A numerical study on the heat and mass transfer characteristics of metal-supported solid oxide fuel cells

The heat and mass transfer characteristics of solid oxide fuel cells (SOFCs) need to be considered when designing SOFCs because they heavily influence the performance and durability of the cells. The physical property models, the governing equations (mass, momentum, energy and species balance equations) and the electrochemical reaction models were calculated simultaneously in a 3-dimensional SOFC simulation. The current density-voltage (I-V) curves measured experimentally from a single SOFC were compared with the simulation data for code validation purposes. The error between the experimental data and the numerical results was less than 5% at operating temperatures from 700 °C to 850 °C. The current density and the mass transfer rate of an anode-supported SOFC were compared with those of a metal-supported SOFC. The metal-supported SOFC had a 17% lower average current density than the anode-supported SOFC because of the bonding layer, but it showed better thermal stability than the anode-supported SOFC because of its more uniform current density distribution. The current density, temperature and pressure drop of the metal-supported SOFC were investigated for several channel designs. A high current density was observed near the hydrogen inlet and at the intersection of the hydrogen and air channels. However, there was a low current density under the rib and at the cell edge because of an insufficient reactant diffusion flux. When the proper channel design was applied to the metal-supported SOFC, the average current density was increased by 45%.     

固体氧化物燃料电池三维模拟与性能分析

建立了平板式阳极支撑固体氧化物燃料电池的三维数学模型,通过耦合电化学动力学和流体动力学模拟了电池的传热传质等传输现象。采用有限容积法计算了质量、动量、组分与能量守恒方程。研究给出了同向流与反向流情况下电流度密度、电压与功率密度分布。结果显示在同向流情况下,电池的最大功率密度较大,温度分布较均匀合理。进一步研究表明多孔电极结构参数（孔隙率、曲折因子与孔径尺寸）对电池性能有十分重要的影响。比较计算的极化性能与文献的实验数据,结果表明两者吻合的较好。     

Sensitivity analysis for solid oxide fuel cells using a three-dimensional numerical model

A three-dimensional numerical solver is developed to model complex transport processes inside all components of a solid oxide fuel cell (SOFC). An initial assessment of the accuracy of the model is made by comparing a numerically generated polarization curve with experimental results. Sensitivity derivatives of objective functions representing the cell voltage and the concentration polarization are obtained with respect to the material properties of the anode and the cathode using discrete adjoint method. Implementation of the discrete adjoint method is validated by comparing sensitivity derivatives obtained using the adjoint technique with results obtained using direct-differentiation and finite-difference methods.     

A direct-flame solid oxide fuel cell (DFFC) operated on methane,propane, and butane

This paper presents an experimental study of a direct-flame type solid oxide fuel cell (DFFC). The operation principle of this system is based on the combination of a combustion flame with a solid oxide fuel cell (SOFC) in a simple, no-chamber setup. The flame front serves as fuel reformer located a few millimeters from the anode surface while at the same time providing the heat required for SOFC operation. Experiments were performed using 13-mm-diameter planar SOFCs with Ni-based anode, samaria-doped ceria electrolyte and cobaltite cathode. At the anode, a 45-mm-diameter flat-flame burner provided radially homogeneous methane/air, propane/air, and butane/air rich premixed flames. The cell performance reaches power densities of up to 120 mW cm⁻², varying systematically with flame conditions. It shows a strong dependence on cell temperature. From thermodynamic calculations, both H₂ and CO were identified as species that are available as fuel for the SOFC. The results demonstrate the potential of this system for fuel-flexible power generation using a simple setup.     

Critical issues in heat transfer for fuel cell systems

The current state of the art in fuel cell system development will be reviewed with an emphasis of the critical issues on heat transfer.

The heat transfer issues for both PEM based systems and SOFC based fuel cell systems will be addressed.

For systems that are based on hydrocarbon fuels a reforming step is needed and critical heat transfer issues are also present in this fuel processing part of the system where the primary feedstock is converted to reformate. Also, in both the PEM and SOFC fuel cell itself, heat transfer is a critical issue. It will be shown what are the implications of the fuel cell heat transfer to the total system architecture for the various fuel cell applications (stationary power, transport).

The heat transfer issues in fuel cell system development will be clarified with several examples.     

Metal-supported solid oxide fuel cells operated in direct-flame configuration

Metal-supported solid oxide fuel cells (MS-SOFC) with infiltrated catalysts on both anode and cathode side are operated in direct-flame configuration, with a propane flame impinging on the anode. Placing thermal insulation on the cathode dramatically increases cell temperature and performance. The optimum burner-to-cell gap height is a strong function of flame conditions. Cell performance at the optimum gap is determined within the region of stable non-coking conditions, with equivalence ratio from 1 to 1.9 and flow velocity from 100 to 300 cm s^?1. In this region, performance is most strongly correlated to flow velocity and open circuit voltage. The highest peak power density achieved is 633 mW cm^?2 at 833 °C, for equivalence ratio of 1.8 and flow velocity of 300 cm s^?1. The cell starts to produce power within 10 s of being placed in the flame, and displays stable performance over 10 extremely rapid thermal cycles. The cell provides stable performance for >20 h of semi-continuous operation.     

平板式阳极支撑固体氧化物燃料电池传质传热仿真研究

利用流体力学计算软件F luen t建立平板式阳极支撑固体氧化物燃料电池(SOFC)的三维数学模型。在阳极与阴极多孔电极中使用尘气模型模拟气体质量传输并采用B rinkm an-Forschhe im er-D acy模型来模拟多孔电极中黏性与惯性效应对气体流动的影响。研究给出了燃料气与空气在同向流与反向流情况下组分浓度、电压与温度分布。结果显示在同向流情况下,电池的最大功率密度较大与温度分布较均匀合理。研究给出了多孔电极结构参数(孔隙率、曲折因子与孔径尺寸)对电池性能的影响。结果表明比较计算的极化性能与文献的实验数据两者较好的吻合。     

Mathematical modeling of ammonia-fed solid oxide fuel cells with different electrolytes

An electrochemical model was developed to study the ammonia (NH₃)-fed solid oxide fuel cells with proton-conducting electrolyte (SOFC-H) and oxygen ion-conducting electrolyte (SOFC-O). Different from previous thermodynamic analysis, the present study reveals that the actual performance of the NH₃-fed SOFC-H is considerably lower than the SOFC-O, mainly due to higher ohmic overpotential of the SOFC-H electrolyte. More analyses have been performed to study the separate overpotentials of the NH₃-fed SOFC-H and SOFC-O. Compared with the NH₃-fed SOFC-H, the SOFC-O has higher anode concentration overpotential and lower cathode concentration overpotential. The effects of temperature and electrode porosity on concentration overpotentials have also been studied in order to identify possible methods for improvement of SOFC performance. This study reveals that the use of different electrolytes not only causes different ion conduction characteristics at the electrolyte, but also significantly influences the concentration overpotentials at the electrodes. The model developed in this article can be extended to 2D and 3D models for further design optimization.     

A two-dimensional fin efficiency analysis of combined heat and mass transfer in elliptic fins

This paper presents a two-dimensional analysis for the efficiency of an elliptic fin under the dry, partially wet and fully wet conditions of a range of value for axis ratios, Biot numbers, and air humidifies. It is shown that the fin efficiencies increase as the axis ratio Ar is increased. For a given axis ratio Ar, the fin efficiency decreases as the fin height l∗ or Biot number is increased. The conventional 1-D sector method overestimates the fin efficiency resulting in increasing error as the axis ratio Ar is increased. In addition, using experimentally determined heat transfer coefficients, it is found that both the fully dry and wet elliptic fin efficiencies are up to 4-8% greater than the corresponding circular fin efficiencies having the same perimeter.     

Micro-scale modelling of solid oxide fuel cells with micro-structurally graded electrodes

A mathematical model was developed for modelling the performance of solid oxide fuel cell (SOFC) with functionally graded electrodes at the micro-scale level. The model considered all forms of overpotentials and was able to capture the coupled electrochemical reactions and mass transfer involved in the SOFC operation. The model was validated by comparing the simulation results with experimental data from the literature. Additional modelling analyses were conducted to gain better understanding of the SOFC working mechanisms at the micro-scale level and to quantify the performance of micro-structurally graded SOFC. It was found that micro-structural grading could significantly enhance the gas transport but had negligible effects on the ohmic and activation overpotentials, especially for thick electrodes. However, for thin electrodes with large particles, too much grading should be avoided as the increased activation overpotentials may result in higher overall overpotentials at a medium or low current density. Among all the cases tested in the present study, the micro-structurally graded SOFC showed significantly higher power density than conventional SOFC of uniform porosity and particle size. The difference between micro-structurally graded SOFC and conventional SOFC is more pronounced for smaller electrode–electrolyte (EE) interfacial particles. Particle size grading is generally more effective than porosity grading and it can increase the maximum power density by one-fold in comparison with conventional SOFC. The present study reveals the working mechanisms of SOFC at the micro-scale level and demonstrates the promise of the use of micro-structural grading to enhance the SOFC performance.     

Optimization of heat transfer device and analysis of heat & mass transfer on the finned multi-tubular metal hydride tank

Based on the previous studies on heat and mass transfer characteristics of hydride tank, whether the reaction heat of hydride bed can be removed quickly is a determinant factor of the reaction rate. As the core part of reaction system, the heat transfer optimization in the tank can significantly enhance the reaction rate. In this paper, the optimization of heat transfer fins for a finned multi-tubular metal hydride tank is presented, and the heat transfer equations of tank with various configuration fins (radius, thickness and number) are derived. By analyzing the effects of fin configurations on the heat transfer device, we found that the thermal resistance of reaction system reduces with the increase of the fin radius, thickness and number. In order to study transient reaction process inside the hydride tank with various configuration and operation conditions, a 3-D mathematical model is developed and validated based on the experimental data from literature. Through simulation and optimization on hydride tank with different configurations, we got that the fin number has the most significant positive effect on the absorption reaction process. The numerical simulation results show that the hydrogen absorption rate is proportional to hydrogen pressure, heat transfer coefficient and fluid flow velocity, and the hydrogen pressure has the most remarkable impact among these factors. The H₂ absorption is accomplished in 1720 s at 1 MPa, and the absorption reaction is completed within 2000 s at the H₂ pressure of 0.8 MPa. Moreover, the maximum difference in absorption completion time is only 190 s under different heat transfer coefficients and fluid flow velocities.     

A direct flame solid oxide fuel cell for potential combined heat and power generation

A sealant-free solid oxide fuel cell (SOFC) micro-stack was successfully operated inside a liquefied petroleum gas (LPG) flame during cooking. This micro-stack consisted of 4 single cells with infiltrated La_0.75Sr_0.25Cr_0.5Mn_0.5O_3-δ (LSCM) based composite anodes, achieving an open circuit voltage of 0.92 V and a peak power density of 348 mW cm⁻². This performance is significantly better than that of stack with its cathode operation outside flame. The results confirmed that the perovskite oxide anode showed good properties of carbon-free, redox-stability, quick-start (less than 1 min) and successful operation under a wide range of oxygen partial pressure. For comparison, the conventional Ni/yttria-stabilized zirconia (Ni/YSZ) anode was prepared and tested under the same conditions, showing an open circuit voltage of 0.915 V and a peak power density of 366 mW cm⁻², but obvious carbon deposition, poor stability and slow/difficult-start. The direct flame SOFC (DFFC) with a new configuration and design has a potential for combined heat and power generation for many applications.     

Transient two-dimensional model of heat and mass transfer in a PEM fuel cell membrane

In the present work, a numerical study of heat and mass transfer within the membrane of a proton exchange membrane fuel cell is presented. The electrolyte membrane is considered an isotropic porous medium and ideal insulator for electrons and reactants. The adopted model in this study is based on the assumption of single-phase and multi-spices flow, supposed two-dimensional and unsteady. For the water transport, the major considered forces are; the convective force, resulting from the pressure gradient, the osmotic force, due to the concentration gradient and the electric force caused by the proton migration from the anode to the cathode. Based on a one-dimensional model, found in the literature, a transient two-dimensional one was proposed. The set of governing equations, written in velocity–pressure formulation, is solved by the implicit finite difference method. An alternating Direct Implicit scheme was used for the calculation. The numerical resolution gives the time- and space-dependent temperature and water concentration. The main focus lies on the influence of different cases of boundary conditions on water concentration and heat transfer variation with the intention of testing the reliability of the proposed computational fluid dynamic (CFD) code.     

Diagnosis methodology and technique for solid oxide fuel cells: A review

The present study aims to identify and recollect the articles existing in literature that deal malfunction or failure causes of SOFC cells and relative diagnostic systems. This work is motivated by the increasing demand for diagnostic techniques aimed at both increasing durability and fully exploiting SOFC benefits throughout system lifetime. This paper reviews SOFC cells degradation phenomena and relevant fault detection methodologies already available, having found a gap in literature, above all relative to SOFC electrode microstructural degradation related, specifically, to sintering of the electrode microstructure, poisoning of the cathode microstructure with chromium products outgassed from the interconnect plates, carbon deposition in the anode, anode sulfur poisoning and boron SOFC cathodes' poisoning. It is therefore encouraged a future effort of the research activity in this specific sector.     

A dimensionless analysis of heat and mass transport in an adsorber with thin fins; uniform pressure approach

A numerical study on heat and mass transfer in an annular adsorbent bed assisted with radial fins for an isobaric adsorption process is performed. A uniform pressure approach is employed to determine the changes of temperature and adsorbate concentration profiles in the adsorbent bed. The governing equations which are heat transfer equation for the adsorbent bed, mass balance equation for the adsorbent particle, and conduction heat transfer equation for the thin fin are non-dimensionalized in order to reduce number of governing parameters. The number of governing parameters is reduced to four as Kutateladze number, thermal diffusivity ratio, dimensionless fin coefficient and dimensionless parameter of Γ which compares mass diffusion in the adsorbent particle to heat transfer through the adsorbent bed. Temperature and adsorbate concentration contours are plotted for different values of defined dimensionless parameters to discuss heat and mass transfer rate in the bed. The average dimensionless temperature and average adsorbate concentration throughout the adsorption process are also presented to compare heat and mass transfer rate of different cases. The values of dimensionless fin coefficient, Γ number and thermal diffusivity ratio are changed from 0.01 to 100, 1 to 10^− 5 and 0.01 to 100, respectively; while the values of Kutateladze number are 1 and 100. The obtained results revealed that heat transfer rate in an adsorbent bed can be enhanced by the fin when the values of thermal diffusivity ratio and fin coefficient are low (i.e., α^? = 0.01, Λ = 0.01). Furthermore, the use of fin in an adsorbent bed with low values of Γ number (i.e. Γ = 10^− 5) does not increase heat transfer rate, significantly.     

A group of improved heat and mass transfer correlations in solar stills

Based on the analogy of heat and mass transfer and an empirical correlation, a group of improved heat and mass transfer correlations in basin type solar stills is established. In order to validate the correlation group, a multi-stage stacked tray solar still with basin area of 0.665×0.650 m² is constructed of aluminum sheets. By comparison of the calculated results with the measurement results, which were obtained from our steady state simulated experiments and reported in previous literature, it is found that the correlation group developed in this work can provide better predictions for the evaporation rate of basin type solar stills at the wide range of Rayleigh number (3.5×10³<Ra<2.26×10⁷) and temperature (35<T_w<86 °C).     

Recent developments of heat and mass transfer in hydromagnetic flows

This review article presents an account of several investigations of heat and mass transfer in the field of magnetohydrodynamics which have been carried out during the last few years by several authors. If an article has been omitted, it is entirely by oversight and not by intention.     

A transient analysis of three-dimensional heat and mass transfer in a molten carbonate fuel cell at start-up

In this paper, we investigate the time-dependent heat and mass transfer in a molten carbonate fuel cell at start-up. Thus, a three-dimensional, transient mathematical model is presented through a comprehensive inclusion of various physical, chemical and electrochemical processes that occur within the different components of molten carbonate fuel cells. The model is proposed as a predictive tool to provide a three-dimensional demonstration of variable variations at system start-up. The local distribution of field variables and quantities are showcased. It reveals that the electrochemical reaction rate is dominated by the over-potential, not by the reactants' molar fraction. Reversible heat generation and consumption mechanisms of the cathode and anode are dominant in the first 10 s while the heat conduction from the solid materials to the gas phase is negligible. Meanwhile, activation and ohmic heating have nearly the same impact within the anode and cathode. Based on these findings, the importance of heat conduction and its main features are finally assessed.     

A mathematical model of a tubular solid oxide fuel cell with specified combustion zone

A numerical model has been developed to simulate the effect of combustion zone geometry on the steady state and transient performance of a tubular solid oxide fuel cell (SOFC). The model consists of an electrochemical submodel and a thermal submodel. In the electrochemical model, a network circuit of a tubular SOFC was adopted to model the dynamics of Nernst potential, ohmic polarization, activation polarization, and concentration polarization. The thermal submodel simulated heat transfers by conduction, convention, and radiation between the cell and the air feed tube. The developed model was applied to simulate the performance of a tubular solid oxide fuel cell at various operating parameters, including distributions of circuits, temperature, and gas concentrations inside the fuel cell. The simulations predicted that increasing the length of the combustion zone would lead to an increase of the overall cell tube temperature and a shorter response time for transient performance. Enlarging the combustion zone, however, makes only a negligible contribution to electricity output properties, such as output voltage and power. These numerical results show that the developed model can reasonably simulate the performance properties of a tubular SOFC and is applicable to cell stack design.