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arXiv · 1906.05355

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

Sandra Carillo·Pedro M. Jordan
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Abstract

We examine second-sound phenomena in a class of rigid, thermally conducting, 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 exhibit a "tongue". The presentation concludes with a discussion of possible follow-on studies.

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Sandra Carillo, Pedro M. Jordan. 2019-06-04. On the propagation of temperature-rate waves and traveling waves in rigid conductors of the Graffi--Franchi--Straughan type. https://doi.org/10.1016/j.matcom.2020.01.017

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