Void Effects on Plane Wave Propagation in a Nonlocal Microstretch Thermoelastic Medium with Initial Stress and Magnetic Field under Three Phase Lag Theory

In this paper, the reflection of plane waves at a free surface of a nonlocal microstretch thermoelastic medium is investigated within the framework of the three-phase-lag (TPL) heat conduction theory. The model incorporates the combined effects of nonlocal elasticity, voids, magnetic field, and initial stress. The governing equations are formulated and solved to obtain analytical expressions for the amplitude ratios and energy ratios of reflected longitudinal and coupled transverse waves propagating with distinct phase velocities. Numerical computations are performed to examine the graphical influence of key physical parameters on wave characteristics. The results indicate that the void parameter generally reduces the amplitude ratios, whereas the nonlocal parameter significantly influences transverse wave components. The magnetic field predominantly affects longitudinal wave reflection, while initial stress produces contrasting variations in amplitude ratios. It is further observed that transverse wave amplitudes vanish at limiting angles of incidence, and the primary longitudinal wave remains dominant. Energy analysis confirms that the sum of energy ratios is unity for all angles of incidence, ensuring conservation of energy. The present study provides useful insights into wave propagation phenomena in complex thermoelastic materials with microstructural effects and external fields.