Entropy Production in the Theory of Heat Conduction in Solids

The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine's minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We suggest a characterization of the evolution of the entropy production of the system through the generalized Fourier modes, showing that they are the only states with a time independent entropy production. The variational approach and a Lyapunov functional of the temperature, monotonically decreasing with time, are discussed. We describe the analytic properties of the entropy production as a function of time in terms of the generalized Fourier coefficients of the system. Analytical tools are used throughout the paper and numerical examples will support the statements

Weakly nonlocal irreversible thermodynamics - the Guyer-Krumhansl and the Cahn-Hilliard equations

Examples of irreversible thermodynamic theory of nonlocal phenomena are given, based on generalized entropy current. Thermodynamic currents and forces are identified to derive the Guyer-Krumhansl and Cahn-Hilliard equations. In the latter case Gurtin's rate dependent additional term is received through the thermodynamic approach.Comment: revise

Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.Comment: 30 pages, no figure

Models of ballistic propagation of heat at low temperatures

Heat conduction at low temperatures show various effects that cannot be described by the Fourier law, like the second sound and ballistic propagation. In this paper the performance of various theories is compared in case of ballistic and wave like propagation of heat pulses in NaF

Entropy production in phase field theories

Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.Comment: 5 pages, no figure

Elastic, thermal expansion, plastic and rheological processes - theory and experiment

Rocks are important examples for solid materials where, in various engineering situations, elastic, thermal expansion, rheological/viscoelastic and plastic phenomena each may play a remarkable role. Nonequilibrium continuum thermodynamics provides a consistent way to describe all these aspects in a unified framework. This we present here in a formulation where the kinematic quantities allow arbitrary nonzero initial (e.g., in situ) stresses and such initial configurations which - as a consequence of thermal or remanent stresses - do not satisfy the kinematic compatibility condition. The various characteristic effects accounted by the obtained theory are illustrated via experimental results where loaded solid samples undergo elastic, thermal expansion and plastic deformation and exhibit rheological behaviour. From the experimental data, the rheological coefficients are determined, and the measured temperature changes are also explained by the theory.Comment: 15 pages, to appear in Period. Polytech. Civil En