Transient thermoelastic responses in spherical elastic porous media using a fractional two-phase-lag model with space-time nonlocality

This study investigated the impact of the fractional Caputo-tempered two-phase-lag (FCT-TPL) heat conduction model on thermoelastic vibrations within a medium containing spherical cavities and voids. In the proposed model, the nonlocality of time and space is integrated to unify classical and generalized thermoelastic theories, enabling a thorough investigation of size-dependent phenomena and the scattering characteristics of thermo-mechanical waves. Also, by integrating fractional calculus with tempered derivatives, the proposed model adeptly captures the complex interaction between localized thermal effects and nonlocal mechanical responses, particularly in materials with pronounced microstructural features. The fractional order and tempering parameter are shown to play a crucial role in controlling thermal relaxation times and the amplitude of thermoelastic vibrations. The findings reveal that the integration of the fractional Caputo-tempered derivative, along with temporal and spatial nonlocal effects, into the two-phase-lag model significantly improves the accuracy of predicting transient thermoelastic responses in materials with cavities and voids.