Effect of catalyst layer configuration on single chamber solid oxide fuel cell performance

Applied Thermal Engineering 100 (2016) 98–104

Contents lists available at ScienceDirect

Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g

Research Paper

Effect of catalyst layer configuration on single chamber solid oxide fuel cell performance Majid Kamvar a,*, Majid Ghassemi b, Masoud Rezaei a a

Mechanical Engineering Faculty, K. N. Toosi University of Technology, Tehran, Iran Centre for Hydrogen and Fuel Cell Research, School of Chemical Engineering, University of Birmingham, Birmingham, UK (on sabbatical from K. N. Toosi University of Technology, Tehran, Iran) b

H I G H L I G H T S

• • •

Performance analysis of three different SCSOFC catalyst layer configurations is done. The ohmic loss plays a key factor in performance enhancement. Stacking the perpendicular configuration cell enhances the SCSOFC performance.

A R T I C L E

I N F O

Article history: Received 7 August 2015 Accepted 26 January 2016 Available online 4 February 2016 Keywords: Single chamber Solid oxide fuel cell Hydrogen–air premixed FEM

A B S T R A C T

The purpose of the current study is to numerically evaluate the effect of coplanar and perpendicular catalyst layer configurations on the performance of a single chamber solid oxide fuel cell (SC-SOFC). Three different catalyst layer configurations, coplanar, single-cell perpendicular and two-cell stack are used. Fuel is a mixture of hydrogen and air (50% hydrogen and 50% air by volume). An in-house computational fluid dynamics code is utilized to solve the nonlinear governing equations of mass, momentum, energy, charge balance and gas-phase species coupled with kinetics equations. Results show that the perpendicular catalyst layer configuration is more suitable for SC-SOFC than the coplanar configuration. This is due to shorter path of the oxygen ion transportation from cathode to anode in perpendicular compared to coplanar configuration. In addition, results indicate that adding another anode and cathode electrode on the other face of the electrolyte and providing a simple two-cell stack improve the cell performance. Finally, in order to present a suitable configuration of a SCSOFC two-cell stack, a parametric study is performed. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Fuel cells directly produce electricity from the external supply of fuel and oxidant [1]. Among different types of fuel cells, solid oxide fuel cells (SOFCs) have gained consideration due to their efficiency and fuel flexibility [2–9]. As known, SOFCs operate in the high temperature range, 700 °C–1000 °C, and face several problems such as material degradation and gas leakage. The gas leakage is the major obstacle of SOFCs for commercialization [2,4,5]. An alternative to SOFC and its mentioned problems is the use of SC-SOFCs. In SCSOFC, a mixture of fuel and oxidant is fed directly into the cell [5]. The goal of much research is to improve the performance of the SC-SOFCS. To date most research is limited to experimental evaluation of the SC-SOFC which only provides information about overall performance of the cell [2,4,7,10–17]. The few existing papers on

* Corresponding author. Tel.: +9821 8406 3414; fax: +9821 8867 7274. E-mail address: [email protected] (M. Kamvar). http://dx.doi.org/10.1016/j.applthermaleng.2016.01.128 1359-4311/© 2016 Elsevier Ltd. All rights reserved.

SC-SOFC numerical models do not provide detailed information about the electrochemical interactions which is needed to improve the performance of SC-SOFC [3,6]. A study by Chung et al. [3] shows that ohmic loss is the major loss in the SC-SOFCs compared to the other two losses (i.e. concentration and activation losses). Their results also reveal that the ohmic loss diminishes by increasing the electrolyte layer thickness. The same results are presented by Akhtar and his team [12]. They reported that increasing the electrolyte layer thickness extends the cross-sectional area available for ionic current flow in lateral direction. Akhtar also evaluated the effect of the cathode to anode distance on gas species as well as the velocity distribution through electrodes. The right-angular configuration for SC-SOFC was initially introduced by Wang et al. [13]. They used methane–air mixture as fuel for this configuration. Wang reported that the right-angular configuration exhibits much better performance than coplanar configuration. This is due to considerable reduction in the ohmic resistance occurring in right-angular type. They also studied the twocell right-angular configuration stack performance and found out

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

that the ohmic resistance is the smallest in this configuration. However, their results are limited to experiments and just give information about the overall performance of the cell. The main aim of the current study is to look at the effect of different catalyst layer configurations on the cell performance. The goal is to advice an anode and cathode setup that minimizes the overall losses and increases the SC-SOFC performance. 2. Problem definition Fig. 1 depicts the schematic of the problem. As shown, a mixture of hydrogen and air (50% hydrogen, 50% air by volume) is used to ensure the system safety. The hydrogen is sufficiently diluted with nitrogen to avoid explosion in the system. As shown by Fig. 1 the positive electrode, electrolyte and the negative electrode (PEN) are placed at the middle of the channel. Three different configurations are selected: coplanar configuration (case 1) in which two electrodes are placed on the same side of the electrolyte, perpendicular configuration (case 2) in which electrodes are placed on two mutually perpendicular planes and a two-cell stack in which two single cells are placed on the electrolyte layer to form a simple stack (case 3). The cell consists of five layers: anode made of nickel (Ni), anode catalyst layer made of nickel–yttria-stabilized zirconia (Ni-YSZ), electrolyte made of yttria-stabilized zirconia (YSZ), cathode catalyst layer made of yttria-stabilized zirconia-lanthanum strontium manganite (YSZ-LSM) and cathode layer made of lanthanum strontium manganite (LSM). Table 1 shows the geometrical parameters. The fluid is assumed to behave as an ideal gas and the flow is steady, two-dimensional, compressible and laminar. All fluid properties vary with temperature. The electrolyte is fully impermeable and the electrodes are selective which means the following reactions occur in the electrodes: Anode oxidation of hydrogen:

H2 + O−2 → H2O + 2e−

Table 1 Geometrical data. Description

Symbol

Value

Channel width Channel height Anode thickness Anode catalyst layer thickness Electrolyte thickness Cathode thickness Cathode catalyst layer thickness Electrolyte width Electrode width x-Value of electrolyte to anode distance (edge to edge)

Wch Hch ta tac te tc tcc We Welec d

150 [mm] 25 [mm] 70 [μm] 5 [μm] 3 [mm] 50 [μm] 5 [μm] 10 [mm] 2 [mm] 1.5 [mm]

The ohmic resistance due to electron transport and thermal diffusion is neglected. This is due to the electronic conductivity of the electrodes that is noticeably higher than the ionic conductivity. The inertia term (Stokes–Brinkman’s assumption) is also neglected. 2.1. Conservation of mass and momentum The continuity equation is as follows [14]:

∇ ⋅ ( ρu ) = ∑ R j

(3)

j

in which ρ is density of the mixture and u is velocity vector. The right hand side of Eq. (3) accounts for mass depletion or creation due to electrochemical reactions (i.e. Eqs (1) and (2)). The mass source term is zero for other layers because electrochemical reactions occur in the catalyst layers. The momentum equation in the porous electrodes based on Darcy’s law is expressed as [14,18]:

(1)

μ μ 2μ T ρu ⋅∇u = ∇ ⋅ ⎛⎜ − p I + ∇u + (∇u ) − (∇ ⋅ u)I⎞⎟⎠ + ρg − ⎛⎜⎝ ⎞⎟⎠ u + F ⎝ ε κ 3

(2)

where μ is the dynamic viscosity of the fluid, and ε and κ are porosity and permeability of porous electrodes respectively and F is the volume force acting on the fluid. By applying

Cathode reduction of oxygen:

O2 + 2e− → O−2

99

(

)

(4)

Anode layer Anode catalyst layer Electrolyte layer

H2/H2O/N2/ O2

Cathode catalyst layer

PEN

Inlet

Outlet

Cathode layer

(a) d

d

Case 1

d

d

Case 2

d

Case 3

(b)

Fig. 1. The schematic of the problem: (a) the whole computational domain with the inlet and the outlet; (b) different catalyst layer configurations considered in modeling.

100

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

Stokes–Brinkman’s assumption the first term for porous electrodes vanishes. In the free media gas chamber, porosity (ε) is equal to one and permeability (κ) is infinity. With this substitution, Eq. (4) can be rewritten as:

2 j i ,a = − j e ,a = Aa J 0H,ref (c H 2 c H 2,ref ) H 2 [exp (α aaF ηact ,a RuT )

γ

− exp ( −α caF ηact ,a RuT )]

(14)

j e,c = − j i,c = Ac J 0O,2ref (c O 2 c O 2,ref ) O2 [exp (α ac F ηact ,c RuT ) γ

(

T ρu ⋅∇u = ∇ ⋅ ⎛⎜ − p I + μ ∇u + (∇u ) ⎝

)

2μ − (∇ ⋅ u)I⎞⎟⎠ + ρg + F 3

(5)

2.2. Species conservation The species equation for an individual species i is as follows [15]:

∇ ⋅ ji + ρ (u ⋅∇ )ω i = R i

(6)

where ji is the relative mass flux vector, ωi is the mass fraction of ith species, and Ri is the source term which accounts for mass deposit or mass creation of ith species. Using the Maxwell–Stefan equations for multicomponent systems, the relative mass flux vector can be written as [15]:

ji = − ρω i ∑ D ik dk

(7)

k

where dk is the driving forces for diffusion of species i in an ideal gas mixture and Dik is the multi-component Fick’s diffusivity which is calculated by [15]:

D ik = 1.883 × 10−2T 1.5 (1 M i + 1 M k )

12

(pσ ik2 ΩD )

(8)

σ is the characteristic length and is in angstrom and ΩD is the diffusion collision integral. The multicomponent Fick’s diffusivities are corrected by the following equation to account for mass transfer resistance in the porous electrodes:

D ikeff = (ε τ )D ik

(9)

τ is the tortuosity of porous media. To account for Knudsen diffusion in small pores, the Dusty Gas Model (DGM) is applied. The eff effective DGM diffusion of coefficient ( DDGM ,ik ) is defined as: eff D DGM ,ik = (ε τ ) (D ik ⋅ D KN ,ik ) (D ik + D KN ,ik )

− exp ( −α cc F ηact ,c RuT )]

(15)

A is the electrochemically active surface area per unit volume 2 and and J 0H,ref J 0O,2ref are reference exchange current densities. γ H 2 and γ O2 are reaction order for hydrogen oxidation and oxygen reduction at reference concentrations c H 2 ,ref and c O2 ,ref , respectively. α is the charge transfer coefficient with value between 0 and 1, F is Faraday’s constant equal to 96,487 C/mol and ηact is the activation over potential. The indexes “a” and “c” in the above equations refer to the anode and cathode sides. The anode and cathode side activation over potentials is calculated by:

ηact ,a = φe − φi

(16)

ηact ,c = φe − φi − VOC

(17)

Voc is the open circuit voltage calculated by Nernst’s equation [17]: 12 VOC = 1.317 − 2.769 × 10−4 T + RuT 2F ln ( p H 2 ⋅ p O1 22 p H 2O ⋅ p ref )

(18)

2.4. Energy conservation The conservation of energy for the entire domain is governed by:

∇ ⋅ ( ρC p uT − k ∇T ) = Q

(19)

Cp is the specific heat, k is the thermal conductivity and Q is the energy source term due to electronic transport resistance, reversibility and irreversibility heat generation. To account for the electrode porosity an effective relationship for specific heat capacity ( ρC p ) and thermal conductivity is used [16]:

(ρC p )eff

= ε ( ρC p )f + (1 − ε ) ( ρC p )s

k eff = εk f + (1 − ε )k s

(20) (21)

(10)

where DKN,ik are the Knudsen diffusivities and are calculated based on the free molecular flow theory [16]:.

the indexes “f” and “s” denote fluid and solid phase, respectively. Specific heat and conductivity for the fluid mixture are determined by [19]:

eff D KN ,ik = 4 3re RuT (M i + M k ) (π M i M k )

C p ,f = ∑ x j C p , j

(22)

k f = ∑ x jk j

(23)

(11)

j

re is the effective pore radius and Ru is the universal gas constant. As stated before, the electrolyte layer is impermeable, and none of the species can diffuse.

j

Cp,j and kj are the gas species specific heat and conductivity, respectively.

2.3. Charge conservation By applying ohm’s law, the ionic and electronic charge conservation equations for the anode and cathode catalyst layers are, respectively:

−∇ ⋅ (σ e ∇φe ) = j e

(12)

−∇ ⋅ (σ i ∇φi ) = j i

(13)

σe and σi are the electronic and ionic conductivity and Φe and Φi are the electric and ionic potential respectively. Based on Eqs. (1) and (2), the electrical and ionic charge source terms (je and ji) for each anode and cathode catalyst layer are formulated using Bulter– Volmer equation [18]:

2.5. Boundary conditions Chamber walls: No jump temperature and no slip boundary conditions are assumed. Also no species can penetrate into the walls. Inlet: The normal velocity inflow and species mass fraction are specified. Outlet: Exit pressure is assumed to be equal to the total pressure. It is also assumed that flow at the exits is normal to the plane (see Fig. 1). The conduction heat transfer term is neglected compared to convection heat transfer. In addition it is assumed that the convection term is the dominant term in the mass transport model. Electrolyte exterior boundaries are assumed to be insulated (i.e., no mass and momentum through the boundary). Note that the

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

electrolyte layer is assumed to be fully impermeable. Furthermore, no electrons can pass through the electrolyte layer and no ions can pass into the chamber. The electric voltage is specified at the upper intersections of the electrode and chamber boundaries. Also the ground and cell voltages are set to the boundaries relevant to the anode and cathode, respectively. Furthermore no ions can cross the electrode–catalyst layer intersections. The continuity boundary condition is set for the rest.

101

1.1

Experimental

1

Current model

V_cell [V]

0.9

3. Numerical procedure

0.8 0.7 0.6 0.5

An in-house computational fluid dynamics (CFD) code based on a finite element method was developed and utilized. The code uses triangular meshes. The mesh consists of 16,439, 24,180, and 53,814 elements for cases 1, 2 and 3 respectively. A set of equations is solved in steps. Initially the code solves the charge conservation coupled with the energy equation. Then it solves the non-linear momentum equations and terminates when the Stefan–Maxwell equation is solved. To improve the accuracy of the code, the second-order elements for the velocity components and species mass fraction are opted. For other dependent variables linear elements are used. The relative tolerance is set to 1 × 10−6. The total computing times for one value of voltage scan were approximately 44 sec, 2.5 min and 13.5 min for cases 1, 2 and 3, respectively. 4. Results and discussion 4.1. Model validation For verification purpose the current model is modified and is compared to Roger’s experimental data [20] and depicted in Fig. 2. All input parameters of the current study are extracted from the Hussain’s study [21]. Table 2 shows the rest of the validation input parameter [10,11,18,21–23]. As shown in Fig. 2 there is a good agreement between the current study and that of Rogers. The deviation in cell voltage for current density between 0.8 and 1.2 is within the standard deviation of the experimental data. 4.2. Performance analysis of SCSOFC In this section, a comparison study between different SCSOFC configurations is performed and reported. In all cases (1, 2 and 3) the

0.4 0.3 0

0.5

1

1.5

2

2.5

3

J [A/cm^2]

Fig. 2. The current model accuracy compared to experimental data provided by Rogers.

anode distance from the electrolyte edge (the “d” parameter shown in Fig. 1) remains constant. All input parameters except the inlet mass fractions and temperature are fixed. At the inlet, the temperature is 750 °C and the mixture consists of 50% hydrogen, 10.5% oxygen and 30.5% nitrogen by volume. Fig. 3 depicts the oxygen ions path for cases 1, 2 and 3 that take places from cathode to anode. As shown the case 2 oxygen ion path is noticeably shorter than case 1. Therefore a better performance is achieved by case 2. In addition, there is no ion transmission at the right hand side of case 2 electrolyte domains (see Fig. 3). Considering a simple two-cell stack (addition of another anode and cathode electrode on the opposite side of the electrolyte, case 3) improves the cell performance and overcome this problem. The normal ionic current density distribution of all cases along the axis across the middle of anode catalyst layers is shown in Fig. 4. As shown, ionic current density is higher at the edge of the anode for all cases where oxygen ions have to pass the shortest path from cathode to anode. The average ionic current density at the anode is about 75 A/m2, 111 A/m2 and 242 A/m2 for case 1, 2 and 3, respectively. These values prove that stacking the cell, case 3, increases the amount of average ionic current density by about 120%. Furthermore, it is expected to observe a reduction in ionic current density as it passes through the catalyst layer; however, the

Table 2 Validation input parameters [10,11,18,21–23]. Description

Symbol

Value

Dimensions

Channel width PEN height Inlet velocity Anode and cathode permeability Universal gas constant Anode thermal conductivity Cathode thermal conductivity Electrolyte thermal conductivity Anode specific heat Cathode specific heat Electrolyte specific heat Anode density Cathode density Electrolyte density Dynamic viscosity of hydrogen Dynamic viscosity of oxygen Dynamic viscosity of nitrogen Dynamic viscosity of water Thermal conductivity of hydrogen Thermal conductivity of oxygen Thermal conductivity of nitrogen Thermal conductivity of water

Wch Hpen uin κ Ru ka kc ke Cp,a Cp,c Cp,e ρa ρc ρe μH 2 μO 2 μN 2 μH 2O k H2 k O2 k N2 k H 2O

25 1 0.5 10−13 8.314 3 3 2 595 573 606 6870 6570 5900 6.162 × 10−6 + 1.145 × 10−8 × T 1.668 × 10−5 + 3.168 × 10−8T 1.435 × 10−5 + 2.642 × 10−8 T 4.567 × 10−6 + 2.209 × 10−8 × T (W/(m·K)) 0.08525 + 2.964 × 10−4 T 0.01569 + 5.69 × 10−5 T 0.01258 + 5.444 × 10−5 T −0.0143 + 9.782 × 10−5 T

mm mm m/s m2 J/mol·K W/m·K W/m·K W/m·K J/kg·K J/kg·K J/kg·K kg/m3 kg/m3 kg/m3 Pa·s Pa·s Pa·s Pa·s W/m·K W/m·K W/m·K W/m·K

102

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

Anode

Cathode

Case 1

Cathode

Case 2

Anode

Cathode

Case 3

Cathode

Anode

Anode

Normal ionic current density (A/m2)

Fig. 3. Ionic current density stream lines.

900 Case 1 Case 2 Case 3- Left Anode Case 3- Right Anode

800 700 600 500 400 300 200 100 0 0

0.5

1 x-coordinate (mm)

1.5

2

distribution of normal ionic current density of both anodes in case 3 stays the same. This is due to symmetry of the cell and the low amount of hydrogen is consumed at right anode (see Fig. 5). Figs. 5 and 6 show the hydrogen and the oxygen molar concentration distribution of all cases through the axis across the middle of anode and cathode catalyst layer. In these locations, the hydrogen and oxygen are consumed and produce electrons and ions according to equations (1) and (2), respectively. The rate of hydrogen consumption varies with SCSOFC configurations, cases 1, 2, and 3, as seen in Fig. 5. The amount of hydrogen molar concentration at case 3 anode is noticeably lower than that of the other two cases. Therefore case 3 consumes higher amount of hydrogen and has better fuel consumption compared to other two cases. Unlike the ionic current density distribution, the amount of

Fig. 4. Normal ionic current density distribution along anode catalyst layer.

0.192 Oxygen molar concentration (mol/m3)

Hydrogen molar concentration (mol/m3)

14.75 14.7 14.65 14.6

Case 1 Case 2 Case 3- Left Anode Case 3- Right Anode

14.55 14.5

0.19 0.188 0.186 0.184 0.182

Case 1 Case 2 Case 3- Left Cathode Case 3- Right Cathode

0.18

14.45

0.178 0

14.4 0

0.5

1 x-coordinate (mm)

1.5

2

Fig. 5. Hydrogen molar concentration distribution along axis of interest, case 1.

0.5

1 y-coordinate (mm)

1.5

2

Fig. 6. Oxygen molar concentration distribution along cathode catalyst layer.

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

103

0.95 d=0[mm]

0.95

d=0.5[mm]

0.85 Case1 Case2 Case3

d=1.5[mm]

0.75 Cell voltage [V]

d=2[mm]

0.75 Cell voltage [V]

0.85

d=1[mm]

d=2.5[mm]

0.65 0.55

0.65

0.45 0.55

0.35 0

0.45

200

400

600

800

1000

1200

1400

Current density [A/m2]

0.35 0

20

40

60

80

100

Fig. 9. Polarization curves for different “d” values of case 3 shown in Fig. 1.

120

Current density (mA/cm2)

12.5 mW/cm2 in its best condition. In addition it is shown that case 3’s (two-cell stack) max power density is about 43.4 mW/cm2 which is more than case 2 by 100%.

Fig. 7. Polarization curve for cases 1, 2 and 3.

4.3. Parametric study of a two-cell SCSOFC stack hydrogen molar concentration is slightly lower at the right anode compared to the left anode. This is due to the consumption of the fuel at left anode causing the lower amount of hydrogen to reach the right anode. As shown in Fig. 6, the oxygen molar concentration for case 1 and 2 is much more non-uniform compared to case 3. Furthermore, a slight consumption of oxygen in left cathode of case 3 causes a brief decrease of oxygen molar concentration at right cathode compared to left cathode. Figs. 7 and 8 show the polarization and I–P curves of case 1, case 2 and case 3, respectively. Fig. 7 shows that as current density increases, the cell voltage decreases as well which is typical of all SOFC’s behavior. As shown by Fig. 4 maximum power density produced by case 2 is 20.9 mW/cm2 whereas case 1 produces only

In previous section, it is shown that stacking a perpendicular type of SCSOFC improves SCSOFC performance. So, it is necessary to perform a parametric study of a two-cell stack in order to advice the best sketch of case 3 showing the best performance. The “d” symbol as shown in Fig. 1 is considered as a parameter. Six different values are opted: 0 mm, 0.5 mm, 1 mm, 1.5 mm, 2 mm and 2.5 mm. The polarization and I-P curves as a function of “d” are illustrated in Figs. 9 and 10 respectively. It is clear from Fig. 9 that total overpotential occurred within the cell increases by growth of “d” value since increasing the cathode to anode distance of each cell enhances the amount of ohmic overpotential. However, increasing the “d” value from 0 to 0.5 mm does not affect the performance of the cell that much. As shown in Fig. 10 the best performance is observed when the “d” value is set to 0 and 0.5 mm. In this case,

50 45

Power density (mW/cm2)

40 35 30 case1

25

case2 20 case3 15 10 5 0 0

20

40

60

80

100

Current density (mA/cm2)

Fig. 8. Power density versus current density for case 1, 2 and 3.

120

104

M. Kamvar et al./Applied Thermal Engineering 100 (2016) 98–104

References

600

Power density [W/m2]

500 400 d=0[mm] d=0.5[mm] d=1[mm] d=1.5[mm] d=2[mm] d=2.5[mm]

300 200 100 0 0

200

400

600

800

1000

1200

1400

Current density [A/m2]

Fig. 10. I-P curves for different “d” values of case 3 shown in Fig. 1.

the maximum power density is obtained as 484.6 W/m 2 and 472.6 W/m2 respectively. Furthermore, the deviation between different “d” values is more evident at high range of current density (approximately above 400 A/m2). 5. Conclusion A performance analysis of three different SC-SOFC catalyst layer configurations is reported. Results show about 44% increase in performance for the perpendicular configuration, case 2, compared to the coplanar configuration, case 1. The maximum power density for case 2 is estimated as 12.5 mW/cm2 and for case 1 about 21.8 mW/ cm2. It is shown that the oxygen ions transportation path, from cathode to anode, plays a key factor in performance enhancement of case 2. By plotting ionic current density stream lines of case 2, it is found that the right hand side of the electrolyte layer is not efficiently used for passing the oxygen ions. One applicable way is to adjust another pair of electrodes on the other face of the electrolyte. In this case, the maximum power density is enhanced by 100%. In addition, the parametric study on case 3 performance shows that the distance from anode to anode affects the cell performance. The best performance is achieved when two anodes are located at the edge of the electrolyte.

[1] EG and G Technical Services, Inc, Science Applications International Corporation, Fuel Cell Handbook, 6th ed., US Department of Energy, 2002. [2] Y. Hao, Z. Shao, J. Mederos, W. Lai, D.G. Goodwin, S.M. Haile, Recent advances in single-chamber fuel cells: experiment and modeling, Solid State Ionics 177 (2006) 2013–2021. [3] C.Y. Chung, Y.C. Chung, Performance characteristics of micro single-chamber solid oxide fuel cell: computational analysis, J. Power Sources 154 (2006) 35–41. [4] S. Ahn, Y. Kim, J. Moon, J. Lee, J. Kim, Influence of patterned electrode geometry on performance of co-planar, single-chamber, solid oxide fuel cell, J. Power Sources 171 (2007) 511–516. [5] M. Yano, A. Tomita, M. Sano, T. Hibino, Recent advances in single-chamber solid oxide fuel cells: a review, Solid State Ionics 177 (2007) 3351–3359. [6] N. Akhtar, S.P. Decent, D. Loghin, K. Kendall, Mixed-reactant, micro-tubular solid oxide fuel cells: an experimental study, J. Power Sources 193 (2009) 39–48. [7] M. Liu, X. Qi, Z. Lu, Q. Meng, Effect of flow geometry on anode-supported single chamber SOFCs arrayed as V-shape, Int. J. Hydrogen Energy 38 (2013) 1976– 1982. [8] M. Andersson, J. Yuan, B. Sunden, SOFC modeling considering hydrogen and carbon monoxide as electrochemical reactants, J. Power Sources 232 (2013) 42–54. [9] K. Wang, D. Hissel, M.C. Pera, N. Steiner, D. Marra, M. Sorrentino, et al., A Review on solid oxide fuel cell models, Int. J. Hydrogen Energy 36 (2011) 7212–7228. [10] N. Akhtar, Micro-tubular, single-chamber solid oxide fuel cell (MT-SC-SOFC) stacks: model development, Chem. Eng. Res. Design 90 (2012) 814–824. [11] N. Akhtar, Modeling of novel porous inserted micro-tubular, single-chamber solid oxide fuel cells (MT-SC-SOFC), Chem. Eng. J. 179 (2012) 277–284. [12] N. Akhtar, K. Kendall, S.P. Decent, Modeling of co-planar type single-chamber solid oxide fuel cells, J. Fuel Cell Sci. Technol 8 (4) (2011) 0410414. [13] Z. Wang, Z. Lu, B. Wei, X. Huang, K. Chen, W. Pan, et al., A right-angular configuration for single-chamber solid oxide fuel cell, Int. J. Hydrogen Energy 36 (2011) 3147–3152. [14] G.K. Batchelor, An Introduction To Fluid Dynamics, Cambridge University Press, 2000. [15] R. Taylor, R. Krishna, Multicomponent Mass Transfer, 1st ed., John Willey & Sons, Inc., 1993. [16] M.F. Serincan, U. Pasaogullari, N.M. Sammes, A transient analysis of a microtubular solid oxide fuel cell (SOFC), J. Power Sources 194 (2009) 864–872. [17] J. Milewski, K. Swirski, M. Santarelli, P. Leone, Advanced Methods of Solid Oxide Fuel Cell Modeling, Springer, 2011. [18] N. Akhtar, S.P. Decent, D. Loghin, K. Kendall, A three dimensional numerical model of a single-chamber solid oxide fuel cell, Int. J. Hydrogen Energy 34 (2009) 8645–8663. [19] M. Andersson, J. Yuan, B. Sunden, SOFC modeling considering electrochemical reactions at the active three phase boundaries, Int. J. Heat Mass Transf. 55 (2012) 773–788. [20] W.A. Rogers, R.S. Gemmen, C. Johnson, M. Prinkey, M. Shahnam, Validation and application of a CFD-based model for solid oxide fuel cells and stacks, Fuel Cell Sci. Eng. Technol. ASME (2003) 517–520. [21] M.M. Hussain, X. Li, I. Dincer, Mathematical modeling of planar solid oxide fuel cells, J. Power Sources 161 (2006) 1012–1022. [22] N. Akhtar, S.P. Decent, K. Kendall, A parametric analysis of a micro-tubular, single-chamber solid oxide fuel cell (MT-SC-SOFC), Int. J. Hydrogen Energy 36 (2011) 765–772. [23] N. Akhtar, K. Kendall, Micro-tubular, solid oxide fuel cell stack operated under single-chamber conditions, Int. J. Hydrogen Energy 36 (2011) 13083–13088.