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

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  • Carillo, Sandra
  • Jordan, Pedro M.

Abstract

We examine second-sound phenomena in a theoretically-motivated class of rigid solids within which the flow of heat is described by a special case of the Maxwell–Catteneo flux law. Employing a combination of analytical and numerical methods, we examine both temperature-rate waves and thermal traveling waves in this class of solids, which have recently been termed Graffi–Franchi–Straughan type (thermal) conductors. The particular temperature-dependent form of the thermal relaxation time, which is the distinguishing feature of this class, gives rise to a variety of nonlinear effects; specifically, finite-time temperature-rate wave blow-up, ‘retrograde’ behavior, and temperature traveling waveforms that exhibit a ‘tongue’. The presentation concludes with a discussion of possible follow-on studies.

Suggested Citation

  • Carillo, Sandra & Jordan, Pedro M., 2020. "On the propagation of temperature-rate waves and traveling waves in rigid conductors of the Graffi–Franchi–Straughan type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 120-133.
    • Handle: RePEc:eee:matcom:v:176:y:2020:i:c:p:120-133
    DOI: 10.1016/j.matcom.2020.01.017
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