Reflection of Coupled Thermoelastic–Diffusive Waves in Biological Tissue with Non-Local Elasticity and Triple Phase-Lag Heat Transfer

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This paper analyzes the reflection of plane waves in a bio-thermoelastic diffusion medium with initial stress, governed by the Moore–Gibson–Thompson (MGT) heat conduction model that incorporates three distinct phase lags—for the heat flux, temperature gradient, and diffusion. The formulation integrates temperature-dependent material properties (TDP), non-local elasticity, and hyperbolic two-temperature (HTT) effects to describe coupled thermomechanical and diffusive behavior in biological tissues. A homogeneous isotropic half-space subject to impedance boundary conditions is considered, and the governing field equations are solved using Helmholtz decomposition to derive closed-form expressions for the amplitude ratios of reflected longitudinal (P), shear (SV), thermal (T), and diffusive (Po) waves. The influence of phase lags, blood perfusion, wave frequency, and temperature-dependent moduli on reflection characteristics is examined. Numerical simulations demonstrate that these factors substantially affect the amplitude ratios and phase relationships between different wave modes. Several limiting cases—absence of diffusion, TDP, or perfusion—are presented for validation. The proposed framework generalizes non-local bio-thermoelastic diffusion theory with three-phase-lag effects, offering insights relevant to thermal therapies, diagnostic imaging, and bio-thermomechanical modeling.