Purpose: The aim of this work is to study porous thermo-elastic behavior in a half-space elastic micro-stretch media enveloped in an unbounded inviscid liquid with a magnetic field, utilizing three-phase lag model (3PHL) and Green–Naghdi theory of type III (G–N III). Methods: The analytical technique used to obtain the ordinary differential equations was normal mode analysis. The Gauthier composite element is employed in an implementation to start comparing the observations—magnetic field on thermo-micro-stretch elastic porous medium completely covered in the endless fluid of G–N III theory with those for the model of 3PHL. Results: The magnetic field has been observed to make a significant impact over all physical quantities. Also, comparisons have been made for four various frequency values which explained that the frequency has an important role on the physical quantities. Conclusion: Overall, the research on the magnetic field effect on thermo-micro-stretch porous media immersed in a liquid has several potential practical implications and engineering applications in various fields, such as biomedical, environmental, chemical, and energy engineering.

Purpose: In this work, the thermoelastic response in a micro-stretch thermoelastic half-space submerged in an unlimited non-viscous fluid under gravity, the medium is studied using the three-phase-lag model (3PHL) and Green-Naghdi theory (G-N III).Design/methodology/approach: The normal mode analysis was the analytic technique used to obtain the exact formula of the physical quantities.Findings: The magnesium crystal element is used as an application to compare the predictions induced by gravity on microstretch thermoelastic immersed in an infinite fluid of the three-phase-lag model with those for Green–Naghdi. Gravity has been noticed to have a major effect on all physical quantities. Comparisons were also made for three values of wave number and three values of the real part frequency.Originality/value: This work is concerned with the thermoelastic micro-stretch solid immersed in an infinite and inviscid fluid and subjected to a gravitational field. The governing equations are formulated in the context of the 3PHL model and G-N theory. An analytical solution to the problem is obtained by employing normal mode analysis. Comparisons of the physical quantities are shown in figures to study the effects of gravity, wave number and the real part of the frequency.