The main interest of the present article is to dealing with wave extension in a fiber-reinforced thermoelastic solid under the influence of magnetic field and initial stress. The immediate problem is represented via different forms of the Green-Naghdi framework. Analytical expressions of the physical variables are acquire by using new analysis of normal mode with eigenvalue approach technique. Numerical outcomes are shown graphically and the results received are analyzed. The most significant points are highlighted. The outcomes are shown the a notable impact of the magnetic field, initial stress, and fiber-reinforcement on the physical fields. The framework is useful in modeling thermoelastic behavior during laser processing, welding, and additive manufacturing, where rapid heating and cooling induce complex stress fields. Fiber-reinforced thermoelastic models are applicable to biological tissues and biomedical devices, particularly in laser-based therapies and thermal diagnostics where finite-speed heat conduction is significant. Applications include reactor components and containment structures where fiber-reinforced materials experience intense thermal gradients and require accurate prediction of thermoelastic stresses under non-Fourier heat transfer.



