A study of the dynamic response of two concentric spheres in the context of thermoelastic diffusion with internal heat source

This work examines the dynamic response of a heat source (inner sphere of radius a) embedded within a concentric spherical body (outer radius b), governed by the one-relaxation-time generalized thermoelastic diffusion theory. The outer sphere is subjected to a thermal load while remaining stress-free. A Laplace transform approach is used to solve the governing equations. The subsequent inverse transform yields the spatial distributions of temperature, displacement, radial stress, concentration, and chemical potential. Numerical results reveal a weak dependence of temperature but strong dependence of displacement and stress on the duration of thermal loading. The study underscores the importance of generalized thermoelastic diffusion theory in accurately modeling complex engineering scenarios.