Wave reflection analysis in nonlocal porous thermoelastic media under hyperbolic two-temperature and higher-order Green-Lindsay models

The reflection behavior of plane waves in a nonlocal porous thermoelastic half-space incorporating hyperbolic two-temperature effects under impedance boundary conditions within the framework of refined the Green-Lindsay theory is investigated. The formulation accounts for nonlocal elasticity, thermal relaxation, and porous interactions, leading to the propagation of four distinct wave modes, namely primary, thermal, porous, and shear vertical waves, each with different phase velocities. Reflection coefficients are derived analytically, and corresponding energy ratios are computed to examine the influence of hyperbolic two-temperature, two-temperature, and one-temperature models, as well as comparisons between the refined Green-Lindsay and simple Green-Lindsay theories. Numerical results reveal strong sensitivity of energy partition to both angle of incidence and thermal parameters. In particular, hyperbolic two-temperature effects significantly modify energy distribution, leading to pronounced deviations from classical the one-temperature model predictions, especially for primary and shear vertical waves incidences. The refined Green-Lindsay model consistently produces higher and more stable energy ratios compared to the simple Green-Lindsay model, indicating improved representation of thermo-mechanical coupling and relaxation effects. Oscillatory behaviour is observed in several reflected energy components, highlighting the combined influence of nonlocality and thermal phase lags on wave interactions. The results demonstrate that the inclusion of hyperbolic two-temperature and nonlocal effects provides a more refined and physically consistent description of wave propagation in porous media. These findings are of practical importance in applications such as soil mechanics, geophysics, and civil engineering, where accurate prediction of wave reflection and energy distribution under thermal loading conditions is essential.