Thermoviscoelastic diffusion analysis of a cylindrical cavity via three-phase-lag law and nonlocality effect

The study explores an infinitely extended Kelvin–Voigt visco-thermoelastic continuum with a cylindrical cavity, applying generalized thermoelastic diffusion theory and focusing on three-phase-lag non-local heat conduction law. The chemical potential at the boundary is considered a known time-dependent function. The analysis assumes a traction-free cavity surface subjected to a smooth, time-dependent heating effect, and the problem is addressed in the Laplace domain. Numerical inversion of the Laplace-transformed solutions is performed. The research juxtaposes the theoretical predictions with those of generalized thermoelastic diffusion theory, examining the influence of the time-nonlocal parameter and visco-thermoelastic relaxation parameter on various thermoelastic quantities. This is achieved by computing and graphically presenting the distributions of temperature, displacement, stress, concentration, and chemical potential. The findings are significant for aerospace engineering, MEMS/NEMS devices, and energy-harvesting systems. The developed framework enhances predictive capabilities for material behavior under transient thermal and mechanical loads. Future research could explore more complex geometries and boundary conditions.