On Thermo-viscoelasticity with Variable Thermal Conductivity and Fractional-Order Heat Transfer

The equations of generalized thermo-viscoelasticity for an isotropic medium with variable thermal conductivity and fractional-order heat transfer are given. The resulting formulation is applied to a half-space subjected to arbitrary heating which is taken as a function of time and is traction free. The Laplace transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. Numerical results for temperature, displacement, and stress distributions are given and illustrated graphically for the problem. The effects of the fractional order and the variable thermal conductivity for heat transfer on a viscoelastic material such as poly(methyl methacrylate) (Perspex) are discussed.