What is it about?
Phonon hydrodynamics is a description of a particular regime of non-Fourier heat transfer in which the evolution equation for the heat flux has a form analogous to the one for the velocity in Newtonian viscous fluids, with the temperature gradient playing the role of the pressure gradient, and a term in the Laplacian of the heat flux (analogous to the viscous term in the Laplacian of the fluid velocity) describing the dissipative effects. In such a paper we have proposed a non-linear generalization of the equation for the heat flux by writing a linear evolution equation for the thermodynamic conjugate to the heat flux.
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Why is it important?
The paper obtains a linear evolution equation for w, the thermodynamic conjugate of the heat flux q. Since w is a non-linear function of q, the linear equation for w yields in a direct way a non-linear equation for q, on a solid thermodynamic basis. Such nonlinear equation for q yields a non-Newtonian behaviour for phonon hydrodynamics, which could be able to describe some recent observations which seem to indicate a non-linear behaviour slightly more complicated than usual phonon hydrodynamics.
Perspectives
In a previous paper with Michele Sciacca in ZAMP we proposed a phenomenological generalization of the equation for phonon hydrodynamics, analogous to the power-law models of non-Newtonian viscous fluids, in order to be able to describe some non-Newtonian effects observed by some authors. In the present paper, we complemented such an approach by starting on a model more directly motivated by basic thermodynamic reasoning, rather than on phenomonological analogy with non-Newtonian viscous fluids.
David Jou
Universitat Autonoma de Barcelona
Read the Original
This page is a summary of: Nonlinear phonon hydrodynamics: A Guyer–Krumhansl equation for the conjugate of the heat flux, Zeitschrift für angewandte Mathematik und Physik, October 2025, Springer Science + Business Media,
DOI: 10.1007/s00033-025-02630-7.
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