Abstract
We have reviewed thermodynamically consistent evolution equations of fluids in an invited review article in the McGill University bicentennial memorial issue [B. C. Eu, Can. J. Chem. (in press) (2021)]. In this article, we apply the generalized hydrodynamic evolution equations of heat fluxes to derive integral equations for thermal conductivity coefficients of fluids in electromagnetic fields, which generalize the linear response theory formula of Green and Kubo to nonlinear heat conduction phenomena. The constitutive equation for the temperature field derived is compared with the temperature evolution equation obtained by Guo et al. [Physica D 342, 24 (2017)] on the basis of extended irreversible thermodynamics. They are considerably different.
Highlights
In the forms of monographs1–4 and reviews of original articles, the present author has formulated and applied in recent years a thermodynamically consistent theory of transport processes in fluids far removed from equilibrium in centrosymmetric intermolecular interaction fields
In the present article, which was originally prepared as an integral part of Ref. 5 but could not be included in it owing to the page limitation, we consider a generalized thermodynamic (GT) theory of anisotropic thermal conduction in matter that strictly obeys the thermodynamic laws and, may be said to be thermodynamically consistent
The generalized hydrodynamics (GT) comes about explicitly as necessary consequences in the studies of thermodynamics of irreversible processes when the theory is formulated from the Clausius inequality with the notions of compensated and uncompensated heats incorporated into it
Summary
In the forms of monographs and reviews (see, for example, Ref. 5) of original articles, the present author has formulated and applied in recent years a thermodynamically consistent theory of transport processes in fluids far removed from equilibrium in centrosymmetric intermolecular interaction fields. Where Rij (more precisely, Rij) is the collision bracket integrals of the kinetic equation for the plasma; c is the speed of light; pi is the partial pressure; Ĉpi is the heat capacity per mass of species i; λ0 is the Chapman–Enskog (linear) heat conductivity; d is the mean diameter of molecules; mr is the reduced mass; n is the number density; A denotes the vector potential of the magnetic field H; and the symbol qn(Q) is an important nonlinear factor representing the energy dissipation that originates from the collision processes underlying the transport phenomena. The formal theoretic aspect of its effect is one of our main interest in this article within the framework of generalized hydrodynamics and irreversible thermodynamics This structure of the kinematic term Z3i implies that the electromagnetic fields appear as a higher-order effect than the temperature gradients driving the evolution of heat fluxes, but if the electromagnetic fields are intense, they could have significant effects on heat conduction. It correctly describes nonlinear dissipative irreversible processes of momentum and energy transfer in matter for many cases, as have been shown in our previous works. Here, we are relying on the insights and experience we have gained through such studies described in the references just cited
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