This work is interested with a thermoelastic response in a micro-stretch half-space submerged in an unlimited non-viscous fluid under rotation, the medium is studied using the theory of Green-Naghdi (G-N III) and the model of three-phase-lag (3PHL). The governing equations are formulated in the context of G-N theory and the 3PHL model. Analytical solution to the problem is acquired by utilizing the normal mode method. The magnesium crystal element is utilized as an application to compare the predictions induced by rotation on microstretch thermoelastic immersed in an infinite fluid of G–N theory with those for the 3PHL model. Rotation has been noticed to have a major effect on all physical quantities. Comparisons were also made for three values of wave number b and three values of the real part frequency ω0.

The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium. A frequency equation is obtained for Rayleigh wave in the medium. The non-dimensional speed of the propagation of Rayleigh wave is computed for a specific model of the material and are shown graphically against frequency and non-dimensional parameter.