Volume 36, Issue 2

The optimal configuration of the expansion process of a heated working fluid inside a cylinder for maximum work output with a movable piston and time-dependent heat conductance is determined in this paper using finite-time thermodynamics. The heat transfer between the working fluid and the external heat bath is assumed to obey the generalized radiative heat transfer law ( q ∝ Δ( T n )). The heat conductance (product of heat transfer coefficient and heat transfer surface area) of cylinder walls is assumed to depend on the time-dependent heat transfer surface area of the walls in contact with gas. Euler–Lagrange formalism is applied to obtain the optimal process that maximizes the work output of the working fluid with fixed initial energy, initial volume, final volume, and total time allowed for the expansion. The optimal initial value of internal energy of the Euler–Lagrange arc is determined by numerical techniques. Numerical examples for the optimal configurations with time-dependent heat conductance for the cases of five special heat transfer laws ( n = –1, 1, 2, 3, and 4) are provided, and the obtained results are compared with those obtained for the cases of constant heat conductance. The optimal configurations with time-dependent heat conductance for the cases of five special heat transfer laws are also compared with each other. The optimization problems with the generalized radiative heat transfer law are helpful for the further understanding of the effect of heat transfer law on the general performance and the inherent character of thermodynamic processes and cycles. The results presented herein can provide the basis for both determining optimal operating conditions and designing real systems operating with the generalized radiative heat transfer law.

In this article, we show that the two expressions W = H λ = λ 2 – H λ = λ 1 and Δ G = – T ln( Z λ = λ 2 / Z λ = λ 1 ), which relate the work W with the Hamiltonian H and the free energy G with the partition function Z for different values of the parameter λ , are not physically valid in general, not because they are fundamentally flawed per se but because they can be applied in ways that violate basic physical principles. One of these unphysical ways is now widespread in the study of non-equilibrium manipulated microsystems: it consists in the straightforward application of the above-mentioned relations for changes of an external parameter that is not a coordinate. We show that the estimates of the free energy differences so obtained are in fact the result of a contradictory use of isoparametric statistical ensembles to analyze anisoparametric processes. We indicate a potential avenue to avoid this contradiction, which brings the study of manipulated microsystems to a conventional non-equilibrium thermodynamics description.

More than a century after Max Planck's 1906 book Theorie der Wärmestrahlung , alternative expressions for the entropy flux as related to thermal black-body radiation under non-equilibrium conditions are still controversially discussed in the scientific literature. In this paper, we consider the radiative heat exchange between two planar black bodies of different temperatures. Solely by exploiting the Second Law, it is shown that the mathematical formula for the related non-equilibrium entropy flux can uniquely be inferred from the Stefan–Boltzmann law, without taking advantage of the statistical Planck distribution. Expressions for the entropy production at the emitting surfaces are derived and an effective temperature associated with the radiation between the two bodies is suggested.

On the basis of the first and second laws of thermodynamics, the general expression of the number of entropy generation units of three-fluid heat exchangers with three thermal communications was derived. The effect of several non-dimensional design parameters on the number of entropy generation units of three-fluid heat exchangers was thoroughly discussed. Furthermore, the detailed comparisons of results have been given for the arrangement of the parallel flow and the counter flow. It is shown that the variation tendencies of the number of entropy generation units with the ratio of the thermal resistances, ratio of the thermal capacities, and number of heat transfer units for the parallel-flow arrangement are different from those of the counter-flow arrangement. There exists an extremum of the number of entropy generation units for the counter-flow arrangement. In addition, the entropy generation for the counter flow is mostly smaller than that of the parallel flow under the same conditions.

It was shown by Velasco et al. [J. Phys. D: Appl. Phys., 34(2001), 1000–1006] that the Feynman's ratchet can operate as a cold or hot ratchet and pawl engine. This paper takes a further step toward analyzing the optimum performances of the cold and hot ratchets and exploring the similarities and differences between them. The power and efficiency performances of both the cold and hot ratchets are analyzed with respect to the internal parameter. The influences of heat leakage and heat reservoir temperature ratio on the performances of the devices are investigated, and performance comparisons between the two kinds of ratchets are performed. Moreover, the analytical expression of the efficiency at maximum power for the hot ratchet is derived by optimizing both the internal and the external parameters. The fundamental optimal relation between power and efficiency for the cold and hot ratchets is explored through detailed numerical examples. The results obtained in this paper for the hot ratchet are further compared with those obtained by Tu [J. Phys. A: Math. Theor., 41(2008), 312003] for the cold ratchet. It is finally concluded that it is better for the Feynman's ratchet to operate as a cold ratchet and pawl engine.

The work deals with further developments of a study previously initiated, in which a macroscopic one-fluid model of inhomogeneous turbulent superfluids, based on extended thermodynamics, had been formulated. In this work the study is carried on. First the influence of the remnant vortices on the propagation of the first and second sound is studied. Then a boundary condition able to explain the reversible flow of superfluid flowing through a thin capillary is postulated and two vector fields, which have the dimensions of velocity and can be interpreted as the velocities of normal and superfluid components, are introduced. By using these new fields, a comparison between this model and the Hall–Vinen–Bekarevich–Khalatnikov model, which uses a two-fluid framework, is performed. The propagation of the fourth sound inside a porous medium is investigated: it is shown that, when the fourth sound is propagated, in addition to the thermodynamic fields (density, velocity, temperature, and heat flux), also the vortex line density vibrates.