An extended thermodynamic model of transient heat conduction at sub-continuum scales

A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer–Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models.

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Effective Thermal Conductivity of Spherical Particulate Nanocomposites: Comparison with Theoretical Models, Monte Carlo Simulations and Experiments

International Journal of Nanoscience ◽

10.1142/s0219581x14500227 ◽

2014 ◽

Vol 13 (03) ◽

pp. 1450022 ◽

Cited By ~ 11

Author(s):

Hatim Machrafi ◽

Georgy Lebon

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Theoretical Models ◽

Irreversible Thermodynamics ◽

Flux Vector ◽

Heat Flux Vector ◽

The Matrix ◽

The Status ◽

Independent Variable ◽

Good Agreement

The purpose of this work is to study heat conduction in systems that are composed out of spherical micro-and nanoparticles dispersed in a bulk matrix. Special emphasis will be put on the dependence of the effective heat conductivity on various selected parameters as dimension and density of particles, interface interaction with the matrix. This is achieved by combining the effective medium approximation and extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by three examples: Silicium-Germanium, Silica-epoxy-resin and Copper-Silicium systems. Predictions of our model are in good agreement with other theoretical models, Monte-Carlo simulations and experimental data.

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A Unified Extended Thermodynamic Description of Diffusion, Thermo-Diffusion, Suspensions, and Porous Media

Journal of Applied Mechanics ◽

10.1115/1.2131087 ◽

2005 ◽

Vol 73 (1) ◽

pp. 16-20 ◽

Cited By ~ 10

Author(s):

Georgy Lebon ◽

Thomas Desaive ◽

Pierre Dauby

Keyword(s):

Porous Media ◽

Evolution Equations ◽

Diffusion Flux ◽

Thermodynamic Description ◽

Fluid Flows ◽

Irreversible Thermodynamics ◽

Heat Fluxes ◽

Flows In Porous Media ◽

Extended Thermodynamic ◽

Higher Order Terms

It is shown that extended irreversible thermodynamics (EIT) provides a unified description of a great variety of processes, including matter diffusion, thermo-diffusion, suspensions, and fluid flows in porous media. This is achieved by enlarging the set of classical variables, as mass, momentum and temperature by the corresponding fluxes of mass, momentum and heat. For simplicity, we consider only Newtonian fluids and restrict ourselves to a linear analysis: quadratic and higher order terms in the fluxes are neglected. In the case of diffusion in a binary mixture, the extra flux variable is the diffusion flux of one the constituents, say the solute. In thermo-diffusion, one adds the heat flux to the set of variables. The main result of the present approach is that the traditional equations of Fick, Fourier, Soret, and Dufour are replaced by time-evolution equations for the matter and heat fluxes, such generalizations are useful in high-frequency processes. It is also shown that the analysis can be easily extended to the study of particle suspensions in fluids and to flows in porous media, when such systems can be viewed as binary mixtures with a solid and a fluid component.

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Heat transfer at nanometric scales described by extended irreversible thermodynamics

Communications in Applied and Industrial Mathematics ◽

10.1515/caim-2016-0013 ◽

2016 ◽

Vol 7 (2) ◽

pp. 177-195 ◽

Cited By ~ 2

Author(s):

Hatim Machrafi

Keyword(s):

Heat Transfer ◽

Particle Size ◽

Irreversible Thermodynamics ◽

Considerable Influence ◽

Flux Vector ◽

Extended Irreversible Thermodynamics ◽

Matrix Interaction ◽

Heat Flux Vector ◽

The Status ◽

Independent Variable

AbstractThe purpose of this work is to present a study on heat conduction in systems that are composed out of spherical and cylindrical micro- and nanoparticles dispersed in a bulk matrix. Special emphasis is put on the dependence of the effective heat conductivity on various selected parameters as particle size and also its shape, surface specularity and density, including particle-matrix interaction. The heat transfer at nanometric scales is modelled using extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by a Copper-Silicium (Cu-Si) system. It is shown that all the investigated parameters have a considerable influence, the particle size being especially useful to either increase or decrease the effective thermal conductivity.

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