Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Recent advances in nanotechnology create a demand for greater scientific understanding of the transient ballistic phonon transport at the nanoscale. It is believed that ballistic phonons may travel for long distances without destruction, but it is unclear how far they can travel. Here, a numerical model is developed to study phonon transport in silicon nanofilms. It is elucidated how thermal pulses are transmitted in silicon nanofilms by longitudinal, ballistic transverse and dispersive transverse phonons. It is found that both ballistic longitudinal and ballistic transverse phonons are highly dissipative so they can only travel for short distances, while dispersive transverse phonons at lower frequencies are less dissipative and can travel for longer distances. There exists a similarity parameter (Knudsen number) in thin-film heat conduction with different thicknesses.

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Generalized hydrodynamics and heat waves

Canadian Journal of Physics ◽

10.1139/p92-006 ◽

1992 ◽

Vol 70 (1) ◽

pp. 62-71 ◽

Cited By ~ 4

Author(s):

R. E. Khayat ◽

Byung Chan Eu

Keyword(s):

Thermal Conductivity ◽

Evolution Equations ◽

Pulse Propagation ◽

Heat Waves ◽

Fluid Dynamic ◽

Propagation Speed ◽

Heat Pulse ◽

Irreversible Processes ◽

Large Temperature ◽

Generalized Hydrodynamics

By using the evolution equations of generalized hydrodynamics we investigate heat-pulse propagation in a Lennard–Jones liquid contained in the annulus between two concentric cylinders at different temperatures. It is found that the heat pulse propagates as a wave of a finite speed when a composite fluid dynamic number [Formula: see text] that depends on the thermal conductivity and wall temperature ratio is above a critical value, but in the subcritical region the heat pulse propagates diffusively as if predicted by a parabolic differential equation with an infinite speed of propagation. Therefore the question of the hyperbolicity of the system of differential (evolution) equations used is mainly determined by the parameter [Formula: see text]. This implies that the hyperbolicity of evolution equations, i.e., the finiteness of pulse-propagation speed, cannot be the main reason for extending the thermodynamics of irreversible processes as believed by some authors in the literature. This study indicates that for a liquid of high thermal conductivity or a large temperature difference the Fourier law of heat conduction is inadequate for use in the description of the temporal evolution of heat and a suitable generalization of hydrodynamics is necessary. The generalized hydrodynamic equations presented in this and previous papers are examples for such a generalization.

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ASDEX heat pulse propagation as a forced boundary value problem

Nuclear Fusion ◽

10.1088/0029-5515/28/9/003 ◽

1988 ◽

Vol 28 (9) ◽

pp. 1509-1518 ◽

Cited By ~ 12

Author(s):

K.S. Riedel ◽

A. Eberhagen ◽

O. Gruber ◽

K. Lackner ◽

G. Becker ◽

...

Keyword(s):

Boundary Value Problem ◽

Pulse Propagation ◽

Boundary Value ◽

Heat Pulse

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Heat-pulse propagation along nonequilibrium nanowires in thermomass theory

Communications in Applied and Industrial Mathematics ◽

10.1515/caim-2016-0005 ◽

2016 ◽

Vol 7 (2) ◽

pp. 39-55

Author(s):

Antonio Sellitto ◽

Patrizia Rogolino ◽

Isabella Carlomagno

Keyword(s):

Temperature Gradient ◽

Transport Equation ◽

Heat Transport ◽

Pulse Propagation ◽

Heat Pulse ◽

Average Temperature ◽

Temperature Ranges ◽

Heat Transport Equation ◽

Heat Pulses ◽

Theoretical Proposal

AbstractWe analyze the consequences of the nonlinear terms in the heat-transport equation of the thermomass theory on heat pulses propagating in a nanowire in nonequilibrium situations. As a consequence of the temperature dependence of the speeds of propagation, in temperature ranges wherein the specific heat shows negligible variations, heat pulses will shrink (or extend) spatially, and will increase (or decrease) their average temperature when propagating along a temperature gradient. A comparison with the results predicted by a different theoretical proposal on the shape of a propagating heat pulse is made, too.

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