temperature-dependent properties on field quantities based on a one-dimensional generalized magnetothermoelastic problem. Wang et al [24] studied generalized thermoelasticity with variable thermal material properties and found that variable thermal material properties significantly affect the thermoelastic behaviors, particularly the magnitude of thermoelastic response.…”