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Abstract
A new theory of generalised thermoelasticity has been constructed by taking into account the deformation of a fibre-reinforced isotropic thermoelastic medium. A general model of the equations of the formulation in the context of the three-phase-lag model and Green–Naghdi theory without energy dissipation theory are applied to study the influence of a mechanical force, temperature dependent and a magnetic field on the wave propagation within a fibre-reinforced isotropic thermoelastic medium. The exact expressions of the displacement components, temperature and stress components are obtained using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically for different values of a mechanical force. Comparisons are made between the results of the two theories in the presence and absence of a magnetic field as well as temperature-dependent properties.