CHAPTER 1: Introduction to Stationary Fuel Cells

Although humankind started with wood as the main source of energy, fossil fuels have been used as the main energy source to produce power since the beginning of the industrial revolution. These fuels have mainly been converted into electricity using technologies such as the internal combustion engine, the gas turbine, and the steam turbine. Due to the increase in the global energy demand in parallel with the increase in the population of the world and in the production of high energy consuming devices, depletion of fossil fuels, and increased concern over the impact of greenhouse gases on global warming, alternative fuel and energy systems are being sought out. Among the alternative energy systems, fuel cells have received significant attention due to the fact that they convert the fuel into electricity in an efficient, effective, and environmentally friendly manner. They also help reduce the dependency on fossil fuel resources and the greenhouse gas emissions to the atmosphere.

Fuel cells are apparently known as electrochemical devices that convert the energy in the fuel into electricity. A fuel cell has mainly three components, as shown in Figure 1.1, namely, anode, cathode, and electrolyte. Fuel and air are continuously supplied to the anode and cathode, respectively. The ions, which are produced during the electrochemical reactions at one of the electrodes (i.e., anode or cathode), are conducted to the other electrode through the electrolyte. The electrons produced during the electrochemical reactions are cycled from one electrode to the other via load. The flow of electrons forms an electric current, which effectuates work on the load. A single cell can only generate a small amount of power, which could be enough for some of the portable applications. However, for stationary applications, many single cells must be brought together to produce the required energy demand; a process referred to as ‘stacking’.¹  This process is generally done by connecting single cells in series using bipolar plates or interconnects. These plates form the air and fuel channels as well as they conduct the electrons from one cell to another.

There are generally different types of fuel cells, which mainly differ from each other in terms of the electrochemical reactions that occur at the electrode and electrolyte interface and the type of ion conducting at the electrolyte. Generally, these fuel cells are categorized into two main groups: low‐ and high‐temperature fuel cells. The most common and promising low‐temperature fuel cell types and their applications are discussed in Section 1.2. There are mainly two high‐temperature fuel cell types, namely, the Solid Oxide Fuel Cell (SOFC) and the Molten Carbonate Fuel Cell (MCFC). SOFC is the most employed high‐temperature fuel cell type, which is the main topic of this chapter. SOFC is discussed in Section 1.3 and the subsequent sections.

Proton Exchange Membrane Fuel Cells (PEMFCs) and Direct Methanol Fuel Cells (DMFCs) are the most common low‐temperature fuel cell types. PEMFC and DMFC consist of a proton conducting membrane, such as Nafion^®, which is chemically highly resistant, mechanically strong, acidic, a good proton conductor, and water absorbent. The main difference between PEMFC and DMFC is the fuel entering the fuel cell: hydrogen in PEMFC and methanol in DMFC. The main reactions, benefits, challenges, and application examples of these fuel cells are compared in Table 1.1.

The alkaline fuel cell (AFC) has become popular particularly for powering space vehicles. However, the successful developments with PEMFC and DMFC have led to a decline in the interest in the AFC mainly due to issues related to cost, reliability, and ease of use. However, some types of AFC such as the Direct Borohydride Fuel Cell (DBFC), which uses a solution of sodium borohydride as fuel, remain promising. As the electrolyte and the fuel are mixed, it is simple to make this fuel cell. In addition, CO₂ poisoning can be prevented when highly alkaline fuel and waste borax are used.²  However, the main challenge of this fuel cell is the side reaction known as hydrolysis reaction in which hydrogen is produced as NaBH₄ and reacts with water. Direct Formic Acid Fuel Cells (DFAFCs) and Direct Ethanol Fuel Cells (DEFCs), which have a proton exchange membrane, utilize formic acid and ethanol as some of the potential fuels, respectively. The main advantages of DFAFC appear to be high catalytic activity, easier water management, and minimal balance of plant. However, the performance of this fuel cell strongly depends on the feed concentration of formic acid due to mass transport limitations. DEFC may be more advantageous due to the benefits of ethanol such as high energy density, safety to use, and ease of storage. However, a lot of acetaldehyde, which is a very flammable and harmful liquid, is produced in the electrochemical reactions. In addition, DEFC reaction kinetics is very slow and ethanol crossover is a challenge.

Biofuel cells (BFCs) may be used in very low power applications. There are mainly two classes of BFC, such as microbial fuel cells and enzymatic fuel cells. The first one is more appropriate for applications such as powering underwater equipment since it has higher efficiency and complete oxidation of fuel. The latter may be used in small‐scale applications such as implantable devices since it has high‐power density but lower efficiency and incomplete oxidation of fuel.

A SOFC is a high‐temperature fuel cell (ranging between 500 °C to 1000 °C) that contains an oxide ion‐conducting electrolyte made from a ceramic material. The main application area of SOFC is stationary power and heat generation. SOFC can be used alone or integrated with other technologies such as gas turbine and gasification systems for this purpose. Another application area of the SOFC is in transportation such as being the auxiliary power unit of luxury automobiles or heavy duty commercial trucks. SOFC can also be used in military applications as this fuel cell can meet the power demands of the soldiers, which has been increasing due the new technologies (e.g. night‐vision devices, global positioning systems, target designators, climate controlled body suits, and digital communication systems); and it could be operated with fuels such as diesel and JP‐8 that are available in the battle area in any part of the world. SOFC can also be used in some specific niche applications such as miniature autonomous systems.

Compared to low‐temperature fuel cells, SOFCs have important advantages including: i) simpler in concept since only solid and gas phases exist; ii) ability to utilize fuels such as carbon monoxide, methane, higher hydrocarbons, methanol, ethanol, and biomass produced gas; iii) internal reforming of the fuel; iv) efficient thermal integration with other technologies such as gas turbines and gasification systems; and v) no need for precious metal electrocatalysts. Some of the main disadvantages of SOFCs over the low‐temperate fuel cells are considered to be i) challenges for construction and durability due to its high temperature; and ii) carbon deposition problem.

The operation principle of a SOFC is simple. Fuel and air are continuously fed into to the fuel and air channels, respectively. Oxygen molecules in the air stream diffuse into the cathode side and react with the electrons, which are cycling via the load, at the cathode and electrolyte interface, to form the oxide ions. These oxide ions pass through the electrolyte and react with the fuel (e.g. hydrogen and carbon monoxide molecules), which diffuse into the anode side, at the anode and electrolyte interface. Hence, gases such as water vapour and carbon dioxide, and electrons are formed. The flow of electrons generates the electric current. The electrochemical reactions at the anode, cathode, and the overall reaction for a hydrogen‐fed SOFC are given as follows.

In general, the following materials are used in a SOFC:¹  Ni‐YSZ for anode, YSZ for electrolyte, LSM for cathode and magnesium‐doped lanthanum chromite for interconnects. However, there is an increasingly crucial need for research to find better materials to help increase the performance of the SOFC. For example, high‐chromium containing steel, such as Crofer22APU or E‐Brite, is currently considered for interconnects.

SOFCs may be classified according to their temperature level, cell and stack design, type of support, flow configuration, and fuel reforming type, as shown in Table 1.2.

SOFCs may be classified as low‐temperature (LT‐SOFC), intermediate‐temperature (IT‐SOFC), or high‐temperature (HT‐SOFC). Increasing operating temperature decreases the resistivity of the cell components and increases the electrode kinetics. They in turn lead to an increase in the performance of the cell. In addition, a higher temperature of the exit of the SOFC will lead to a better thermal integration with other technologies, which results in better thermal efficiency. On the other hand, a higher operating temperature will cause problems such as weaker structural integrity, higher corrosion rates, higher materials costs, and longer start‐up and shut‐down time.

According to the cell and stack design, SOFCs may be classified as tubular, planar, and segmented‐in‐series (or integrated‐planar). Among these design types, planar and tubular are the most common types. Planar design is more compact than the tubular design, since cells can be stacked without giving large voids. In addition, bipolar plates as used in the planar design provide simpler series of electrical connection between cells and shorter current path. The manufacturing cost of planar SOFC is also lower. However, in the planar design, there is a need for gas‐tight sealing; whereas in tubular design, the cells may expand and contract without any constraints. The segmented‐in‐series SOFC is a cross between tubular and planar geometries which have the advantages of thermal expansion freedom like the tubular and low‐cost component manufacturing like the planar.

SOFCs may be manufactured as anode‐supported, cathode‐supported, or electrolyte‐supported. The electrolyte‐supported type may be suitable for HT‐SOFC as the temperature of a SOFC increases, the ionic resistivity of its electrolyte decreases. For IT‐SOFC and LT‐SOFC, the electrolyte is generally manufactured in a very thin form and the fuel cell is either manufactured as anode or cathode‐supported. These three types of manufacturing may also be called self‐supporting configuration. SOFCs may also be supported externally, such as interconnect‐supported and porous substrate supported SOFC.

The flow configuration in a SOFC can be cross‐flow, co‐flow, or counter‐flow. The choice of this configuration affects the temperature distribution within the cell and the stack. Recknagle et al.³  showed that the co‐flow configuration has the most uniform temperature distribution and the smallest thermal gradients for similar fuel utilization and average cell temperature. Schematics of planar co‐, counter‐ and cross‐flow SOFC stacks are shown in Figure 1.2.

Fuels that can be fed into SOFC (e.g. methane and syngas) are reformed into H₂ and/or CO, which are electrochemically oxidized in the SOFC. This reforming process may be outside the stack, which is called external reforming, or inside the stack, which is called internal reforming. There are two possible types of internal reforming which are called indirect internal reforming (IIR‐SOFC) and direct internal reforming (DIR‐SOFC). In the IIR‐SOFC, the reformer section is separate from the other components inside the cell but in close thermal contact with the anode section; whereas in the DIR‐SOFC, the reforming takes place directly on the anode catalyst. IIR‐SOFC is effective in eliminating the carbon deposition problem. However, it is difficult to preserve the uniform temperature distribution in the stack in IIR‐SOFC since the cells closer to the reforming section will be cooler due to the endothermic reforming reaction.

SOFC, when designed properly, might be operated with several fuels such as hydrogen, carbon monoxide, methane, higher hydrocarbons (e.g. butane), methanol, ethanol, ammonia, hydrogen sulfide, biogas, and syngas. Such fuels, excluding hydrogen and carbon monoxide, must be reformed into these gases to be electrochemically oxidized in the fuel cell. The steam reforming reactions for hydrocarbons (e.g. methane and butane), methanol, and ethanol are given in Eqs. (4) to (6), respectively. These reactions generally occur together with water‐gas shift reaction, which is shown in Eq. (7). As can be seen in these equations, as a result of these equations, the fuel is reformed into hydrogen and carbon monoxide, as given below:

The other fuel option for SOFCs may be ammonia, which is an inexpensive and convenient way of storing hydrogen. A catalytic cracking of ammonia reaction, which represents the production of hydrogen from ammonia, is given in Eq. (8). One possible of usage of ammonia for SOFCs is vehicular applications. In a recent publication by Ehsan et al.,⁴  an ammonia‐fed SOFC based on proton conducting electrolyte with a heat recovery option is proposed and analyzed, as shown in Figure 1.3.

Lu and Schaefer⁵  studied the possibility of using hydrogen sulfide, which is known to be an extremely corrosive and noxious gas, as a fuel in SOFC. They suggested the usage of a H₂S decomposition reactor integrated with an SOFC as the direct use of H₂S in an SOFC causes anode deterioration over time. The decomposition reaction of H₂S is given as follows.

The decomposition of H₂S:

Gas mixture produced from the conversion of biomass (e.g. wood, crops, and municipal solid waste) is another fuel option for SOFC. The conversion methods of several biomass feed stocks and their products are shown in Table 1.3. Among these products, syngas obtained from the biomass gasification and biogas obtained from the anaerobic digestion are the most applicable fuel for biomass‐fed SOFCs. Syngas produced by the system mainly consists of carbon monoxide, carbon dioxide, hydrogen, methane, water vapour, nitrogen, but also contaminants. The composition of the syngas depends mainly on the fuel, gasifier type, and gasification agent. Biogas mainly consists of methane and carbon dioxide, but also some amounts of nitrogen, oxygen, and contaminants. The product gases from gasification and anaerobic digestion need extensive cleanup before they are fed into SOFC. There are two different types of cleanup processes: a cold process involving gas cleaning at a reduced temperature and a hot process involving gas cleaning at a high temperature. The choice of the cleanup system depends on the temperature level of the SOFC and the other components in an integrated system. Bio‐oil produced from pyrolysis of biomass is a liquid mixture of oxygenated compounds containing various chemical functional groups (e.g. carbonyl, carboxyl, and phenolic).⁶  This mixture should be reformed to hydrogen with a steam reforming process before it is used in SOFC. The overall steam‐reforming reaction of bio‐oil is written as follows:

A high exit temperature of SOFC provides an opportunity to achieve higher thermal efficiencies when SOFC is integrated with other systems. There are mainly two common types of integrated SOFC systems, namely, integrated SOFC and gas turbine systems and integrated SOFC and gasification systems. A configuration for the first system is shown in Figure 1.4. In this particular system, fuel and air compressors increase the pressure of fuel and air, respectively, according to the operating pressure level of SOFC. The unutilized fuel in the SOFC exit stream is burned in an afterburner to increase the temperature of this stream. The gas mixture leaving the afterburner enters the gas turbine to generate power. The expanded gas provides the energy for increasing the temperature of the fuel (natural gas) and air compressor exits according to the SOFC inlet temperature requirement. The remaining energy of the gas mixture is used to provide the heat to generate steam in an evaporator. The steam produced in the evaporator enters the SOFC inlet to initiate the reformation process. The steam to carbon ratio should be well adjusted to prevent the carbon deposition possibility in the stack. A study by Zamfirescu et al.⁷  has shown that the energy and exergy efficiencies of such a system can reach up to 70 and 80%, respectively.

Integrated SOFC and gasification systems have also been given significant attention from the SOFC community recently. Gasification systems can be fueled by either coal or biomass. As the latter one is a renewable resource, biomass is a more promising fuel for SOFCs for better environmental sustainability.

An integrated SOFC and biomass gasification are shown in Figures 1.5a and 1.5b, respectively. In both of these systems, wet biomass should be first dried as high levels of moisture in the feedstock can reduce the reaction temperature in the gasifier and lead to poorer product gas with higher levels of tar. In the conventional system, the gas mixture produced from the combustion of dried biomass process supplies heat to the HRSG where steam is produced. The steam produced in HRSG enters the steam turbine where the power is produced.

In the integrated SOFC and biomass gasification system, the dried biomass enters the gasifier where syngas is produced. A gas cleanup system cleans the syngas according to the SOFC impurity levels, in order not to cause any degradation in the SOFC. The cleaned syngas enters the SOFC, where the electricity is produced. Here, some amount of depleted fuel stream can be recirculated to the SOFC inlet to prevent the carbon deposition possibility in the SOFC. The fuel and air streams exiting the SOFC enter the afterburner to burn the unused fuel and increase the temperature of these streams. The gas mixture leaving the afterburner supplies heat to the following components, respectively: the blower, the HRSG, and the dryer. This gas mixture is emitted to the environment after exiting the dryer.

In an integrated SOFC and biomass gasification system, selection of gasifier and gasification agent plays an important role in the performance and cost of the system. Gasifiers may be classified according to the heat addition method and reactor type. Heat can be added in two ways: autothermal or allothermal. In autothermal gasification, necessary heat is provided by partial oxidation within the process; whereas in allothermal gasification, an external source is needed to supply the necessary amount of heat. There are also various reactor types that can be used in such a system, as can be seen in Table 1.4. In these gasifiers, air, oxygen, steam, or a combination of these may be used as gasification agents. A study by Colpan et al.⁸  revealed that using steam as the gasification agent yields better electrical and exergetic efficiencies for such an integrated SOFC system.

In this section, the fundamentals of SOFC modelling are discussed. The model discussed in this section may be called a zero‐dimensional SOFC model. Please note that there are various other models (e.g. multi‐dimensional, transient, and micro‐level) available in the literature. A 2D and transient model is discussed in the next section.

The current generated due to the flow of electrons in a SOFC is proportional to the hydrogen utilized in the cell as shown in Eq. (11).

where F is the Faraday constant, which is approximately equal to 96485 C/mol.

The Nernst voltage (reversible cell voltage) may be shown as

The Nernst voltage may be given in terms of some non‐dimensional parameters^1,12 

where the fuel utilization ratio is the amount of hydrogen that is electrochemically reacted to the amount of hydrogen in the inlet stream; whereas air utilization ratio is the amount of oxygen that is electrochemically reacted to the amount of oxygen in the inlet stream. Fuel and air utilization ratios can be calculated using the following equations:

Here, the value of the actual cell voltage depends on the values of the ohmic, activation and concentration polarizations; and can be found using:

The ohmic polarization occurs due to the resistance to the flow of oxide ions through the electrolyte and resistance to the flow of electrons through the anode, cathode, and interconnects. The relationship between voltage drop and current density is written as follows, using Ohm’s law:

where the material resistivities are generally determined through conducting experimental measurements. The most significant resistance occurs at the electrolyte in a SOFC. The temperature dependence of the resistivity of YSZ, which is found using the Arrhenius equation, is given as follows:¹³ 

Here, it should also be noted that although there is contact resistance between the layers of the SOFC, this resistance is generally neglected in modelling.

The second type of polarization is called activation polarization which occurs due to the sluggishness of the reactions. The Butler‐Volmer equation, which is shown in Eq. (19) can be used to find this polarization. Please note that charge transfer coefficient for anode and cathode is assumed as 0.5, as given in the following equation:

The third polarization is the concentration polarization, which is related to the voltage loss due to the diffusion of the gases in porous media. More specifically, when gases at the channels diffuse through the porous anode and cathode, the gas partial pressure at the electrochemically reactive sites becomes less than that in the bulk of the gas stream. Hence, a voltage drop occurs. If the microstructure is assumed not to be a function of position, this polarization may be given as follows (e.g., ref. 14):

The power output of the cell may then be found as

The electrical efficiency of the cell is calculated as

As a case study, a conventional biomass fueled power production system (Figure 1.5a) is compared with an integrated biomass gasification and SOFC system (Figure 1.5b) in terms of efficiency and environmental impact. Both electrical and exergetic efficiencies, and specific greenhouse gas emissions are calculated for performance and greenhouse gas emission comparisons, respectively.

In the modelling of the conventional biomass‐fueled power production system (Figure 1.5a), two basic thermodynamic laws, such as the first law and the second law, are considered and the respective balance equations are written for the components of the system. In this model, it is assumed that complete combustion is achieved using 100% theoretical air. The heat recovered from the HRSG is first calculated applying an energy balance around the control volume enclosing the HRSG. Using the isentropic efficiencies of the components and the thermodynamic relations, steam produced in the HRSG is then calculated. Finally, using these findings, the power output of the steam turbine, power demand for the pump, and the net power output of the system are calculated.

For the SOFC, the transient heat transfer model developed by Colpan et al.¹⁵  is used. The approach and main features of this model are as follows: A control volume around the repeat element found in the middle of a planar SOFC stack is taken. It is assumed that the other repeat elements show the same characteristics with this repeat element. The solid structure, i.e. electrodes, electrolyte, and interconnects, is modelled in 2D; whereas the air and fuel channels are modelled in 1D. Since the gases flow with low velocity to obtain high fuel utilization, it is assumed that fully developed laminar flow conditions are achieved at the air and fuel channels. Natural convection at the heat‐up stage, forced convection at the start‐up stage, conduction heat transfer between the solid parts, and all the voltage losses, i.e. activation, concentration, and ohmic, are taken into account in the modelling. The input parameters of this model are cell voltage, Reynolds number at the fuel channel inlet, excess air coefficient, temperature at the air and fuel channel inlets, pressure of the cell, molar gas composition at the air and fuel channel inlets, and the geometrical dimensions of the SOFC. The output parameters are the current density, temperature, molar gas composition, and carbon activity distributions, the heat‐up and start‐up time, the fuel utilization, the power output and the electrical efficiency of the cell. This model is validated with IEA benchmark test¹⁶  and Braun’s model.¹⁷  The main equations of this model can be found in Tables 1.5 to 1.7. Equations to find the cell voltage and power density can be found in Section 1.5.

In the modelling part, the integrated SOFC and biomass gasification system, firstly, the syngas composition and the external heat needed for the gasifier are calculated by solving the set of equations derived from the thermodynamic modelling of the gasifier. These equations include three atom balances, two chemical equilibrium relations and the energy balance around the control volume enclosing the gasifier. Secondly, using the syngas composition and the heat transfer model of the SOFC, number of the SOFC stacks, molar flow rate of gases at the inlet and exit of the air and fuel channels, temperature at the exit of the air and fuel channels, and power output of the cell are found. Thirdly, combining the outputs of the gasifier and SOFC models, the molar flow rate of the dry biomass is calculated. Fourthly, applying thermodynamic principles to the components of the system, the enthalpy flow rate of all the states are calculated. Finally, using the laws of thermodynamics, work input to the auxiliary components, i.e. blower and pump, and net power output of the system are calculated.

Both electrical and exergetic efficiencies are selected as the performance assessment parameters. The electrical efficiency, as written in Eq. (24), is defined as the ratio of the net power output of the system to the lower heating value of the fuel. In regards to the exergetic efficiency, it is necessary to identify both a product and a fuel for the system being analyzed. The product represents the desired output produced by the system. The fuel represents the resources expended to generate the product. This efficiency can also be written in terms of the total exergy destructions and losses within the system, given as follows:

In addition, the environmental impact of these systems can be assessed calculating the specific greenhouse gas emissions, which is defined as the ratio of the GHG emission from the system to the net power output of the system. From the viewpoint of energy and environment, the lower the ratio is, the more environmentally friendly the system is.

The input data used in this case study are tabulated in Table 1.8.

The models discussed in Section 1.6 are simulated to find the performance and environmental impact of the systems studied using the data given in Table 1.1. The results and discussion of these calculations and simulations are given in this section.

For the integrated SOFC and biomass gasification system shown in Figure 1.5b, the syngas composition is first calculated as: 2.08% CH₄, 42.75% H₂, 25.80% CO, 9.44% CO₂ and 19.93% H₂O. Using this composition and the data given in Table 1.1, the SOFC model is simulated. It is found that the fuel utilization ratio of the SOFC is 82%; and the average current density is 0.253 A/cm² for the cell operating voltage of 0.7 V. The distribution of the current density with respect to the flow direction is also shown in Figure 1.6. The carbon activity distribution through the flow direction is found to check the carbon deposition possibility (i.e. the conditions where the carbon activity exceeds 1 for any location). In general, the carbon deposition possibility is more severe at the fuel channel inlet, as can be seen in Figure 1.6. It is also found that the carbon activity is less than 1 for all the locations for this case study.

Figure 1.7 shows the temperature distribution of the SOFC when the system reaches the steady‐state condition. As can be seen from this figure, there is a sudden temperature drop at the x direction, i.e. flow direction, due to the endothermic steam reforming reaction and then the temperature increases due to exothermic electrochemical and water‐gas shift reactions. This figure also shows that there is not a significant temperature change at the y direction, i.e. cell thickness direction. At the exit of the fuel and air channels, the temperatures of these exits are both found to be 1000 °C.

The electrical and exergetic efficiencies of the System‐I (Figure 1.5a) and System‐II (Figure 1.5b) are compared for the operating data given in Table 1.1. As shown in Figure 1.8, the electrical and exergetic efficiencies of the System‐I are found as 8.3% and 7.2%, respectively; whereas the electrical and exergetic efficiencies of the System‐II are found to be 44.9% and 41.1%, respectively.

The environmental impact of the systems studied is compared calculating the specific GHG emissions from these systems. It is found that System‐I (Figure 1.5a) has higher GHG emissions compared to System‐II (Figure 1.5b). As shown in Figure 1.9, the specific GHG emissions from System‐I and System‐II are found as 4.564 g‐CO₂.eq/Wh and 0.847 g‐CO₂.eq/Wh, respectively.

SOFCs are considered as one of the most feasible energy power generating devices for converting fuel into electricity, due to their high efficiency and low greenhouse gas emissions. A wide range of fuel (e.g. natural gas, syngas, and ammonia) can be used in these fuel cells. In addition, integrating SOFC with other systems (e.g. gas turbine and gasification systems), the thermal efficiency of the system can be increased significantly. However, there are challenges for construction and durability due to its high temperature. Furthermore, carbon deposition should be controlled by recirculating the depleted fuel stream or sending external steam to the SOFC inlet. A case study is presented to compare the performances and environmental impacts of an advanced biomass gasification and SOFC system with a conventional biomass fueled power production system using a steam turbine as the electricity generator. A heat transfer model for the SOFC and thermodynamic models for the rest of the components of the systems are used in the analyses. The results of the case study conducted showed that the SOFC and biomass gasification system has higher electrical and exergetic efficiencies, and lower specific GHG emissions.

A

cross‐sectional area, cm²

c_p

specific heat at constant pressure, J g⁻¹ K⁻¹

D

diffusivity, cm² s⁻¹

Exergy rate, kW

F

Faraday constant, C

specific molar gibbs free energy, J mole⁻¹

h

heat transfer coefficient, W cm⁻² K⁻¹

specific molar enthalpy, J mole⁻¹

enthalpy flow rate, W

i

current density, A cm⁻²

i_o

exchange current density, A cm⁻²

I

current, A

k

thermal conductivity, W cm⁻¹ K⁻¹

L

length of the cell, cm

LHV

lower heating value, J mole⁻¹

mass flow rate, g s⁻¹

M

molecular weight, g mole⁻¹

molar flow rate, mole s⁻¹

P

pressure, bar

heat transfer rate, W

conversion rate, mole s⁻¹

R

universal gas constant, J mole⁻¹ K⁻¹

Reynolds number in an internal flow

t

time, s; thickness, cm

T

temperature, K

U_a

air utilization ratio

U_f

fuel utilization ratio

V

voltage, V; volume, cm³

V_o

reference volume, cm³

V_v

Porosity

w

width, cm

power output, W

x

molar concentration

exergetic efficiency

ρ

electrical resistivity of cell components, ohm cm; mass density, g cm⁻³

electrical efficiency

λ_air

excess air coefficient

τ

tortuosity

μ

viscosity, g s⁻¹ cm⁻¹

α

thermal diffusivity, cm² s⁻¹

σ

first principal thermal stress, MPa; specific greenhouse gas emissions, g·CO_2eq/Wh

σ_o

characteristic strength, MPa

a

anode; air

ac

air channel

act

activation

ai

anode interconnect

ave

average

c

cathode; convection

ci

cathode interconnect

conc

concentration

D

destruction

e

electrolyte

el

electrochemical; electrical

F

fuel

fc

fuel channel

fi

fuel channel inlet

ohm

ohmic

L

loss

mix

mixture

N

Nernst

o

standard

P

product

PEN

positive/electrolyte/negative

prod

product

r

reaction; radiation

react

reactant

s

solid structure

str

steam reforming reaction for methane

w

wall

wgs

water gas shift reaction

b

bulk

o

standard state