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

Sandra Carillo and Pedro M. Jordan

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 176, issue C, 120-133

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.

Keywords: Graffi–Franchi–Straughan conductors; Maxwell–Cattaneo law; Temperature-rate waves; Traveling wave solutions; Lambert W-function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:176:y:2020:i:c:p:120-133

DOI: 10.1016/j.matcom.2020.01.017

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