<p>Classical Fourier and Fick laws fail to capture the coupled thermoelastic-diffusive behavior under extreme thermal and chemical stresses due to their prediction of infinite signal speeds and their neglect of microstructural interactions. This study presents a unified nonlocal continuum model for hollow cylindrical solids that integrates spatial nonlocality—accounting for long-range microstructural effects—with multiple relaxation times reflecting thermal inertia and diffusion memory. The resulting framework describes finite-speed wave propagation for thermal, elastic, and diffusive signals at micro- and nanoscales. Governing equations are derived and solved both analytically and numerically to examine how nonlocal parameters and relaxation times affect dynamic response. Findings demonstrate that nonlocality increases material stiffness and modifies wave profiles, while relaxation times critically regulate signal attenuation and dispersion—effects that are absent in classical theories. Validation against established models confirms superior accuracy under rapid transient conditions. This framework offers transformative applications: precise control in ultrafast laser processing, enhanced thermal management in advanced electronics, and improved reliability of diffusion-sensitive alloys for aerospace and nuclear technologies. Ultimately, the model provides an essential predictive tool for designing next-generation materials where coupled thermoelastic-diffusive interactions determine performance and durability.</p>