Dynamic analysis to the fractional order thermoelastic diffusion problem of an infinite body with a spherical cavity and variable material properties

Abstract

Based on the generalized thermoelastic diffusion theory with fractional order derivative, the dynamic response of an infinite thermoelastic medium with a spherical cavity is investigated. The thermoelastic and diffusive properties of the medium are assumed to be temperature-dependent, and the medium is subjected to a thermal shock and a chemical potential shock at the inner surface of the spherical cavity simultaneously. The governing equations of the problem are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, radial stress, concentration and chemical potential are obtained and illustrated graphically. In calculation, the effects of the fractional order parameter and the temperature-dependent properties on the variations of the considered variables are presented and discussed in detail. The results show that the fractional order parameter and the temperature-dependent properties significantly influence the variations of all the considered variables. The present investigation may be valuable in heat and mass transfer, waste disposal or petroleum engineering, etc.