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

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

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

Influence of electron and phonon temperature on the efficiency of thermoelectric conversion

In the framework of Extended Irreversible Thermodynamics it is developed a two-temperature model (for electrons and phonons, respectively) of thermoelectric effects. The expression of the maximum efficiency in terms of these two temperatures is derived as well. It is proved that, for the electron temperature higher than the phonon temperature, the two-temperature model yields an efficiency which is higher with respect to that of the single-temperature model. Two possible experiments to estimate the electron temperature are suggested

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

Exploitation of the Second Law: Coleman–Noll and Liu Procedure in Comparison

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.A comparison is made between two classical methods for the exploitation of the second law of thermodynamics: the Coleman–Noll and the Liu procedure. On the example of a rigid heat conductor with general entropy flux, it is shown that the two procedures are equivalent. This equivalence is demonstrated in the case of a state space including the wanted fields, only, as well as in the case of gradients being relevant for constitutive equations, too. Also, the possible importance of an internal variable or an internal degree of freedom is considered