Boundary Conditions for Diffusive-Hyperbolic Systems in Non-Equilibrium Thermodynamics

A model of a heat conductor with on internal variable, describing thermodiffusion as well as thermal wave propagation is developed. Boundary conditions for the obtained diffusive-hyperbolic system are derived from the second law of thermodynamics. Propagation of weak and strong discontinuities for the hyperbolic sub-system is analyzed

A generalized Coleman–Noll procedure for the exploitation of the entropy principle

A generalization of the classical Coleman–Noll procedure for the exploitation of second law of thermodynamics in the presence of first-order non-local constitutive functions is proposed. The local balance of entropy is regarded as a differential inequality constrained by the governing equations for the set of the unknown fields as well as by their gradient extensions. The thermodynamic compatibility of such a class of materials is achieved without any modification of the basic thermodynamic laws. The results so obtained are applied to model nonlinear heat conduction in solids, in the presence of a dynamical semi-empirical temperature scale

Thermomechanics of Interstitial Working at Liquid Boundaries

A model of material interface, for which the metric tensor is regarded as an internal variable, is considered. Both a local and a non-local evolution equation for such a variable are analyzed. The consequences of the second law of thermodynamics are derived in both cases

Thermoelectric efficiency of silicon–germanium alloys in finite-time thermodynamics

We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T = 300K, T = 400K, T = 500K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out

The effects of nonlocality on the evolution of higher order fluxes in non-equilibrium thermodynamics

The role of gradient dependent constitutive spaces is investigated on the example of Extended Thermodynamics of rigid heat conductors. Different levels of nonlocality are developed and the different versions of extended thermodynamics are classified. The local form of the entropy density plays a crucial role in the investigations. The entropy inequality is solved under suitable constitutive assumptions. Balance form of evolution equations is obtained in special cases. Closure relations are derived on a phenomenological level.Comment: 16 pages, 1 figur

Local versus nonlocal constitutive theories of nonequilibrium thermodynamics: the Guyer–Krumhansl equation as an example

On the example of the celebrated Grad’s 13-moment system of kinetic theory of rarefied gases and phonon hydrodynamics, it is proved that the constitutive equations of nonequilibrium thermodynamics must be nonlocal. A thermodynamic model of Guyer–Krumhansl heat-transport equation is derived within the frame of weakly nonlocal Rational Thermodynamics. The constitutive equation for the entropy flux is analyzed as well. Some nonlinear generalizations of Maxwell–Cattaneo equation are studied in view of the experiments on thermal wave propagation

Weakly nonlocal thermodynamics of anisotropic rigid heat conductors revisited

The thermodynamic theory of anisotropic rigid heat conductors with gradient constitutive equations is revisited in the framework of both extended irreversible thermodynamics and rational thermodynamics. The Second Law is exploited through a generalized Coleman–Noll procedure. Some interesting physical properties of the entropy flux and the entropy production are pointed out