Volume 42, Issue 4 -

We show how classical irreversible thermodynamics is used to derive relaxation equations for dielectric polarization processes in insulators. We calculate susceptibilities for multiple polarization processes and show how coupling arises thermodynamically. Furthermore, we derive evolution equations for electromagnetic fields by combining the dielectric relaxation equations with Maxwell’s equations. Analytical solutions for various frequency regimes will be briefly discussed. A complete analogy exists between the dielectric problem, the Kelvin–Voigt viscoelasticity of solid media, and the non-equilibrium (reactive, vibrational) gasdynamic flow. Also, numerical solutions, using the method of characteristics, are given for a generic signal problem in half-space.

In this paper, the micromorphic approach, previously developed in the mechanical context is applied to heat transfer and shown to deliver new generalized heat equations as well as the nonlocal effects. The latter are compared to existing formulations: the classical Fourier heat conduction, the hyperbolic type with relaxation time, the gradient of temperature or entropy theories, the double temperature model, the micro-temperature model or micro-entropy models. A new pair of thermodynamically-consistent micromorphic heat equations are derived from appropriate Helmholtz-free energy potentials depending on an additional micromorphic temperature and its first gradient. The additional micromorphic temperature associated with the classical local temperature is introduced as an independent degree of freedom, based on the generalized principle of virtual power. This leads to a new thermal balance equation taking into account the nonlocal thermal effects and involving an internal length scale which represents the characteristic size of the system. Several existing extended generalized heat equations could be retrieved from constrained micromorphic heat equations with suitable selections of the Helmholtz-free energy and heat flux expressions. As an example the propagation of plane thermal waves is investigated according to the various generalized heat equations. Possible applications to fast surface processes, nanostructured media and nanosystems are also discussed.

In this paper an estimate for the reversible molar heat supply needed for fully separating a certain mixture is given on the basis of thermodynamic balance equations. It is shown that in order to estimate this heat supply one should solve the problem of selecting the optimal separation sequence. The algorithm solving this task is given. This algorithm allows to select the separation sequence on the basis of preliminary calculations, knowing only the properties of the component that one wants to separate. The solution algorithm is demonstrated for an exemplary system: a gas-fractionation plant.

In previous papers a phase field model for λ$\lambda$–transition in 4$^4$He was proposed, which is able to describe the influence of the heat flux on the temperature transition. The model presented here generalizes previous results taking into account of a homogeneous presence of quantized vortices below the λ$\lambda$–transition. As parameter that controls the transition, a dimensionless field f$f$ linked to the modulus of the condensate wave function is used. In addition to the field f$f$, the resulting model chooses the following field variables: density, velocity, temperature and heat flux. Nonlocal terms to describe inhomogeneities in the field variables and dissipative effects of mechanical and thermal origin are also taken into account. Under the hypothesis that the liquid is at rest, the second sound propagation near the superfluid transition is studied. It is seen that the order parameter modifies the speed and the attenuation of the second sound, as well as the presence of a small tangle of vortices. This shows that the influence of the order parameter is not restricted to the description of the lambda transition, but its presence influences also other features, as the second sound speed and attenuation. In addition to the second sound a new mode is present, corresponding to a perturbation in the order parameter f$f$, which is attenuated within a short number of wavelengths.

A five-dimensional treatment of the Boltzmann equation is used to establish the constitutive equations that relate thermodynamic fluxes and forces up to first order in the gradients for simple charged fluids in the presence of electromagnetic fields. The formalism uses the ansatz first introduced by Kaluza back in 1921, proposing that the particle charge–mass ratio is proportional to the fifth component of its velocity field. It is shown that in this approach, space–time curvature yields thermodynamic forces leading to generalizations of the well-known cross-effects present in linear irreversible thermodynamics.