Gradient Catastrophe in Heat Propagation with second Sound

Author(s):  
S Messaoudi ◽  
A Al Shehri
2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Zhiwei Ding ◽  
Ke Chen ◽  
Bai Song ◽  
Jungwoo Shin ◽  
Alexei A. Maznev ◽  
...  

AbstractSecond sound refers to the phenomenon of heat propagation as temperature waves in the phonon hydrodynamic transport regime. We directly observe second sound in graphite at temperatures of over 200 K using a sub-picosecond transient grating technique. The experimentally determined dispersion relation of the thermal-wave velocity increases with decreasing grating period, consistent with first-principles-based solution of the Peierls-Boltzmann transport equation. Through simulation, we reveal this increase as a result of thermal zero sound—the thermal waves due to ballistic phonons. Our experimental findings are well explained with the interplay among three groups of phonons: ballistic, diffusive, and hydrodynamic phonons. Our ab initio calculations further predict a large isotope effect on the properties of thermal waves and the existence of second sound at room temperature in isotopically pure graphite.


2008 ◽  
Vol 7 (2) ◽  
pp. 1-9
Author(s):  
S. Pranesh

This paper deals with linear stability analysis of the effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell - Cattaneo law in Rayleigh - Benard convection in second order fluid is studies. Coleman-Noll constitutive equaion is used to give a viscoelastic correction. The eigenvalue is obtained for free - free isothernal boundary combination. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.


2008 ◽  
Vol 7 (1) ◽  
pp. 26-40
Author(s):  
S. Pranesh

The effects resulting from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law in Rayleigh-Benard convention in micropolar fluid is studied. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical sign values are less than the classical ones.


2019 ◽  
Author(s):  
I. V. Kudinov ◽  
A. V. Eremin ◽  
K. V. Trubitsyn ◽  
E. V. Stefanyuk
Keyword(s):  

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