Acoustic and heat waves in Fourier thermoelastic materials

We investigate acoustic waves and transient heat transfers in homogeneous Fourier thermoelastic materials. We first define the domain of validity of the thermoelastic system which describes such media. Then, a dimensional analysis of this system and the presence of a separation of scales point out two different models. Under an acoustic excitation, Fourier thermoelastic materials exhibit adiabatic acoustic waves and apparent hyperbolic heat waves at the first order of approximation: the temperature is carried along by the acoustic wave. This model is different from the Cattaneo model. On an other hand, under a transient heat excitation, these materials show parabolic heat transfers which carry along elastostatic variations of stresses at the first order of approximation: the apparent momentum balance is parabolic. The domains of validity of these models are investigated.