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On the propagation of second-sound in linear and nonlinear media: Results from Green-Naghdi theory |
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| Authors: | S. Bargmann P.M. Jordan |
| Affiliation: | a Chair of Applied Mechanics, University of Kaiserslautern, PO Box 3049, 67653 Kaiserslautern, Germany b Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5, 91058 Erlangen, Germany c Code 7181, Naval Research Laboratory, Stennis Space Center, MS 39529, USA |
| 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. |
| Keywords: | Green-Naghdi theory Second-sound Temperature rate waves Traveling wave solution Lambert W-function |
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