Second-sound phenomena in inviscid, thermally relaxing gases

Pedro M. Jordan

doi:10.3934/dcdsb.2014.19.2189

Article Contents

2014, Volume 19, Issue 7: 2189-2205. Doi: 10.3934/dcdsb.2014.19.2189

This issue Previous Article Strain gradient theory of porous solids with initial stresses and initial heat flux Next Article Going to new lengths: Studying the Navier--Stokes-$\alpha\beta$ equations using the strained spiral vortex model

Second-sound phenomena in inviscid, thermally relaxing gases

Pedro M. Jordan^1,

1.
Acoustics Div., U.S. Naval Research Laboratory, Stennis Space Ctr., MS 39529

Received: March 31, 2013

Revised: July 31, 2013

Published: August 2014

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Abstract

We consider the propagation of acoustic and thermal waves in a class of inviscid, thermally relaxing gases wherein the flow of heat is described by the Maxwell--Cattaneo law, i.e., in Cattaneo--Christov gases. After first considering the start-up piston problem under the linear theory, we then investigate traveling wave phenomena under the weakly-nonlinear approximation. In particular, a shock analysis is carried out, comparisons with predictions from classical gases dynamics theory are performed, and critical values of the parameters are derived. Special case results are also presented and connections to other fields are noted.

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Mathematics Subject Classification: Primary: 76L05, 76N15, 80A20; Secondary: 35L70, 44A10.

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