On the propagation of temperature-rate waves and traveling waves in rigid conductors of the Graffi--Franchi--Straughan type

We examine second-sound phenomena in a class of rigid, thermally conduct- ing, solids that are described by a special case of the Maxwell–Catteneo flux law. Employing both analytical and numerical methods, we examine both temperature-rate waves and thermal traveling waves in this class of thermal conductor, which have recently been termed Graffi–Franchi–Straughan type conductors. In the present study, the temperature-dependent nature of the thermal relaxation time, which is the distinguishing feature of this class of conductors, gives rise to a variety of nonlinear effects; in particular, finite-time temperature-rate wave blow-up and temperature traveling waveforms which ex- hibit a “tongue”. The presentation concludes with a discussion of possible follow-on studies.