Phonon- and electron-temperature waves in a Maxwell-Cattaneo heat-conduction theory

Abstract

A two-temperature model, which is fully compatible with the Maxwell-Cattaneo heat-conduction theory, is developed. It allows to account for different heat carriers’ temperatures, as well as for their mutual energy exchange. Its physical consistency is proved by means of the second law of thermodynamics. The propagation of phonon- and electron-temperature waves is also analyzed, and the results are plotted in the case of a ${\text{Bi}}_2{\text{Te}}_3$ sample at $300\mathrm{K}.$

Keywords:

• Acceleration wave
• electron temperature
• non-equilibrium temperature
• phonon temperature
• thermal-wave propagation

PACS numbers:

• 44.10.+i
• 66.70.-f
• 05.70.Ln

Acknowledgments

Work performed under the auspices of the Italian National Group of Mathematical Physics (GNFM-INdAM) which supported the present research by means of” Progetto Giovani 2018/Heat-pulse propagation in FGMs”.

Additional information

Funding

The author also acknowledges the University of Salerno for the financial support under grants no. 300395FRB18SELLI and no. 300395FRB19SELLI.