scholarly journals Entropy Production in the Theory of Heat Conduction in Solids

Entropy ◽  
2016 ◽  
Vol 18 (3) ◽  
pp. 87 ◽  
Author(s):  
Federico Zullo
Keyword(s):  
Heat Conduction ◽  
Entropy Production

scholarly journals Entropy and Entropy Production in Multiscale Dynamics

2019 ◽  
Vol 44 (3) ◽  
pp. 217-233 ◽  
Author(s):  
Miroslav Grmela ◽  
Michal Pavelka ◽  
Václav Klika ◽  
Bing-Yang Cao ◽  
Nie Bendian
Keyword(s):  
Heat Conduction ◽  
Entropy Production ◽  
Total Entropy ◽  
Approach To Equilibrium ◽  
Multiscale Dynamics ◽  
Classical Thermodynamics ◽  
Point Of Departure ◽  
Total Entropy Production ◽  
Classical Entropy

Abstract Heat conduction is investigated on three levels: equilibrium, Fourier, and Cattaneo. The Fourier level is either the point of departure for investigating the approach to equilibrium or the final stage in the investigation of the approach from the Cattaneo level. Both investigations bring to the Fourier level an entropy and a thermodynamics. In the absence of external and internal influences preventing the approach to equilibrium the entropy that arises in the latter investigation is the production of the classical entropy that arises in the former investigation. If the approach to equilibrium is prevented, then the entropy that arises in the investigation of the approach from the Cattaneo level to the Fourier level still brings to the Fourier level the entropy and the thermodynamics even if the classical entropy and the classical thermodynamics are absent. We also note that vanishing total entropy production as a characterization of equilibrium state is insufficient.

Temperature and entropy production operator in Fourier heat conduction

1995 ◽  
Vol 52 (1) ◽  
pp. 623-626 ◽  
Author(s):  
Ferenc Márkus ◽  
Katalin Gambár
Keyword(s):  
Heat Conduction ◽  
Entropy Production ◽  
Fourier Heat Conduction

scholarly journals Validation of accuracy and stability of numerical simulation for 2-D heat transfer system by an entropy production approach

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 97-104
Author(s):  
Ali Brohi ◽  
Haochun Zhang ◽  
Kossi Min-Dianey ◽  
Muhammad Rafique ◽  
Muhammad Hassan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Conduction ◽  
Entropy Production ◽  
Heat Conduction Problem ◽  
Current Approach ◽  
Transfer System ◽  
Heat Transfer System ◽  
The Stability ◽  
Accuracy And Stability

The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.

scholarly journals Fractional-order heat conduction models from generalized Boltzmann transport equation

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190280 ◽  
Author(s):  
Shu-Nan Li ◽  
Bing-Yang Cao
Keyword(s):  
Heat Conduction ◽  
Entropy Production ◽  
Production Rate ◽  
Fractional Order ◽  
Mean Square Displacement ◽  
Linear Response Theory ◽  
Entropy Density ◽  
Entropy Production Rate ◽  
Boltzmann Transport ◽  
Entropy Flux

The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼  t γ is established, namely, κ eff  ∼  t γ −1 , which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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