Dynamic response of a spherical cavity under thermal and chemical shock with fractional thermoelastic diffusion theory

Abstract

Based on fractional thermoelastic diffusion theory, the dynamic response of an infinite structure with a spherical cavity is considered. The inner surface of the cavity is free of traction and subjected to thermal and chemical potential shock. The problem is solved through the Laplace transform and the Laplace numerical inverse transform. To verify the correctness of the theoretical derivation, numerical results are degenerated to compare with previous research conducted by Abbas. Then, the effects of fractional order parameters, time parameters, thermal conductivity, and diffusion coefficient on each quantity are considered, respectively. Numerical results show that the fractional order parameter has a slight effect on the displacement field but has a great effect on other physical quantities. As the action time of thermal and chemical potential shock increases, the changes in each quantity are more pronounced. The temperature variation coefficient has a significant effect on the quantities, while the diffusion coefficient has a significant effect on chemical potential but has a slight effect on other quantities. It can be easily concluded that it is necessary to take the fractional thermoelastic diffusion theory into account when handling practical engineering problems.