A generalized refined three-phase lag model for analyzing non-local thermoelastic waves in biological media

This study focuses on the effects of thermoelastic wave propagation and reflection in biological tissues, utilizing the refined three-phase lag theory (RTPL) alongside Eringen’s non-local elasticity theory. This research primarily employs the RTPL theory and non-local elasticity theory. Analytical derivations of the wave propagation speeds (phase velocity) and the attenuation coefficients are conducted using three distinct thermoelasticity theories: RTPL, Moore–Gibson–Thompson (MGT), and Green-Naghdi type-III (GN-III). The present study examines two types of waves: (a) two coupled longitudinal waves, namely, the thermal mode wave and the elastic mode wave and (b) one uncoupled transverse shear wave. Additionally, this study investigates wave reflection at boundaries (insulated and isothermal) by calculating the reflection coefficients for both the longitudinal and transverse incident waves. The results are compared across the three different thermoelastic theories to emphasize the influence of angular frequency, non-local parameters, and boundary conditions. The purpose of this present work is to aid in thermal treatments in biological tissues and to elevate the understanding of mechanical and thermal responses in biological tissues, along with therapeutic applications involving wave-based diagnostic treatments.