Energy propagation of thermal waves

Although waves are ubiquitous in nature it is difficult to give a precise and unambiguous definition of what a wave is. Actually the distinction between wave-like and non-wave-like behaviour can be fuzzy, as it is the case of a solid sample excited by a periodic heat source. The resulting temperature oscillations inside the sample have the same mathematical expression as highly damped waves, the so-called thermal waves. The aim of this paper is to stress the energy propagation as the key to affirm whether there is wave motion. In this way it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy. This result has been obtained not only in the frame of the parabolic heat conduction equation that evidences the diffusive nature of the heat conduction process, but also in the frame of the hyperbolic heat conduction equation, that is a wave equation.