Description of mechanism of thermal conduction and internal damping by means of two-component Cosserat continuum

Abstract

A new approach to the derivation of the theory of thermoviscoelasticity is proposed. Neither the hypothesis of fading memory nor rheological models are used within the framework of this approach. The proposed approach is based on the mechanical model of a one-rotor gyrostat continuum. In special cases, the mathematical description of this model is proved to reduce to the equations of the coupled problem of thermoelasticity, the self-diffusion equation, and the equation describing the flow of a viscous incompressible fluid. In the context of this model, we consider the original treatment of the physical nature of the mechanism of thermal conduction and internal damping. The first part of the paper contains the aforesaid theoretical results. The second part of the paper is devoted to the determination of some parameters of the model. On the base of the proposed theory, we obtain the dependence of the acoustic wave attenuation factor on a signal frequency. This dependence is in close agreement with the classical dependence in the low-frequency range and agrees with the dependence obtained on the base of the phonon theory in the hypersonic frequency range. We discuss some ways of determining of the volume and shear viscosities and the heat flow relaxation timescale by using known values of the sound velocity and the acoustic wave attenuation factor. The obtained values of the heat flow relaxation timescale are compared with the values derived from the phonon theory.