On the thermodynamics of second sound in dielectric crystals

DOI10.1007/BF00250739zbMath0501.73008OpenAlexW2030809500MaRDI QIDQ1172416

Bernard D. Coleman, David R. Owen, Mauro Fabrizio

Publication date: 1982

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00250739

zbMATH Keywords

internal energysecond sounddependent upon heat fluxdielectric crystalsMaxwell-Cattaneo-Law

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• The thermodynamics of elastic materials with heat conduction and viscosity
• A mathematical foundation for thermodynamics
• On thermodynamics and elastic-plastic materials
• On thermodynamics and intrinsically equilibrated materials
• Entropy and hidden variables in continuum thermodynamics
• A general theory of heat conduction with finite wave speeds
• Thermodynamics and departures from Fourier's law of heat conduction
• Thermoelastic waves in anisotropic solids

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