Time-Fractional Heat Conduction Effects on the Dynamic Response of a Magneto-Thermoelastic Half-Space Subjected to a Thermal Shock

Abstract

In this study, we investigate the dynamic response of a two-dimensional half-space solid subjected to a thermal shock, considering magneto-thermoelastic coupling and time-fractional heat conduction effects. The material under consideration is homogeneous, isotropic, thermally and electrically conducting, with a free surface exposed to the thermal shock. We employ the L–S model of generalized thermoelasticity, incorporating fractional derivative heat transfer to account for second sound effects. Additionally, an initial magnetic field is applied parallel to the plane boundary of the medium. Through normal mode analysis and the eigenvalue approach, we solve the resulting non-dimensional coupled field equations to derive exact expressions for temperature, displacement, and thermal stresses. Numerical results for these dimensionless quantities are presented graphically and analyzed, with comparisons drawn between cases with and without the magnetic field.