Volume 26, Issue 3

The covariant form of entropy change (or balance) is expressed in the metric of the Schwarzschild line element. In this metric the rate of entropy change depends only on the time component of the metric tensor; it is then different at different points in space and appears to be slower in the presence than in the absence of a gravitational field. The linear equations originated by the internal entropy sources depend on both the time and radial components of the metric tensor and the transport processes behave anisotropically, being slower along the radial coordinate than in the directions of the others. The extent of rate reduction is expressed by the kinetic (transport) quantities which assume different values at different points in space.

In this paper the micropolar medium exposed to the action of mechanical, thermal and electromagnetic fields is considered. The generalization of the global evolution criterion of nonequilibrium thermodynamics of micropolar media in the case of nonvanishing electromagnetic fields is derived. Interaction with the environment is modeled by the black-body radiation. Application of the criterion to liquid crystals in equilibrium state is given and the complete set of fundamental equations is derived.

The mathematical properties of thermodynamics with internal variables are investigated in a general framework, both for the local and gradient theory. The consequences of the Second Law of Thermodynamics on the constitutive equations, together with some peculiar properties of the equilibrium states, are proved. The evolution equations of the internal variables are derived as a system of Hamilton equations resulting from a suitable Legendre's transformation.

The linear instability of a layer of Newtonian fluid superposing a Maxwell viscoelastic fluid layer in a microgravity environment is studied. With the aid of a complex variation of the Newton-Raphson method, the effects of the relaxation time and the ratio of heat diffusivities on the onset of oscillatory stabilities in this two-layer system are investigated.

In this paper the problem of magnetically undeformable polarizable media in the presence of an electromagnetic field is analyzed from a thermodynamic viewpoint. The thermodynamic transformations are explicited as functions in the state space in which one of the variables, characterizing the magnetic polarization, is given as an internal variable. The entropy form along the thermodynamic transformation is calculated for para- and diamagnetic media and the necessary conditions for its existence are given.

A generalized analysis of the local entropy production of a simple fluid is used to show that, if intrinsic angular momentum is taken into account, rotational viscosity must arise in the linear non-equilibrium regime. As a consequence, the stress tensor of dense rotating matter, such as the one present in neutron stars, posseses a significant non-vanishing antisymmetrical part. A simple argument suggests that, due to the extreme magnetic fields present in neutron stars, the relaxation time associated to rotational viscosity is large (∼10 21 ). The formalism leads to generalized Navier-Stokes equations useful in neutron star physics which involve vorticity in the linear regime.

The equilibrium Rayleigh-Brillouin spectrum for a Maxwell fluid in which heat conduction is governed by the classical Fourier law is computed. This is done by using fluctuating hydrodynamics and by the alternative procedure used by Mountain. It is found that both calculations render the same results only if the fluctuation-dissipation relations in the former are the ones prescribed by Landau and Lifshitz for the case where a dispersive dissipation coefficient is present. This result brings up the question of whether extended irreversible thermodynamics is the proper underlying nonequilibrium thermodynamic framework for the Maxwell fluid. It also suggests that at least the version of fluctuating hydrodynamics based on extended irreversible thermodynamics as introduced by Jou and Casas-Vázquez many years ago [18] must be revised, since it leads to a different form for the fluctuation-dissipation relations.

The sole irreversibility considered in an endoreversible Carnot refrigerator model is the loss of heat resistance between the refrigerator and its surrounding heat reservoirs. This paper presents a generalized irreversible Carnot refrigerator model by taking into account several additional internal irreversibilities of the refrigerator, such as heat leakage, friction, turbulence and other undesirable factors. This is done by means of a constant parameter and a constant coefficient, together with the loss of heat resistance. The relation between optimal cooling load and coefficient of performance (COP) is derived based on a generalized heat transfer law Q α Δ(T n ). The effect of heat leakage, internal irreversibility, and heat transfer law on the optimal performance of the generalized irreversible Carnot refrigerator is investigated.