On the heat dissipation function for irreversible mechanical phenomena in anisotropic media

The heat dissipation function for anisotropic media in which viscous and inelastic flows occur is derived as a generalization of the heat dissipation function studied in the case that the media are isotropic. The methods of the Thermodynamics of irreversible processes are used. It is seen that the linearization of the theory leads to a stress-strain-temperature relation for anisotropic viscoanelastic media and that the heat dissipation function is quadratic expression in the components of the stress tensor, the strain tensor, the time derivative of the latter tensor and the temperature. Finally, the obtained results are applied to the particular case of viscous fluids, Maxwell, Kelvin (Voigt), Poynting-Thomson, Jeffreys, Prandtl-Reuss and Hooke media.