On the propagation of second-sound in linear and nonlinear media: Results from Green-Naghdi theory

Bargmann, S., Steinmann, P. and Jordan, P.M. (2008) On the propagation of second-sound in linear and nonlinear media: Results from Green-Naghdi theory. Physics Letters A, 372(24), pp. 4418-4424. (doi: 10.1016/j.physleta.2008.04.010)

Abstract

We investigate thermal wave propagation in one-dimensional media according to Green–Naghdi's heat conduction theory. Under the linearized theory, the dynamic propagation of a Heaviside input signal in a half-space is examined. Exact analytical solutions are derived for the three cases (i.e., types I–III) of this theory. We then numerically compare the evolution of the linear and nonlinear type-II temperature profiles, and track the finite-time blow-up of the latter's temperature rate wave, in the setting of an initial-boundary value problem involving a sudden sinusoidal input signal. Lastly, an exact traveling wave solution of a lossless, nonlinear equation, which arises under type-II theory, is determined and analyzed.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Bargmann, S., Steinmann, P., and Jordan, P.M.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Physics Letters A
• Publisher: Elsevier
• ISSN: 0375-9601

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