Reflection of plane waves from the impedance boundary of a magneto-thermo-microstretch solid with diffusion in a fractional order theory of thermoelasticity

Abstract

In this research article, the effect of the impedance boundary on the reflection problem in a magnetized thermo-microstretch diffusion solid half-space is analyzed. The governing equations in generalized Sherief’s Model of fractional-order magneto-thermo-microstretch elasticity with diffusion in specialized x-y plane are derived and are solved for a plane-wave solution. The plane-wave solution indicates the existence of four coupled longitudinal waves namely CLD-1, CLD-2, CLD-3, CLD-4 waves and two coupled transverse waves namely CTD and CTM waves propagating with distinct speeds in the half-space. The thermally insulated/isothermal plane surface of a half-space is subjected to impedance boundary conditions. The expressions for reflection coefficient and energy ratios for the reflected waves are obtained and the numerical results are illustrated graphically to observe the effect of the magnetic field, fractional-order and diffusion parameters against the angle of incidence on the reflection coefficient and energy ratios of reflected waves.