Effect of scale length parameter on plane wave propagation under size-dependent thermoelasticity with one relaxation time

This study explores the propagation of harmonic plane waves in elastic media within the framework of size-dependent thermoelasticity (SDT), incorporating the Lord-Shulman heat conduction model. Analytical calculations are derived to find the precise answers for the dispersion relation for the longitudinal plane wave. Asymptotic expansions are presented for high- and low-frequency regimes, characterizing key wave field parameters such as phase velocity, specific loss, attenuation coefficient, and penetration depth of dilatational waves. Numerical results are provided to validate the analytical findings and investigate the influence of varying scale length parameters. We compare the results of this study with the corresponding results in the context of generalized thermoelasticity theory with one relaxation time, as reported previously. Also, we analyze the impact of the thermal relaxation parameter on the plane wave in the presence of the scale length parameter. Some limiting cases are also noted and discussed.