Thermal stress analysis of a planar SOFC stack

The aim of this study is, by using finite element analysis (FEA), to characterize the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack during various stages. The temperature profiles generated by an integrated thermo-electrochemical model were applied to calculate the thermal stress distributions in a multiple-cell SOFC stack by using a three-dimensional (3D) FEA model. The constructed 3D FEA model consists of the complete components used in a practical SOFC stack, including positive electrode–electrolyte–negative electrode (PEN) assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seals. Incorporation of the glass-ceramic sealant, which was never considered in previous studies, into the 3D FEA model would produce more realistic results in thermal stress analysis and enhance the reliability of predicting potential failure locations in an SOFC stack. The effects of stack support condition, viscous behavior of the glass-ceramic sealant, temperature gradient, and thermal expansion mismatch between components were characterized. Modeling results indicated that a change in the support condition at the bottom frame of the SOFC stack would not cause significant changes in thermal stress distribution. Thermal stress distribution did not differ significantly in each unit cell of the multiple-cell stack due to a comparable in-plane temperature profile. By considering the viscous characteristics of the glass-ceramic sealant at temperatures above the glass-transition temperature, relaxation of thermal stresses in the PEN was predicted. The thermal expansion behavior of the metallic interconnect/frame had a greater influence on the thermal stress distribution in the PEN than did that of the glass-ceramic sealant due to the domination of interconnect/frame in the volume of a planar SOFC assembly.     

Thermal stress analysis of planar solid oxide fuel cell stacks: Effects of sealing design

A three-dimensional multi-cell model based on a prototypical, planar solid oxide fuel cell (pSOFC) stack design using compliant mica-based seal gaskets was constructed in this study to perform comprehensive thermal stress analyses by using a commercial finite element analysis (FEA) code. Effects of the applied assembly load on the thermal stress distribution in the given integrated pSOFC stack with such a compressive sealing design were characterized. A comparison was made with a previous study for a similar comprehensive multi-cell pSOFC stack model but using only a rigid type of glass-ceramic sealant instead. Simulation results indicate that stress distributions in the components such as positive electrode-electrolyte-negative electrode (PEN) plate, PEN-supporting window frame, nickel mesh, and interconnect were mainly governed by the thermal expansion mismatch rather than by the applied compressive load. An applied compressive load of 0.6 MPa could eliminate the bending deformation in the PEN-frame assembly plate leading to a well joined structure. For a greater applied load, the critical stresses in the glass-ceramic and mica sealants were increased to a potential failure level. In this regard, a 0.6 MPa compressive load was considered an optimal assembly load. Changing the seal between the connecting metallic PEN-supporting frame and interconnect from a rigid type of glass-ceramic sealant to a compressive type of mica gasket would significantly influence the thermal stress distribution in the PEN plate. The critical stress in the PEN was favorably decreased at room temperature but considerably increased at operating temperature due to such a change in sealing design. Such differences in the stress distribution could be ascribed to the differences in the constrained conditions at the interfaces of adjacent components under various sealing designs.     

Modeling of cooperative defect transport and thermal mismatch in a planar solid oxide fuel cell

Mixed ionic-electronic conducting (MIEC) membranes are widely applied as cathode material in solid oxide fuel cells (SOFCs). Nonetheless, the chemical expansion of an MIEC membrane caused by point defects (oxygen vacancies and small polarons) during oxygen transport induces cell failure. In this study, a multilayer thermo-chemical-mechanical model was proposed to consider defect diffusion under sudden changes in the cathode atmosphere, thermal expansion mismatch, and mechanical bending deformation. Under the set boundary conditions, the overall structural curvature of the multilayer system was relieved when the cathode was subjected to a high tensile stress. The influences of relevant parameters on the transient stress field were also investigated, and the overall stress of the multilayer structure decreased significantly when the oxygen partial pressure in the inlet channel was constrained. Reducing the sintering temperature and chemical expansion coefficient could improve the reliability of the planar SOFC. In addition, the effect of constraints in different directions on the multilayer system stresses is also investigated. This study provides theoretical support for use in designing the stabilities and gas supply strategies of planar solid fuel cells.     

Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part I: Probability of failure of the cells

Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation.The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process-modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit.The different layers of the cell, i.e. anode, electrolyte, cathode and compensating layer were considered in the analysis by using the sub-modelling capabilities of the finite-element tool. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cells, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets.The results generated by the models are presented in two papers: Part I, focuses on the assessment of the risks of failure of the cell, which was performed by Weibull analysis, while the issues related to the other components are discussed in Part II.Only the anode support contributed to the probability of failure, since the other layers underwent compressive stresses independently of the operating conditions. The cell at room temperature after the reduction procedure was revealed as a critical case. Thermal gradients and the shape of the temperature profile generated during transient operation induced high probabilities of failure. The computed reliability is incompatible with commercialisation, but the scatter induced by the experimental data covers several orders of magnitude. Alternatively, the computed required strength of the anode material to fulfil a probability of failure of 10⁻² in a 50-cells stack during steady-state operation appears achievable. Finally, extreme care is required when using the maximum thermal gradient or temperature difference over the SRU as an indicator for cell cracking.     

Modeling of thermal stresses and lifetime prediction of planar solid oxide fuel cell under thermal cycling conditions

A typical operating temperature of a solid oxide fuel cell (SOFC) is above 600 °C, which leads to severe thermal stresses caused by the difference in material mechanical properties during thermal cycling. Interfacial shear stress and peeling stress are the two types of thermal stresses that can cause the mechanical failure of the SOFC. Two commonly used SOFC configurations (electrolyte-supported and anode-supported) were considered for this study. The paper developed a mathematical model to estimate the thermal stresses and to predict the lifetime of the cell (Ni/8YSZ-YSZ-LSM). Due to the mismatch of the material mechanical properties of the cell layers, a crack nucleation induced by thermal stresses can be predicted by the crack damage growth rate and the initial damage distribution in the interfacial layer for each thermal cycle. It was found that the interfacial shear stress and peeling stress were more concentrated near the electrode free edge areas. The number of cycles needed for failure decreased with the increase in the porosity of electrode. The number of cycle for failure decreased with increase in electrolyte thickness for both anode- and electrolyte-supported SOFC. The model provides insight into the distribution of interfacial shear stress and peeling stress and can also predict damage evolution in a localized damage area in different SOFC configurations.     

Computational model to predict thermal dynamics of planar solid oxide fuel cell stack during start-up process

Solid oxide fuel cell (SOFC) systems have been recognized as the most advanced power generation system with the highest thermal efficiency with a compatibility with wide variety of hydrocarbon fuels, synthetic gas from coal, hydrogen, etc. However, SOFC requires high temperature operation to achieve high ion conductivity of ceramic electrolyte, and thus SOFC should be heated up first before fuel is supplied into the stack. This paper presents computational model for thermal dynamics of planar SOFC stack during start-up process. SOFC stack should be heated up as quickly as possible from ambient temperature to above 700 °C, while minimizing net energy consumption and thermal gradient during the heat up process. Both cathode and anode channels divided by current-collecting ribs were modeled as one-dimensional flow channels with multiple control volumes and all the solid structures were discretized into finite volumes. Two methods for stack-heating were investigated; one is with hot air through cathode channels and the other with electric heating inside a furnace. For the simulation of stack-heating with hot air, transient continuity, flow momentum, and energy equation were applied for discretized control volumes along the flow channels, and energy equations were applied to all the solid structures with appropriate heat transfer model with surrounding solid structures and/or gas channels. All transient governing equations were solved using a time-marching technique to simulate temporal evolution of temperatures of membrane-electrode-assembly (MEA), ribs, interconnects, flow channels, and solid housing structure located inside the insulating chamber. For electrical heating, uniform heat flux was applied to the stack surface with appropriate numerical control algorithm to maintain the surface temperature to certain prescribed value. The developed computational model provides very effective simulation tool to optimize stack-heating process minimizing net heating energy and thermal gradient within the stack.     

Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part II: Loss of gas-tightness, electrical contact and thermal buckling

Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation.The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit.The different layers of the cell in exception of the cathode, i.e. anode, electrolyte and compensating layer were considered in the analysis to account for the cell curvature. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cell, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets.The results generated by the models are presented in two papers: Part I focuses on cell cracking. In the present paper, Part II, the occurrences of loss of gas-tightness in the compressive gaskets and/or electrical contact in the gas diffusion layer were identified. In addition, the dependence on temperature of both coefficients of thermal expansion and Young's modulus of the metallic interconnect (MIC) were implemented in the finite-element model to compute the plastic deformation, while the possibilities of thermal buckling were analysed in a dedicated and separate model.The value of the minimum stable thickness of the MIC is large, even though significantly affected by the operating conditions. This phenomenon prevents any unconsidered decrease of the thickness to reduce the thermal inertia of the stack. Thermal gradients and the shape of the temperature profile during operation induce significant decreases of the contact pressure on the gaskets near the fuel manifold, at the inlet or outlet, depending on the flow configuration. On the contrary, the electrical contact was ensured independently of the operating point and history, even though plastic strain developed in the gas diffusion layer.     

Long-term evolution of mechanical performance of solid oxide fuel cell stack and the underlying mechanism

Mechanical performance analysis is important for ensuring the long-term reliability of solid oxide fuel cells (SOFCs). Thermal-mechanical models are constructed to conduct time-dependent mechanical performance analysis of SOFC stack with temperature field obtained by multiphysics modeling. The volume-averaged temperature field is used as comparison. The creep strains are examined with a time step of 10 h for 10,000 h. It reveals: (1) Uniform temperature significantly decreases the stresses, strains, failure probabilities of all stack components. (2) The failure probability of sealant reduced rapidly and the sealant becomes mechanically safer for long-term operation. (3) Creep strain is dominant for anode/sealant/interconnect, but negligible for electrolyte/cathode. All components are predictably safe against strain failure for 100,000 h (4) Creep strains of stack components interact with each other. Coupled analysis of creep strains of anode/sealant/interconnect is mandatory, but the creep strains of electrolyte/cathode may be neglected for studying mechanical evolutions.     

Cathode-side electrical contact and contact materials for solid oxide fuel cell stacking: A review

In a planar solid oxide fuel cell (SOFC) stack, a number of individual cells are stacked together to increase the voltage and power output. At both the cathode– and anode–interconnect interfaces, electrical contact layers are applied between the interconnect and electrodes during cell fabrication process or stack assembly to increase the electrode-interconnect contact area and to compensate for dimensional tolerance variation of the contacting components, thus minimizing ohmic contact resistance throughout the stack. As such, electrical contact is an essential component in SOFC stacks. In this paper, we review the cathode-side electrical contact design and contact materials for application in SOFC stacks. Following an introduction of the function and working principles of electrical contact, the material requirements for cathode-side contact layer in SOFC stacks are outlined. The current materials for the cathode–interconnect contact are thoroughly reviewed, including noble metals, conductive ceramics (e.g. perovskites and spinels), composites, and other more complex structures. Several potential directions for cathode–interconnect contact material research and development are also highlighted.     

Study of geometric stability and structural integrity of self-healing glass seal system used in solid oxide fuel cells

A self-healing glass seal has the potential to restore its mechanical properties upon being reheated to the solid oxide fuel cell (SOFC) stack operating temperature. Such a self-healing feature is desirable for achieving high seal reliability during thermal cycling. Self-healing glass is also characterized by its low mechanical stiffness and high creep rate at SOFC operating temperatures. Therefore, the geometric stability and structural integrity of the glass seal system are critical to its successful application in SOFCs. This paper describes studies of the geometric stability and structural integrity of the self-healing glass seal system and the influence of various interfacial conditions during the operating and cooling-down processes using finite element analyses. For this purpose, the test cell used in the leakage tests for compliant glass seals, conducted at Pacific Northwest National Laboratory (PNNL), was taken as the initial modeling geometry. The effect of the ceramic stopper on the geometric stability of the self-healing glass sealants was studied first. Two interfacial conditions of the ceramic stopper and glass seals, i.e., bonded (strong) or unbonded (weak), were considered. Then the influences of interfacial strengths at various interfaces, i.e., stopper/glass, stopper/PEN, as well as stopper/IC plate, on the geometric stability and reliability of glass during the operating and cooling processes were examined.     

A modeling study on the thermomechanical behavior of glass-ceramic and self-healing glass seals at elevated temperatures

Hermetic gas seals are critical components of planar Solid Oxide Fuel Cells (SOFCs). This article focuses on the comparative evaluation of a glass-ceramic seal developed by the Pacific Northwest National Laboratory (PNNL) and a self-healing glass seal developed by the University of Cincinnati. The stress and strain levels in the Positive electrode–Electrolyte–Negative electrode (PEN) seal in a single-cell stack are evaluated using a multi-physics simulation package developed at PNNL. Simulations were carried out with and without consideration of a clamping force and a stack body force, respectively. The results indicate that the overall stress and strain levels are dominated by the thermal expansion mismatches between the different cell components. Further, compared with the glass-ceramic, the self-healing glass results in a much lower steady state stress value due to its much lower stiffness at the operating temperature of the SOFC. It also exhibits much shorter relaxation times due to a high creep rate. It is also noted that the self-healing glass seal will experience continuing creep deformation at the operating temperature of a SOFC therefore resulting in possible overflow of the sealant material. Therefore, a stopper material may be required to maintain its geometric stability during operation.     

Modeling of thermal stresses and probability of survival of tubular SOFC

The temperature profile generated by a thermo-electro-chemical model was used to calculate the thermal stress distribution in a tubular solid oxide fuel cell (SOFC). The solid heat balances were calculated separately for each layer of the MEA (membrane electrode assembly) in order to detect the radial thermal gradients more precisely. It appeared that the electrolyte undergoes high tensile stresses at the ends of the cell in limited areas and that the anode is submitted to moderate tensile stresses. A simplified version of the widely used Weibull analysis was used to calculate the global probability of survival for the assessment of the risks related to both operating points and load changes. The cell at room temperature was considered and revealed as critical. As a general trend, the computed probabilities of survival were too low for the typical requirements for a commercial product. A sensitivity analysis showed a strong influence of the thermal expansion mismatch between the layers of the MEA on the probability of survival. The lack of knowledge on mechanical material properties as well as uncertainties about the phenomena occurring in the cell revealed itself as a limiting parameter for the simulation of thermal stresses.     

A computational fluid dynamics and finite element analysis design of a microtubular solid oxide fuel cell stack for fixed wing mini unmanned aerial vehicles

Computational fluid dynamics (CFD) and finite element analysis (FEA) are important modelling and simulation techniques to design and develop fuel cell stacks and their balance of plant (BoP) systems.The aim of this work is to design a microtubular solid oxide fuel cell (SOFC) stack by coupling CFD and FEA models to capture the multiphysics nature of the system. The focus is to study the distribution of fluids inside the fuel cell stack, the dissipation of heat from the fuel cell bundle, and any deformation of the fuel cells and the stack canister due to thermal stresses, which is important to address during the design process. The stack is part of an innovative all-in-one SOFC generator with an integrated BoP system to power a fixed wing mini unmanned aerial vehicle. Including the computational optimisation at an early stage of the development process is hence a prerequisite in developing a reliable and robust all-in-one SOFC generator system. The presented computational model considers the bundle of fuel cells as the heat source. This could be improved in the future by replacing the heat source with electrochemical reactions to accurately predict the influence of heat on the stack design.     

Modeling design and analysis of multi-layer solid oxide fuel cells

The thermo-mechanical analytical model proposed for different solid oxide fuel cell (SOFC) designs addresses the deformation behavior and mechanical stability of SOFCs at various thermal stresses, specifically the creep resistance and the long-term endurance beyond the elastic limit.The model considers the deformation of multi-layer SOFC in the temperature range of 600-800 °C and presents the combination of the correlated parameters for SOFC performance evaluation, stability and long-term endurance under realistic operating conditions and temperature gradients. The numerical analysis of the thermo-mechanical properties of the SOFC materials is presented in terms of mechanical behavior at failure conditions and the influence of rheological and structural properties on SOFC long-term endurance. The SOFC thermal behavior, creep parameters of the SOFC materials and long-term stability are analyzed in terms of stresses, deformations and displacements.In terms of broader impact, the algorithms for Maurice-Levi and Voltaire theorems and their validity for non-elastic, e.g. viscous-elastic, viscous-plastic, and elastic-plastic deformations were confirmed. This result allowed us to apply the stress condition of non-elastic body to the stress condition of the elastic body which is relevant to the SOFC operation at elevated temperatures.     

Numerical investigation of flow/heat transfer and structural stress in a planar solid oxide fuel cell

The present work investigates the effects of the temperature and thermal stress distributions in a planar solid oxide fuel cell (SOFC) unit cell. A computational fluid dynamic (CFD) analysis of a planar anode-supported SOFC that considers electrochemical reactions is performed, and the thermal stresses are calculated. The static friction coefficients are assumed to range from 0.05 to 0.3, and conservatively, a perfectly bonded condition is assumed. The results show that the electrolyte is the weakest component and has the maximum stress because the electrolyte is the thinnest and the Young modulus is the highest. Thus, the contact between the anode electrode and the electrolyte, and between the cathode electrode and the electrolyte, would be the perfectly bonded condition. As a result, this research showed that the stresses induced by constraint forces with various contact conditions were dominant for the structural stability in a SOFC. Therefore, static friction coefficients on operative high temperature conditions are important to predict the structural integrity in a SOFC, and they will be investigated in future works in order to improve the structural stability in a stack design as well as in a SOFC.     

Investigation of solid oxide fuel cell sealing behavior under stack relevant conditions at Forschungszentrum Jülich

Hermetic sealing is a key requirement for the operation of solid oxide fuel cell (SOFC) stacks in a system environment. The sealant material has to withstand stresses due to mechanical loading, mismatch in thermal expansion coefficient and thermal gradients that arise during operation. Based on leakage tests performed at Forschungszentrum Jülich it was obvious that stacks, having been operated successfully in a furnace, are not necessarily usable in a system, e.g. because of deviating pressure differences and temperature gradients. Thorough investigations including stack and stack dummy tests, and finite element modeling (FEM) were performed to get a comprehensive understanding of the various parameters, influencing the leak tightness of the sealing material. It was found that even small temperature differences especially in the area of gas and air manifolds can create excessively high tensile stresses. Based on initial FEM analyses, a better understanding of the problem has been obtained and a tool was developed that can assist in the design of more robust stacks. These investigations and modeling activities will be continued with a main focus on thermal cycling, which is the next step in the list of requirements.     

Thermal stress and probability of failure analyses of functionally graded solid oxide fuel cells

Thermal stresses and probability of failure of a functionally graded solid oxide fuel cell (SOFC) are investigated using graded finite elements. Two types of anode-supported SOFCs with different cathode materials are considered: NiO-YSZ/YSZ/LSM and NiO-YSZ/YSZ/GDC-LSCF. Thermal stresses are significantly reduced in a functionally graded SOFC as compared with a conventional layered SOFC when they are subject to spatially uniform and non-uniform temperature loads. Stress discontinuities are observed across the interfaces between the electrodes and the electrolyte for the layered SOFC due to material discontinuity. The total probability of failure is also computed using the Weibull analysis. For the regions of graded electrodes, we considered the gradation of mechanical properties (such as Young’s modulus, the Poisson’s ratio, the thermal expansion coefficient) and Weibull parameters (such as the characteristic strength and the Weibull modulus). A functionally graded SOFC showed the least probability of failure based on the continuum mechanics approach used herein.     

Thermal start-up behaviour and thermal management of SOFC's

Solid oxide fuel cells (SOFCs) have many attractive features for widespread applications. The high operating temperature provides a valuable heat source and in contrast to low temperature fuel cells they not only tolerate substances such as CO but can even use them as fuel. Thus, reforming of hydrocarbon fuels for SOFCs can be done without additional gas purification. As both stack and hydrocarbon reformer unit have to be operated at high temperatures (700–1000 °C), thermal management plays an important role in the successful operation of SOFC systems. As the SOFC system contains ceramic components, both large thermal gradients in the system and thermal expansion coefficient (TEC) mismatch must be avoided.Matching TECs is done by selecting the suitable materials. Avoiding high temperature gradients is done by selecting the right system design and control strategies. In order to achieve both, we have built a finite element simulation for a complete SOFC systems which allows to study system parameters both during steady operation and during transients. Examples of the thermal start-up behaviour for several system configurations are given for selected components as well as internal temperatures of the SOFC-stack during start-up. The simulation model includes also the option to simulate the effects of internal methane reformation in the SOFC stack.As the minimum operation temperature is high, cooling down of the system has to be avoided if instant operation is desired. This can be achieved either passively by selecting suitable thermal insulation materials and/or actively by adopting a strategy for maintaining the temperature.     

3D multiphysics modeling aided APU development for vehicle applications: A thermo-structural investigation

Solid oxide fuel cells (SOFC) are suitable for on-board electricity generation as Auxiliary Power Unit (APU) to support the electric power supply in heavy-duty vehicles. In order to satisfy the requirements of a lightweight fuel cell stack for mobile applications, thin-walled components must be used for the stack structure. This necessity is associated with material, process and design difficulties that must be solved in order to achieve a successful utilization. In this work a novel lightweight SOFC stack design with metal-supported cell was studied both numerically and experimentally. The metallic components are made from the Intermediate Temperature Metal (ITM), a high performance, high chromium ferritic stainless steels alloy. The multiphysics modeling approach (fluid dynamics, heat transfer, structural mechanics) was utilized in this work to predict the temperature distribution and the thermo-structural behavior of the new developed design. Geometric details of the fuel cell stack components as well as appropriate nonlinear, temperature and time-dependent constitutive models were developed to describe the material behavior. Experimental data were used to determine the material model parameters and validated the simulation results. The three-dimensional stress and deformation distributions in the individual stack components were evaluated and their maximum values for elements at risk were identified. Thus, the developed model enables the investigation of sustainability and serviceability of the structural elements to ensure a reliable operation of the stack. The developed computational model can be used as a design tool for parametric studies and optimization analysis to investigate the effects of process boundary conditions, material properties as well as geometrical design parameters and their variation on the induced thermal stresses.     

Two-dimensional temperature distribution estimation for a cross-flow planar solid oxide fuel cell stack

The uniform temperature distribution of a cross-flow planar solid oxide fuel cell (SOFC) stack plays an essential role in stack thermal safety and electrical property. However, because of the strict requirements in stack sealing struture, it is hard to acquire the temperature inside the stack using thermal detection devices within an acceptable cost. Therefore, accurately estimating the two-dimensional (2-D) temperature distribution of the cross-flow stack is crucial for its thermal management. In this paper, Firstly, a 2-D mechanism model of a cross-flow planar SOFC stack is established. The stack is divided into 5*5 nodes along the gas flow directions, which can reflect the stack states with moderate computational burden. Then, experimental test data is utilized to modify and validate the stack model, guaranteeing the model accuracy as well as the reliability of model-based state estimator design. Finally, easily-measured stack inputs and outputs are selected, and a temperature distribution estimator combined with unscented kalman filter (UFK) approach is developed to achieve accurate and fast temperature distribution estimation of a cross-flow SOFC stack. Simulation results demonstrate that the UKF-based temperature distribution estimator can precisely and quickly achieve the temperature distribution estimation of the cross-flow stack under both static state and dynamic state changes and is applicable to cross-flow stacks with different size or cell number as well, the maximum estimated absolute error is less than 0.15 K with an absolute error rate of 0.015%, which indicates the developed estimator has good estimation performances.