Second-sound phenomena in type II conductors with Stefan-Boltzmann source

Employing both analytical and numerical tools, we consider a particular case of Green and Naghdi's type II theory of second-sound (i.e., thermal waves) in rigid conductors, and generalize it to include solids capable of radiating thermal energy to their external environments. Assuming the radiation process is described by the Stefan-Boltzmann law, we investigate singular surface and traveling wave phenomena in thin, homogeneous and isotropic, 1D rods. Our analysis reveals, among other things, a characteristic temperature associated with, and a shortcoming exhibited by, the present model.