On the nonequilibrium behavior of solids that transport heat by second sound

AbstractIn earlier work Coleman, Fabrizio, and Owen observed that if a constitutive equation for the heat flux q employed in theories of second sound in dielectric solids is assumed to hold for large values of q, then thermodynamical principles require that the equation of state for the internal energy contain a term that is quadratic in q. Here the resulting field equations for unidimensional heat flow are studied. It is shown that they are compatible with the occurrence of oscillatory traveling waves containing discontinuities in temperature and heat flux. The class of waves constructed contains limiting cases in which the heat flux and temperature exhibit small amplitude, high frequency, fluctuations about their mean. Such a traveling wave would appear to an experimenter as a strong and nearly constant flow of heat in a nearly uniform temperature field