Abstract
Most existing phenomenological heat conduction models are expressed by temperature and heat flux distributions, whose definitions might be debatable in heat conductions with strong non-equilibrium. The constitutive relations of Fourier and hyperbolic heat conductions are here rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). The entropic constitutive relations are then generalized by Boltzmann–Gibbs–Shannon (BGS) statistical mechanics, which can avoid the debatable definitions of thermodynamic quantities relying on local equilibrium. It shows a possibility of modeling heat conduction through entropic constitutive relations. The applicability of the generalizations by BGS statistical mechanics is also discussed based on the relaxation time approximation, and it is found that the generalizations require a sufficiently small entropy production rate.
Highlights
Fourier’s law of heat conduction is the most classical heat conduction model, which has been proved by numerous experiments and widely applied to engineering
The constitutive relations of Fourier and hyperbolic heat conduction models are rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT) [1,15,16] and extended irreversible thermodynamics (EIT) [16,17]
The constitutive relations in Fourier and hyperbolic heat conductions are rewritten by the entropy and entropy flux distributions
Summary
Fourier’s law of heat conduction is the most classical heat conduction model, which has been proved by numerous experiments and widely applied to engineering. Fourier’s law describes the constitutive relation between the temperature gradient and heat flux q(x, t) = −λ∇ T (x, t),. It should be noted that wave-like transport with finite speeds of heat propagation can be predicted by Fourier’s law in the cases of temperature-dependent thermal properties. The non-Fourier models aim at exhibiting more detailed non-equilibrium effects than Fourier’s law, their constitutive relations are still expressed by the temperature and heat flux distributions paired with their derivatives. The constitutive relations of Fourier and hyperbolic heat conduction models are rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT) [1,15,16] and extended irreversible thermodynamics (EIT) [16,17]. The medium discussed in this work is limited to solids
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