Impact of variable thermal conductivity on plane waves between a magneto-thermoelastic medium with Hall current, voids and a magneto-thermoelastic medium with Hall current

Magnetic properties and voids in solids are important phenomena in a variety of engineering approaches and scientific disciplines. For this purpose, the magneto-thermoelastic (MTE) theory is utilized to study the impact of variable thermal conductivity (VTC) on plane waves within two distinct MTE mediums having Hall current (HC) and voids. The study is conducted using the dual phase lag theory of thermoelasticity. It has been noted that four reflected coupled waves and three transmitted coupled waves propagate through the medium with different speeds. Suitable boundary conditions are employed to derive energy and amplitude ratios for transmitted and reflected waves. The results for transmission and reflection coefficients, along with energy distribution across different incidence angles, are evaluated and displayed graphically. The results of the numerical simulation reveal that amplitude ratios of reflected and transmitted waves are profoundly affected by variations in thermal conductivity, HC parameter, and void parameter. The outcomes have shown that throughout the transmission and reflection phenomena, there is no dissipation of energy. Ultimately, it is demonstrated that, under specific conditions, our findings encompass prior results from the literature as special cases. A lot of research has been carried out in recent years on MTE medium, but not much attention has been given to study the refraction phenomena of plane waves within two distinct MTE mediums having HC, VTC, and voids. This research holds practical relevance across diverse fields, including composite engineering, geology, seismology, and the exploration of valuable subterranean materials.