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The aim of this paper is to find the electrical representation of a solid oxide fuel cell (SOFC) that enables the application of typical exploitation characteristics of fuel cells for estimation of fuel cell parameters (for example, exchange current) and easy analysis of phenomena occurred during the fuel cell operation.

Three-layer structure of an SOFC, where a thin semi-conducting layer of electrolyte separates the anode from the cathode, shows a strong similarity to typical semiconductor devices built on the basis of P-N junctions, like diodes or transistors. Current–voltage (I-V) characteristics of a fuel cell can be described by the same mathematical functions as I-V plots of semiconductor devices. On the basis of this similarity and analysis of impedance spectra of a real fuel cell, two electrical representations of the SOFC have been created.

The simplified electrical representation of SOFC consists of a voltage source connected in series with a diode, which symbolizes a voltage drop on a cell cathode, and two resistors. This model is based on the similarity of Butler-Volmer to Shockley equation. The advanced representation comprises a voltage source connected in series with a bipolar transistor in close to saturation mode and two resistors. The base-emitter junction of the transistor represents voltage drop on the cell cathode, and the base-collector junction represents voltage drop on the cell anode. This model is based on the similarity of Butler-Volmer equation to Ebers-Moll equation.

The proposed approach based on the Shockley and Ebers-Moll formulas enables the more accurate estimation of the ion exchange current and other fuel cell parameters than the approach based on the Butler-Volmer and Tafel formulas. The usability of semiconductor models for analysis of SOFC operation was proved. The models were successively applied in a new design of a planar ceramic fuel cell, which features by reduced thermal capacity, short start-up time and limited number of metal components and which has become the basis for the SOFC stack design.

The purpose of this paper is to develop a new two-dimensional differential concentration corrosion mathematical model based on the knowledge that oxygen distribution on the surface of the seawater pipe is two-dimensional.

The ionic conductive layer element near the pipeline wall is regarded as the research object, and the finite element method is adopted to obtain the oxygen distribution in the layers and the natural corrosion potential and natural corrosion current of each element. Then, these element sets are regarded as a whole circuit and each element as a node on the circuit; the equation is satisfied by the corrosion potential after polarization is derived for each element according to Kirchhoff’s second law.

Matlab is used to solve the equation sets, and the overall corrosion current is calculated. The results are quite different from those considered without the differential concentration corrosion. If the differential concentration corrosion is not considered, the location with high oxygen concentration on the pipeline wall has a large corrosion potential and current. If corrosion is considered, the potential will cause polarization and the positions with original higher corrosion potential will produce anodic polarization. Meanwhile, the speed of corrosion also decreases. At the same time, the position with original lower corrosion potential will produce cathodic polarization, and the corrosion current is also increased, namely, the corrosion current and the potential will be homogenized.

A two-dimensional model for the study of concentration corrosion is proposed creatively. Based on the knowledge of electricity, a discrete equation of corrosion potential after polarization is derived. The distribution of corrosion potential and corrosion current is obtained by solving the equation, and the mechanism of concentration corrosion is analyzed. The law of concentration polarization corrosion is also obtained.

The purpose of this paper is to introduce a robust mathematical model and finite element‐based numerical approach to solve solid oxide fuel cell (SOFC) problems.

A robust mathematical model is constructed by studying pros and cons of different SOFC and other fuel cell models. The finite element‐based numerical approach presented is a unified approach to solve multi‐disciplinary aspects arising from SOFC problems. The characteristic‐based split approach employed here is an efficient way of solving various flow, heat and mass transfer regimes in SOFCs.

The results presented show that both the model and numerical algorithm proposed are robust. Furthermore, the approaches proposed are general and can be easily extended to other similar problems of practical interest.

The model proposed is the first of this kind and the unified approach for solving flow, heat and mass transfer within a fuel cell is also novel.

The purpose of this paper is to describe two‐ and three‐dimensional numerical modelling of solid oxide fuel cells (SOFCs) by employing an accurate and stable fully matrix inversion free finite element algorithm.

A general and detailed mathematical model has been developed for the description of the coupled complex phenomena occurring in fuel cells. A fully matrix inversion free algorithm, based on the artificial compressibility (AC) version of the characteristic‐based split (CBS) scheme and single domain approach have been successfully employed for the accurate and efficient simulation of high temperature SOFCs.

For the first time, a stable fully explicit algorithm has been applied to detailed multi‐dimensional simulation transport phenomena, coupled to chemical and electrochemical reactions, in fluid, porous and solid parts of a SOFC. The accuracy of the present results has been verified via comparison with experimental and numerical data available in the literature.

For the first time, thanks to a stabilization analysis conducted, the AC‐CBS algorithm has been successfully used to numerically solve the generalized model, applied in this paper to describe transport phenomena through free fluid channels and porous electrodes of SOFCs, without the need of further conditions at the fluid‐electrode interface.

Distribution of the electric potential and current density in the electrode of the proton exchange membrane fuel cell.

Multicomponent model based on Maxwell‐Stefan equations is used to formulate generalized Fick's law. Next, mass conservation laws for gas components and equation of continuity for current density vector are formulated.

The problem is expressed by three non‐linear partial differential equations in total molar contraction of the gas mixture, oxygen and water vapor concentration describing multicomponent Maxwell‐Stefan mass transport and fourth equation for electric potential distribution. The final system of partial differential equations describing the problem is highly non‐linear and mutually coupled not only directly but also through the non‐linear boundary condition and is solved by finite element method.

There are some convergence problems for some sets of the material parameters. Only one part of the fuel cell was modeled.

This approach allows one to calculate all important parameters required to develop and design the practical systems as well to optimize the performance from the geometrical and material parameters point of view.

The presented approach combines distribution of mass transport using Maxwell‐Stefan model and electric potential described by Laplace equation.

The purpose of this paper is to optimize experimental parameters and gain further insights into the plating process in the fabrication of high-density interconnections of printed circuit boards (PCBs) by the rotating disc electrode (RDE) model. Via metallization by copper electrodeposition for interconnection of PCBs has become increasingly important. In this metallization technique, copper is directly filled into the vias using special additives. To investigate electrochemical reaction mechanisms of electrodeposition in aqueous solutions, using experiments on an RDE is common practice.

An electrochemical model is presented to describe the kinetics of copper electrodeposition on an RDE, which builds a bridge between the theoretical and experimental study for non-uniform copper electrodeposition in PCB manufacturing. Comsol Multiphysics, a multiphysics simulation platform, is invited to modeling flow field and potential distribution based on a two-dimensional (2D) axisymmetric physical modeling. The flow pattern in the electrolyte is determined by the 2D Navier–Stokes equations. Primary, secondary and tertiary current distributions are performed by the finite element method of multiphysics coupling.

The ion concentration gradient near the cathode and the thickness of the diffusion layer under different rotating velocities are achieved by the finite element method of multiphysics coupling. The calculated concentration and boundary layer thicknesses agree well with those from the theoretical Levich equation. The effect of fluid flow on the current distribution over the electrode surface is also investigated in this model. The results reveal the impact of flow parameters on the current density distribution and thickness of plating layer, which are most concerned in the production of PCBs.

By RDE electrochemical model, we build a bridge between the theoretical and experimental study for control of uniformity of plating layer by concentration boundary layer in PCB manufacturing. By means of a multiphysics coupling platform, we can accurately analyze and forecast the characteristic of the entire electrochemical system. These results reveal theoretical connections of current density distribution and plating thickness, with controlled parameters in the plating process to further help us comprehensively understand the mechanism of copper electrodeposition.

The restoration and strengthening of QT600 is an industry bottleneck challenge. The Co-12 cladding layer has great wear and corrosion resistance. The purpose of this paper is to quantitatively reveal the transient evolution law of the corrosion process of Co-12 cladding layer on QT600 surface.

In this paper, a three-dimensional numerical model of the corrosion process of Co-12 cladding layer by QT600 laser cladding is established. The interaction between pitting pits and corrosion medium is considered to reveal the transient evolution of ion concentration, electrode potential, pH and corrosion rate at different locations.

The calculation shows that the ion concentration in pitting pit changes Cl⁻>Co²⁺>Na⁺, pH value decreases from top to bottom and corrosion rate at bottom is greater than that at top. The electrochemical corrosion test of Co-12 cladding layer was carried out. It is shown that the current density of QT600 increases by an order of magnitude compared to the Co-12 cladding layer, and the corrosion rate is 4.862 times higher than that of the cladding layer.

The results show that Co-12 cladding layer has great corrosion resistance, which provides an effective way for QT600 protection.

The simulation of lithium-ion batteries is a challenging research topic. Since there are many electrochemical processes involved in charging and discharging, models which aim to include these processes are in general complex and therefore slow. This paper seeks to address these issues.

For many tasks, e.g. in optimization, a repeated solution of a model is necessary.

In this paper, a speed up in simulations, with acceptable error in results, is obtained by combining proper orthogonal decomposition with empirical interpolation method.

The authors report a speed up factor between 10 and 15.

This paper aims to study the effect of temperature on the process and kinetic parameters of the hydrogen evolution reaction of X80 under cathodic protection (CP) in 3.5% NaCl solution.

Potentiodynamic polarization combined with the hydrogen permeation test is used to analyze the hydrogen evolution reaction (HER) process and the rate-determining step for which is diagnosed through the electrochemical impedance spectrum method. Then, the influence of temperature on kinetic parameters of HER can be known from the results obtained by using the Iver-Pickering-Zamenzadeh model for data analysis.

The results show that the HER proceeds through Volmer–Tafel route with the Volmer reaction acting as the rate-controlling step; Increasing temperature gives a higher activity of the HER on X80, it also accelerates the hydrogen desorption and diffusion of hydrogen into the metal.

There exist few studies on the topic of how temperature affects the HER process. It is imperative to conduct a relevant study to give some instruction in cathodic protection system design and this paper fulfills this need.