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The aim of the present paper is to study the wave propagation in anisotropic  viscoelastic medium in the context of the theory threephase- lag model of  thermoelasticity. It is found that there exist two quasi-longitudinal waves  (qP1, qP2) and two transverse waves (qS1, qS2). The governing equations for  homogeneous transversely isotropic thermoviscoelastic are reduced as a  special case from the considered model. Different characteristics of waves  like phase velocity, attenuation coefficient, specific loss and penetration  depth are computed from the obtained results. Viscous effect is shown  graphically on different resulting quantities for two-phase-lag model and  three-phase-lag model of thermoelasticity. Some particular cases of interest  are also deduced from the present investigation

Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model