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We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs–-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell–Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

Oxygen reduction in a solid oxide fuel cell cathode involves a nonequilibrium process of coupled mass and heat diffusion and electrochemical and chemical reactions. These phenomena occur at multiple temporal and spatial scales, making the modeling, especially in the transient regime, very difficult. Nonetheless, multiscale models are needed to improve the understanding of oxygen reduction and guide cathode design. Of particular importance for long-term operation are microstructure degradation and chromium oxide poisoning both of which degrade cathode performance. Existing methods are phenomenological or empirical in nature and their application limited to the continuum realm with quantum effects not captured. In contrast, steepest-entropy-ascent quantum thermodynamics can be used to model nonequilibrium processes (even those far-from equilibrium) at all scales. The nonequilibrium relaxation is characterized by entropy generation, which can unify coupled phenomena into one framework to model transient and steady behavior. The results reveal the effects on performance of the different timescales of the varied phenomena involved and their coupling. Results are included here for the effects of chromium oxide concentrations on cathode output as is a parametric study of the effects of interconnect-three-phase-boundary length, oxygen mean free path, and adsorption site effectiveness. A qualitative comparison with experimental results is made.

A fractional generalized hydrodynamic (GH) model of the concentration fluctuations correlation function is analyzed. Our analysis is based on a previously proposed irreversible thermodynamics non-fractional model that describes the first GH deviations in a finite frequency and wavelength regime where the local equilibrium assumption is not valid. Our basic purpose is to generalize this theory to investigate the time fractional effects on the intermediate scattering function (ISF) of a model of a binary mixture. We discuss two different forms of introducing the fractional derivatives into the hydrodynamic time evolution equation of the ISF and examine their consistency in the non-fractional limit. We calculate analytically the fractional intermediate scattering function (FISF) and compare it with the non-fractional one. We find that although the FISFs are in general less than ISF, the FISF may be a significant fraction of the ISF (∼36%) and might be measurable by light or neutron scattering techniques. We show that fractional time derivatives provide a consistent description of this correlation function in the GH regime and reduce to its well-known behavior in the Navier–Stokes limit (NS) where local equilibrium is restored. We also suggest an experimental verification of our results for near equilibrium states. Finally, we summarize the main results of our work and make some further physical remarks.

The entropy production rates as obtained from the exergy analysis, entropy balance and the nonequilibrium thermodynamics approach are compared for two distillation columns. The first case is a depropanizer column involving a mixture of ethane, propane, n-butane and n-pentane. The other is a weighed sample of Mexican crude oil distilled with a pilot scale fractionating column. The composition, temperature and flow profiles, for a given duty and operating conditions in each column, are obtained with the Aspen Plus V8.4 software by using the RateFrac model with a rate-based nonequilibrium column. For the depropanizer column the highest entropy production rate is found in the central trays where most of the mass transfer occurs, while in the second column the highest values correspond to the first three stages (where the vapor mixture is in contact with the cold liquid reflux), and to the last three stages (where the highest temperatures take place). The importance of the explicit inclusion of thermal diffusion in these processes is evaluated. In the depropanizer column, the effect of the coupling between heat and mass transfer is found to be negligible, while for the fractionating column it becomes appreciable.

A thermodynamic model of a thermoelectric cooler driven by thermoelectric generator (TEG-TEC) device is established considering Thomson effect. The performance is analyzed and optimized using numerical calculation based on non-equilibrium thermodynamic theory. The influence characteristics of Thomson effect on the optimal performance and variable selection are investigated by comparing the condition with and without Thomson effect. The results show that Thomson effect degrades the performance of TEG-TEC device, it decreases the cooling capacity by 27 %, decreases the coefficient of performance (COP) by 19 %, decreases the maximum cooling temperature difference by 11 % when the ratio of thermoelectric elements number is 0.6, the cold junction temperature of thermoelectric cooler (TEC) is 285 K and the hot junction temperature of thermoelectric generator (TEG) is 450 K. Thomson effect degrades the optimal performance of TEG-TEC device, it decreases the maximum cooling capacity by 28 % and decreases the maximum COP by 28 % under the same junction temperatures. Thomson effect narrows the optimal variable range and optimal working range. In the design of the devices, limited-number thermoelectric elements should be more allocated appropriately to TEG when consider Thomson effect. The results may provide some guidelines for the design of TEG-TEC devices.