Transported Entropy of Ions and Peltier Coefficients in 8YSZ and 10Sc1CeSZ Electrolytes for Solid Oxide Cells.

In this study, the transported entropy of ions for 8YSZ and 10Sc1CeSZ electrolytes was experimentally determined to enable precise modeling of heat transport in solid oxide cells (SOCs). The Peltier coefficient, crucial for thermal management, was directly calculated, highlighting reversible heat transport effects in the cell. While data for 8YSZ are available in the literature, providing a basis for comparison, the results for 10Sc1CeSZ show slightly smaller Seebeck coefficients but higher transported ion entropies. Specifically, at 700°C and an oxygen partial pressure of pO2=0.21 bar, values of SO2-*=52±10 J/K·F for 10Sc1CeSZ and SO2-*=48±9 J/K·F for 8YSZ were obtained. The transported entropy was also validated through theoretical calculations and showed minimal deviations when comparing different cell operation modes (O2||O2-||O2 and H2, H2O||O2-||O2). The influence of the transported entropy of the ions on the total heat generation and the partial heat generation at the electrodes is shown. The temperature has the greatest influence on heat generation, whereby the ion entropy also plays a role. Finally, the Peltier coefficients of 8YSZ for all homogeneous phases agree with the literature values.

Numerical Calculation of the Irreversible Entropy Production of Additively Manufacturable Off-Set Strip Fin Heat-Transferring Structures.

In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80-920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence.

Coupled Transport Effects in Solid Oxide Fuel Cell Modeling.

With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick's law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring U,j-characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At T=1123.15 K and j=8000 A/m2, 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials.

Impact of Multi-Causal Transport Mechanisms in an Electrolyte Supported Planar SOFC with (ZrO2)x-1(Y2O3)x Electrolyte.

The calculation of the entropy production rate within an operational high temperature solid oxide fuel cell (SOFC) is necessary to design and improve heating and cooling strategies. However, due to a lack of information, most of the studies are limited to empirical relations, which are not in line with the more general approach given by non-equilibrium thermodynamics (NET). The SOFC 1D-model presented in this study is based on non-equilibrium thermodynamics and we parameterize it with experimental data and data from molecular dynamics (MD). The validation of the model shows that it can effectively describe the behavior of a SOFC at 1300 K. Moreover, we show that the highest entropy production is present in the electrolyte and the catalyst layers, and that the Peltier heat transfer is considerable for the calculation of the heat flux in the electrolyte and cannot be neglected. To our knowledge, this is the first validated model of a SOFC based on non-equilibrium thermodynamics and this study can be extended to analyze SOFCs with other solid oxide electrolytes, with perovskites electrolytes or even other electrochemical systems like solid oxide electrolysis cells (SOECs).

Radiation and Energetic Analysis of Nanofluid Based Volumetric Absorbers for Concentrated Solar Power.

Recently, several publications gave attention to nanofluid based solar absorber systems in which the solar radiation energy is directly absorbed in the volume of the fluid. This idea could provide advantages over conventionally used surface absorbers regarding the optical and thermal efficiency. For the evaluation of this concept, a numerical approach is introduced and validated in this contribution. The results show that the optical efficiency of a volumetric absorber strongly depends on the scattering behavior of the nanofluid and can reach competitive values only if the particle size distribution is narrow and small. If this is achieved, the surface temperature and therefore the heat loss can be lowered significantly. Furthermore, the surface absorber requires very high Reynolds numbers to transfer the absorbed energy into the working fluid and avoid overheating of the absorber tube. This demand of pumping power can be reduced significantly using the concept of volumetric absorption.

Pressure derivatives in the classical molecular-dynamics ensemble.

The calculation of thermodynamic state variables, particularly derivatives of the pressure with respect to density and temperature, in conventional molecular-dynamics simulations is considered in the frame of the comprehensive treatment of the molecular-dynamics ensemble by Lustig [J. Chem. Phys. 100, 3048 (1994)]. This paper improves the work of Lustig in two aspects. In the first place, a general expression for the basic phase-space functions in the molecular-dynamics ensemble is derived, which takes into account that a mechanical quantity G is, in addition to the number of particles, the volume, the energy, and the total momentum of the system, a constant of motion. G is related to the initial position of the center of mass of the system. Secondly, the correct general expression for volume derivatives of the potential energy is derived. This latter result solves a problem reported by Lustig [J. Chem. Phys. 109, 8816 (1998)] and Meier [Computer Simulation and Interpretation of the Transport Coefficients of the Lennard-Jones Model Fluid (Shaker, Aachen, 2002)] and enables the correct calculation of the isentropic and isothermal compressibilities, the speed of sound, and, in principle, all higher pressure derivatives. The derived equations are verified by calculations of several state variables and pressure derivatives up to second order by molecular-dynamics simulations with 256 particles at two state points of the Lennard-Jones fluid in the gas and liquid regions. It is also found that it is impossible for systems of this size to calculate third- and higher-order pressure derivatives due to the limited accuracy of the algorithm employed to integrate the equations of motion.

Transport coefficients of the Lennard-Jones model fluid. III. Bulk viscosity.

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This third of a series of four papers presents the results for the bulk viscosity. With comprehensive simulation data at over 350 state points, the temperature and density dependences of the bulk viscosity are characterized in this work over a wide range of fluid states. The bulk viscosity exhibits a large critical enhancement similar to that known for the thermal conductivity, but it extends much farther into the supercritical region and can be observed even at 4.5 times the critical temperature. An investigation of the pressure-fluctuation autocorrelation functions shows that the enhancement is caused by extremely slowly decaying pressure fluctuations.

Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion.

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This second of a series of four papers presents the results for the self-diffusion coefficient, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. The uncertainty of the self-diffusion data is estimated to be 1% in the gas region and 0.5% at high-density liquid states. With the very accurate data, even fine details in the shape of the self-diffusion isotherms are resolved, and the previously little-investigated behavior of the self-diffusion coefficient at low-density gaseous states is analyzed in detail. Finally, aspects of the mass transport mechanisms on the molecular scale are explored by an analysis of the velocity autocorrelation functions.

Transport coefficients of the Lennard-Jones model fluid. I. Viscosity.

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This first of a series of four papers presents the results for the viscosity, and discusses and interprets the behavior of this transport coefficient in the fluid region of the phase diagram. Moreover, the kinetic-kinetic, kinetic-potential, and potential-potential viscosity contributions are resolved over the whole range of fluid states, and their characteristic dependence on temperature and density is described. Finally, an additional analysis of the shear-stress correlation functions reveals aspects of the momentum-transport mechanisms on the molecular scale.