### Speaker

### Description

In most of the engineering problems, the classical constitutive laws such as Fourier and Navier-Stokes equations are applicable. However, there are certain cases when these models require the generalization of the constitutive equations [1]. Such deviation can be observed also in case of rarefied gases. The deviation occurs due to the so-called ballistic propagation effects [2].

In this talk, different interpretations are shown for ballistic propagation; one of them is related to a specific heat conduction experiment on NaF samples performed by McNelly et al. The other one is related to an experiment on rarefied gases conducted by Rhodes. For the NaF experiment, the so-called ballistic-conductive model is tested with success and its theoretical background is implemented for the coupled system of Navier-Stokes-Fourier (NSF) in order to obtain a similar generalization.

The resulting generalization of NSF equations is tested on Rhodesâ experiment; furthermore, its compatibility with kinetic theory is investigated [3]. It turned out that the exact same generalization of entropy applied for heat conduction, also applicable for the NSF theory and called as âballistic generalizationâ that highlights some thermodynamic equivalence of different conducting medium where ballistic propagation occurs.

References

[1] S. Both et al.: Deviation from Fourier law at room temperature heterogeneous materials. Journal of Non-Equilibrium Thermodynamics, 41(1), 2016.

[2] R. KovĂĄcs: On the rarefied gas experiments. Entropy 21(7), Paper: 718, 2019.

[3] R. KovĂĄcs, P. Rogolino, D. Jou: When theories and experiments meet: Rarefied gases as a benchmark of non-equilibrium thermodynamic models, International Journal of Engineering Science, 169, Paper: 103574, 2021.