Processes Involving in the Temperature Variations in Solid Oxide Fuel Cells In-Situ Analyzed through Electrode-Segmentation Method

We aim to mitigate the spatial temperature variations contributing to the thermal stresses in solid oxide fuel cells. We thus analyze the involving processes through spatial temperature, current, and impedance variations in-situ measured by the electrode-segmentation method in a microtubular solid oxide. We ﬁnd that, despite the preheating, the excess air ﬂow commonly supplied in the practical applications for the convective cooling is the prevailing factor on the temperature variations causing a signiﬁcant temperature gradient in the air inlet region, that poses a high risk of mechanical failure. In terms of the ﬂow conﬁguration, counter-ﬂow shows larger temperature and current variations. The impedance variations clarify the impact of the temperature distribution on the current variations. Namely, high temperature in the fuel upstream accompanied with the high hydrogen concentration boosts the local current density, thus, results in larger Nernst-loss in the downstream wherein temperature is lower as well. We conclude that the excess air ﬂow indirectly contributes to the thermal stresses and thus we recommend the reduction of the excess ﬂow.

The thermal stresses are accounted for the mechanical failure of solid oxide fuel cells (SOFC). [1][2][3] To resist the thermal stresses at maximum achievable electrochemical performance, SOFCs are designed in various forms, for instance flat-tubular, tubular, and planar, etc. For in-situ investigating the properties spatially varying regardless of the SOFC form, microtubular SOFCs (mt-SOFCs) are quite practical owing to the simple form. Besides, a mt-SOFC with a small diameter can represent a unit gas flow channel in other forms. We thus elaborate the temperature, current, and concentration variations in mt-SOFCs.
A mt-SOFC fundamentally consists of three main components, anode, electrolyte, and cathode. The cell fabrication requires sequential high temperature heat-treatment processes (1473-1673 K) for each component, thus, the induction of the residual stresses to the cell is inevitable. 1,2,4,5 Because the components are made of distinct ceramicbased materials, they possess diverse intrinsic coefficients of thermal expansion (CTE). Selimovic et al. reports the CTEs of Ni/YSZ, 8YSZ, and LSM as 13 × 10 −6 , 10 × 10 −6 , 11 × 10 −6 1/K, respectively. The CTE and temperature are the main parameters determining the thermal strain of materials as Eq. 1 states ε th = α (T − T ref ) [1] where ε th is the thermal strain, α (1/K) the CTE, T (K) temperature, and T ref (K) the stress-free reference temperature. According to Eq. 1, even a small difference among the CTEs of the components can result in thermal stresses due to the high operation temperature of mt-SOFCs. 1,2,4,6,7 The cell components are hence required to be made of materials featuring similar CTEs. Even if the materials exhibit similar CTEs, longitudinal temperature variations over the cell surface induce thermal stresses. [1][2][3][4][6][7][8][9] While a cell is operating with hydrogen and -excess air-, due to the electrochemical hydrogen oxidation reaction (HOR)  [3] where j 0 (A/cm 2 ) stands for the exchange current density, c * i (mol/m 3 ) the concentration of the species i on the triple phase boundary, α the symmetry coefficient for the HOR, n the number of moles of electron per molecule of hydrogen, F (C/mol) the Faraday's constant, η (V) the mixed overpotential arising from both the activation and concentration limitations, R (J/mol K) the universal gas constant, and T (K) temperature.
While generating electricity in the cell, the heat fluxq tot (W/m 2 ) can be described aṡ q tot (x) = T (x) Ṡ + j (x) (η rev (x) + η irev (x)) [4] where η rev (V) is the overpotential associated with the Nernst-loss and η irev (V) the irreversible overpotentials composed of the activation, ohmic and concentration overpotentials. Herein, the variation in the entropy due to the temperature variations is neglected. Based on this description, the longitudinally growing Nernst-loss contributes to the temperature variations. [10][11][12][13] Besides, in the practical systems, air is blown at high velocities (excess amounts) to removeq tot via the convective cooling that intuitively influences the longitudinal temperature variations. 7,[14][15][16][17] On the other hand, alike the activation and concentration overpotentials (Eq. 3), the ohmic overpotential η ohm (V) is a function of temperature η ohm (x) = j (x) /σ el (x) [5] via the ionic conductivity of the electrolyte σ el (x) (S/m) usually defined as where σ 0 is the pre-exponential constant, E a (J) the activation energy for the ionic conduction, and k (J/K) the Boltzmann constant. Since temperature affects the overpotentials, the longitudinal temperature variations are anticipated to influence the current variations. Thereby, in-situ investigation of the impact of the longitudinal temperature variations on the current variations has been of interest, too.

F217
The experimental difficulties in measuring the longitudinal temperature and current variations over the cell surface due mainly to the high operation temperature of SOFCs have been leading researchers to create numerical models. 9,18 Researchers have been developing thermoelectrochemical models by which they have been exploring the longitudinal variations of temperature, current, and concentration of the concerning species. They have been transferring the temperature variations to the Finite Element Method (FEM) models for predicting the induced thermal stresses. 1,2,6,7,19 Although the thermo-electrochemical models are usually validated with experimental current-voltage (I-V) curves, they are hardly validated in terms of the in-situ measured temperature variations.
For in-situ measuring the longitudinal temperature variations, there have been valuable attempts indeed. Morel et al. have predicted the temperature variations over a planar cell relying on the impact of temperature on the ionic conductivity. 9 Razbani et al. have reported the gas temperature variations measured by thermocouples positioned in the gas stream of a planar SOFC. 3 Santarelli et al. measured the local temperatures at the inlet, middle and outlet of a 1.5 m long tubular cell bundle; unfortunately, they do not provide sufficient information on the positions of the thermocouples. 20 To investigate the endothermic cooling associated with the internal reforming of syngas, recently we in-situ acquired the longitudinal temperature and current variations along a mt-SOFC by the electrode-segmentation method. 13 In order to alleviate the temperature variations contributing to the thermal stresses, in this study, we explore the effect of the involving processes on the temperature variations in mt-SOFCs. Regarding as the main involving processes, we focus on the current variations and the convective heat transfer due to the fact that air is extensively fed at excess rates for the cooling purpose in the practical systems. Thereby, we analyze the variations with the co-and counter-flow configurations. We conduct the analyses based on the spatial properties in-situ measured through the electrode-segmentation method, that distinguishes our study from the above mentioned studies. In addition to the thermal stresses, we also show the influence of the temperature variations on the current and concentration variations via analyzing the spatial impedance variations.

Experimental
Spatial characterization method: electrode-segmentation.-In order to characterize the local properties that are spatially varying, the electrochemical active area (EASA) of a fuel cell can be divided into electronically isolated small partitions. We refer to these partitions hereafter as "segments". The segments can be separately connected to thermocouples, electric loads, and frequency response analyzers (FRA), etc. for measuring the local temperature, current, and impedance, etc. By analyzing the longitudinal variation of these local properties, we can elaborate the concerning physical and electrochemical processes, such as ionic conductivity, kinetic limitations, and mass transport limitation, etc. 12,13 We call this spatial characterization method "segmentation". Especially in polymer electrode membrane fuel cells, the segmentation is usually realized on the gas distribution plates due to practical restrictions. In this method, because the EASA is not divided into segments, there might be current flow in the lateral direction depending on the potential difference between the segments, that might affect the accuracy of the measurements. In SOFCs, however, the ceramic-based components enable the segmentation on the EASA. We thus divided the cathodes of the anode supported mt-SOFCs into segments as shown in Fig. 1. We hence call this method more specifically "electrode-segmentation".
The resolution of the spatial characterization is dependent on the dimension of the segments. As the dimension of the segment reduces, the resolution increases. This in turn enlarges the total electronic isolation area among the segments. With the larger isolation area, the deviation among the measured and the intrinsic values grows. 12,13 Moreover, the configuration of the peripheral equipment becomes practically more difficult. Considering all these parameters, we divided the cathode of the cell into three segments as shown in Fig. 1.

Longitudinal
temperature, current, and impedance measurements.-The segment temperatures were sensed on the cathode surfaces by K-type thermocouples, separately. The segment currents were measured through three electrical loads (ELZ 175, Keisoku Giken Co. Ltd.), separately connected to the segments as depicted in Fig. 1. We carried out the electrical measurements by the four point probe method to eliminate the peripheral resistances. In addition to the segmentation of the cathode, we ensured the uniform voltage distribution along the cell with the potentiostatic mode that prevents the lateral current flow among the segments. At a voltage, the temperatures and currents were simultaneously recorded by a data logger (midi LOGGER GL800, Graphtec Co. Ltd.) per 200 ms for at least 30 s. The acquired current and temperature data populations are averaged and plotted. The standard deviation for the current measurements is approximately 0.01 whereas it is circa 0.1 for the temperature measurements.
We measured the segment impedances at a DC voltage of 0.7 V to identify the variations under the realistic conditions. We used an NF 5022 FRA (NF Co. Ltd.) that swept the frequency from 100 kHz to 0.1 Hz for an AC perturbation voltage of 10 mV (pk-pk). With the same FRA and settings, we measured the segment impedances sequentially. Due to the instability between 100 kHz-10 kHz that presumably arose from the incompatibility among the FRA and the external electric load, we could not measure the ohmic resistances (high frequency resistance) of the segments. To measure the ohmic resistance, we employed a Solartron 1280Z FRA (Solartron Analytical) that ensured the compatibility between the FRA and its internal electric load (no external electric load).

Fabrication of the cathode-segmented anode-supported microtubular SOFC.-
We preferred a commercial tubular anode substrate that is manufactured by Repton Co. Ltd. The substrate was composed of NiO/YSZ (65:35 wt%). Upon reduction, this substrate yields a porosity of ∼37%. We dip-coated the substrates with 8YSZ electrolyte and then sintered at ∼1700 K for two hours. By masking the electronically-isolated areas for the electrode-segmentation, we brushcoated the cathode slurry of LSM/YSZ (La 0.7 Sr 0.3 MnO 3 /YSZ,10:3 wt%, Daiichi Kiganso Kagaka Kogyo Co. Ltd.) onto the electrolyte surface. We sintered the cathodes at ∼1323 K for two hours, so that we obtained the cells resemble the one in Fig. 1. Moreover, we coated silver-paste onto the cathode (segment) surfaces to enhance the electronic conductivity. Finally, thermocouples and silver wires were connected for temperature, current, and impedance measurements.
Cell operation conditions.-Prior to the gas supply, the segment temperatures were risen to ∼1073 K by an electric furnace depicted in Fig. 1. Though the cell was placed in a quartz tube to prevent the heat loss to the surrounding for maintaining a constant temperature along the cell, the segment temperatures slightly (±1 K) diverged, which is in the precision range of the thermocouples. 21,22 The fuel inlet tube was preheated to avoid the convective cooling in the anode side. The fuel outlet tube was also heated to inhibit the condensation of the product water vapor. On the cathode side, the inlet air temperature was raised about 1048 K by the electric furnace before reaching the cathode surface. From this perspective, we can state that the air was preheated as well. The flow configuration was switched between coand counter-flow by simply exchanging the fuel inlet and outlet, i.e., the air flow direction was kept the same, as Fig. 1 illustrates. Gas flow rates were metered at 298 K and 100 kPa with mass-flow-controllers (SEC-E40MK3, Horiba STEC) governed by LabVIEW 8.6. In order to reduce NiO to Ni, a dry mixture of H 2 /N 2 = 40/40 cm 3 /min (99.99% pure) was initially fed to the anode for two hours.
Although we have devoted this study to the fundamental understanding of the temperature variations, as pointed out in the previous paragraphs, we paid a particular attention on choosing the experimental conditions (furnace temperature, flow rates, pressure, etc.) appearing in the practical applications. Considering the design of a single mt-SOFC, our experimental setup also resembles that employed in reality. Despite we conduct this study on a single mt-SOFC, a number of mt-SOFCs are bundled for the real applications. Owing to the fact that the same processes involve in the temperature variations, this fundamental study sheds light on the bundles as well.

Results and Discussion
To be consistent throughout the analyses of the variations in the co-and counter-flow configurations, we call the segments "up-, mid-, and down-segments" referring to the positions depicted in Fig. 1. We plot the segment temperatures as "temperature rise ( T seg )" that is the difference between the segment temperature (T seg ) and the furnace The prevailing process on the longitudinal temperature variations.-Since the reversible and irreversible losses are effective on the longitudinal temperature variations, 11,23 and these losses are dependent upon current, elimination of the current variations is essential to disclose the other involving processes. Therefore, we begin our analysis at a high fuel flow rate to keep the fuel utilization low (U f = 29.3% at 0.4 V). Under these conditions with the co-flow configuration, the measured segment I-V curves are depicted in Fig. 2. In this figure, the I-V curves almost overlap, i.e., the current variations are quite small among the segments through the voltage range. Thereby, we expect insignificant temperature variations. Fig. 3 provides sufficient evidence to justify our expectation for the longitudinal temperature variations. In this figure, all the segment temperatures are higher than the furnace temperature at open circuit voltage (OCV). The temperature rise at OCV stems from the combustion of the leaking hydrogen that mainly occurs around the sealant (Aremco, Ceramabond 552) among the cell and metal holders. The  extent of the hydrogen leakage can be estimated via analyzing the heat balance within the system. For this analysis, the initial state of the system right after the hydrogen and air supply was regarded; and the segment temperatures were in-situ measured as plotted in Fig. 4.
In the transition state, the total heat production rate Ḣ HOR (kW) is released via the combustion of the leaking hydrogen ṅ H2 (mol/s) Ḣ HOR = h HOR ṅ H2 [8] ṅ H2 =ṅ H2,in −ṅ H2,out =ṅ H2,leak [9] While Q cell (kJ) is absorbed by the cell,Q conv (kW) is simultaneously removed by the air flow via the convective heat transfer on the cathode surface. Owing to the relatively low heat conductivity of the sealant (k = 30 W/mK 24 ), the conductive heat transfer to the adjacent piping is neglected. Since the segment surfaces are coated with silver-paste that resembles the gray body (poor radiative properties), the radiative heat transfer is ignored, too. 25 In this regard, the heat balance within the system can be formulated as conv dt [10] Herein the time interval for the temperature rise in the segments t = 140 s from Fig. 4. When the Q cell andQ conv are calculated,ṅ H2,leak (mol/s) can be found. Due to the varying thermo-physical property of the cell components [11] where the subscript "a" stands for the anode, "el" for the electrolyte, and "c" for the cathode. For i ∈ (a, el, c) where V (m 3 ) represents the solid volume of the cell. The density ρ and the heat adsorption coefficient C p of the cell components are given as 3310, 5160, and 3030 (kg/m 3 ); and 450,470, and 430 (J/kgK) for Ni/YSZ (anode), 8YSZ (electrolyte), and LSM/YSZ (cathode), respectively. 16,26 According to the Newton's law where A (m 2 ) is the surface area over which the convection takes place and the heat transfer coefficient h = 2.8 W/m 2 K calculated from the Nusselt number which is accepted due to the rather low Reynolds number (Re = 6.98 2300 (laminar flow)). 27 Herein, D h (m) is the hydraulic diameter and k (W/mK) the heat conductivity of air. T ∞ = 1048 K is taken from Fig. 4. Considering the arithmetic average temperature of the segments at t = 140 s as T cell = T seg,up + T seg,mid + T seg,down /3 [15] The fuel leakage ratė n H2,leak /ṅ H2,in × 100 = 0.77 [16] Such amount of leakage rate is acceptable considering the operation at high temperature. In Fig. 3 the slight temperature drops with the rising segment currents in the low current density region are associated with the reduction in the fuel leakage rate owing to the increasing consumption of hydrogen by the electrochemical reaction. Though the up-and downsegments are nearest to the main combustion areas (sealant), at OCV the down-segment exhibits the smallest temperature whereas the midand up-segments' temperatures are similar and rather high. Since the cell is positioned in the geometrical centre of the furnace, and the segment temperatures were set approximately the same prior to the gas supply, we do not expect such variations from the radiative and conductive heat transfers upon supplying the gases. Thereby, we ascribe this temperature distribution profile to the convective heat transfer. In fact, this argument is verified by Fig. 5 wherein the temperature of the down-segment at 0.7 V significantly drops with the rising air flow velocity. Note that no mass transport limitation exists in the cathode side in this velocity domain.
As Fig. 1 displays, the convective heat transfer is occurring in two distinct interfaces: firstly, between the quartz tube and air, secondly, between air and the cell. The air is initially heated about 1048 K (Fig. 4) by the quartz tube which is in direct contact with the furnace. This heated air proceeds along the cell; and cools it down. Although the flow velocity range shown in Fig. 5 is quite small, forming laminar flow (Re = 6.98 at 2.0 cm/s), the thermal boundary layer is not developed within the entrance region of the cell. This means that the flow in the entrance regions is not laminar yet. As a result, the local Nusselt number/heat transfer coefficient within the entrance region of the cell is higher than what we assumed while estimating the hydrogen leakage rate 8,25 and it is a function of the flow velocity. The entrance length L h (m) is given as 25 L h ≈ 0.05ReD h [17] From Eq. 17, L h = 12.9 mm can be calculated, being slightly longer than the length of the down-segment (9 mm). The down-segment's temperature is thus highly affected by the air flow velocity. In this  respect, the hydrogen leakage is anticipated to be somewhat higher than 0.77%. However, the flow is fully developed around the midsegment, so that the mid-and up-segments exhibit similar temperatures. As a result, the temperature gradient becomes significant along L h . Assuming that temperature rises from the air inlet along the L h linearly, and T seg,down = 12 K represents the local temperature at x = 4.5 mm, the longitudinal temperature gradient ∂ T /∂x = 4000 K/m. According to Chiang et al., the temperature gradient must be below 2666 K/m to inhibit the crack formation. 19 Besides, 4000 K/m is relatively higher than what is estimated to be small by Fischer et al. 1 Regarding these references, the temperature gradient developing in the entrance length is likely to pose crack formation.
Since temperature is effective on the involving physical and electrochemical processes (ionic conductivity, kinetic, etc.), such a longitudinal temperature distribution profile points out the limitation in the down-segment by the lower temperature that probably reduces the local fuel utilization and thus lets the mid-and up-segments to produce larger currents owing to their higher temperatures. Ultimately, the current variations become quite small as shown in Fig. 2. This hypothesis can be justified by switching the gas flow configurations to counterflow (reversing the fuel flow direction), so that the up-segment would receive the highest hydrogen concentration with similar longitudinal temperature distribution profile by the prevailing impact of convective heat transfer.
Upon switching the gas flow configuration to counter-flow, we measured I-V curves depicted in Fig. 6. In contrast to the I-V curves measured with the co-flow configuration, we observe current variations among the segments despite the low fuel utilization (U f = 31% at 0.4 V). The mid-and up-segments produce higher currents than the down-segment through the voltage range. In terms of the flow configuration, at 0.4 V the counter-flow configuration enhances the midand up-segments' currents while the down-segment's current remains nearly the same. As a result, the fuel utilization (total current output) at 0.4 V with counter-flow is slightly higher than that observed with co-flow.
In fact, the longitudinal current variation profile in Fig. 6 resembles the longitudinal temperature variation profile shown in Fig. 7, which is acquired with the counter-flow configuration. This resemblance justifies our hypothesis that the temperature variations affect the current variations. In Fig. 7, the development of such a temperature distribution profile at OCV again confirms the prevailing impact of convective heat transfer. This prevailing impact can be clearly seen in Fig. 8 as well. Alike the co-flow case (Fig. 3), herein, the segment temperatures are higher than the furnace temperature at OCV, that stems from the As we have shown in the previous figures, the mid-and upsegments exhibit similar temperatures owing to the convective heat transfer. While analyzing the effect of the longitudinal temperature variations on the concerning processes in the next subsection, we will thus consider only the up-segment's temperature for the sake of simplicity.
Influence of the temperature variations on the ohmic resistance along the cell.-As mentioned previously, assuming that the main contribution to the ohmic resistance of an SOFC comes from the ionic resistance, Morel et al. proposed a method for predicting the temperature variations over a cell comprised a rather thick (500 μm) electrolyte by using the relationship between the ionic conductivity and temperature given by Eq. 6. In fact, the thickness of the electrolyte in our study is relatively smaller (∼20 μm), and approximately constant along the cell. However, the significant temperature variation between the down-and up-segments depicted in Figs. 5 and 8 causes notable ohmic resistance difference between them. Table I presents  the resistances measured by impedance spectroscopy for the co-and counter-flow configurations. At 1.0 cm/s, the ohmic resistance in the down-segment is ∼16% higher than that in the up-segment with both flow configurations. As the air flow velocity increases, the down-segment's temperature drops (Figs. 5 and 8), which results in higher local ohmic resistance. In contrast, the temperature of the up-segment is weakly dependent on the air flow velocity, thus, the ohmic resistance of this segment changes slightly. Consequently, the resistance difference along the cell rises. This implies that at a constant cell voltage, the down-segment suffers from both ohmic and kinetic limitations that influence both the current and temperature variations.

Longitudinal current variations arising from the nernst-loss coupled with the temperature variations.-While
analyzing the impact of the convective heat transfer on the longitudinal temperature variations in the preceding subsection, high fuel flow rate (low fuel utilization) was opted to eliminate the contribution from the Nernst-loss. This analysis has disclosed the effect of the temperature variations on the current variations (counter-flow). However, we are aware of the fact that the Nernst-loss in the realistic fuel flow conditions is significant. 12 Therefore, we will analyze the impacts of both temperature variations and Nernst-loss on the current variations under the realistic conditions in the following. Fig. 9 illustrates the longitudinal current variations measured at the realistic fuel flow conditions with the co-flow configuration. In comparison to the high fuel flow rate, herein the fuel utilization is rather high (U f = 50% at 0.4 V). As a result, the current variations are larger, especially at lower voltages. Despite the higher temperature of the up-segment shown in Fig. 10 (mid-and up-segments have similar Figure 9. I-V curves of the segments with the co-flow configuration for H 2 /N 2 = 40/40 cm 3 /min and Air = 500 cm 3 /min. Figure 10. Impact of the convective heat transfer on the segment temperatures at 0.7 V with the co-flow configuration for H 2 /N 2 = 40/40 cm 3 /min. 500 cm 3 /min is equivalent to 0.5 cm/s. temperatures), the lower performances of the mid-and up-segments indicate that the Nernst-loss is limiting factor. On the other hand, the longitudinal current distribution profile is different, i.e., the upsegment exhibits better performance than the mid-segment. Taking merely the continuous hydrogen consumption into account, such a current distribution profile would not be acceptable. However, it is known that the increasing concentration of the product water favors the HOR to an extent. 13,28 Relying on the development of a similar longitudinal temperature distribution profile with the counter-flow configuration owing to the prevailing convective heat transfer, we can analyze the interrelation among the temperature and current variations. We will carry out this analysis on Fig. 11 that presents the I-V curves measured under the realistic conditions with the counter-flow configurations. Herein, the current variations are quite large and they become larger with the rising fuel utilization (decreasing cell voltage). Beyond 0.5 V, the down-segment's current reduces whereas the other segments' currents rise; namely, the down-segment experiences severe fuel depletion. In comparison to the co-flow case (Fig. 9), the longitudinal current distribution profile is distinct as well. Since the only difference between Figs. 9 (co-flow) and 11 (counter-flow) is the fuel flow direction, we  can attribute the large current variations to the high temperature of the up-segment (Fig. 12) that boosts the local current production. Eventually, the Nernst-loss becomes more significant in the down-segment, changing the longitudinal current distribution profile.
Even though the longitudinal temperature and current variations at low fuel utilization conditions are analogous in terms of the flow configurations, they become rather different under the realistic operation conditions where the temperature and concentration variations couple. Through the analyses of Figs. 9-12, it is evident that the temperature and current variations are larger with the counter-flow configuration. The larger temperature and current gradients are in good agreement with the numerical studies which estimates quantitatively higher gradients indeed. 6,15,17 The boost in the up-segment's current production attributed to the high local temperature (Fig. 12) can be elaborated through the impedance analysis in a wide frequency range. In fact, we have already discussed the ohmic resistance of the up-and down-segments on Table I. We have concluded that the up-segment exhibits smaller ohmic resistance owing to its higher temperature. The effect of the high temperature on the other processes will be analyzed through longitudinal impedance variations.
Impedance spectra of the up-and down-segments measured with the counter-flow configuration are illustrated in Fig. 13. Though it is not easy to distinguish, we can define three different frequency ranges, ∼10 kHz − 376 Hz, ∼376 Hz − 4 Hz, and ∼4 Hz − 0.1 Hz, as the high frequency impedance (HFI), the medium frequency impedance (MFI), and the low frequency impedance (LFI), respectively. Herein, the significant impedance difference in the MFI and LFI of the segments is obvious. This notable impedance difference confirms the I-V curves depicted in Fig. 11. Namely, the total impedance is remarkably smaller in the up-segment that operates at high temperature (Fig. 12) and receives hydrogen at the highest concentration. Owing to the small impedance, the up-segment's current is boosted, so that the Nernstloss rises toward the down-segment. As a result, the down-segment does not only suffer from the Nernst-loss, but also from the rather low temperature shown in Fig. 12.
In contrast to the counter-flow, with the co-flow configuration the longitudinal temperature variations (Fig. 10) promote the uniformity of the current production along the cell. Fig. 14 depicts the impedance spectra of the up-and down-segments acquired with the co-flow configuration. Due to the lower temperature in the down-segment, the MFI is larger than that of the up-segment implying the higher activation impedance. Despite the highest hydrogen concentration delivered to this segment, current production is kinetically limited. This limitation favorably restricts the boost in the Nernst-loss. Although the up-segment receives hydrogen at a smaller concentration, the total impedance of this segment is smaller than that of the down-segment owing to the higher temperature and restricted Nernst-loss. Namely, the current distributions are levelled by the temperature variations. As a result, the further temperature variations stemming from the current variations are mitigated.
Comparison of the "upstream" segments in the co-and counterflow configurations supports the coupling of the temperature and current variations. Herein the "upstream" segment refers to the segment that receives the highest hydrogen concentration, i.e., the up-segment in the counter-flow case (Fig. 13) whereas the down-segment in the co-flow case (Fig. 14). Fig. 15 plots the impedance spectra of the upstream segments in both flow configurations. In this figure, the difference between the impedances of the up-and down-segments comes from the temperature difference. As the up-segment operates at higher temperature (Figs. 10 and 12), the MFI and LFI in this segment are smaller. Consequently, the current in the up-segment is boosted, resulting in larger Nernst-loss in the down-segment and eventually increasing the current variations (Fig. 11). In contrast, the down-segment operates at lower temperature that raises the MFI and thus reduces the   Nernst-loss. Ultimately, the longitudinal current variations become smaller (Fig. 9).
Since the activation and mass transport (including the Nernst-loss) impedances are coupled in the previous impedance analyses, the sensitivity of the local impedance to the temperature cannot be observed evidently. Yet, due to the direct impact of the convective heat transfer on the down-segment's temperature, it is possible to control the temperature of this segment at the same hydrogen concentration owing to the almost constant currents in the mid-and up-segments for identifying the effect of the local temperature on the local impedance. With this intention, we measured the impedance spectra of the down-segment at various air flow velocity with the counter-flow configuration as plotted in Fig. 16. In this figure, the sensitivity of the MFI and LFI to the local temperature is clearly shown. As the air flow velocity rises, the down-segment's temperature drops (Fig. 12), which in turn increases the MFI and LFI in this segment.

Conclusions
Aiming the mitigation of the longitudinal temperature variations that give rise to the thermal stresses, we investigated the contribution of the processes involving in the temperature variations in a microtubular solid oxide fuel cell. Giving particular emphasis on the current variations and the convective heat transfer, we conducted the analyses on the properties which we in-situ obtained by the electrodesegmentation method for the co-and counter-flow configurations. In order to disclose the impact of the temperature variations on the current variations, we elaborated the interrelationship among the temperature, current, and impedance variations. Through these analyses, we reach the following conclusions: 1. Air flow at excess rates dominate on the longitudinal temperature variations causing a remarkable temperature gradient in the air entrance region, that poses high risk of mechanical failure. 2. In terms of the flow configuration, counter-flow exhibits larger temperature, current, and impedance variations than the co-flow configuration. 3. Although the current variations are reduced in the co-flow configuration, they are enhanced in the counter-flow configuration by the temperature variations. 4. Despite the preheating, the air flow velocity exhibits substantial impact on the longitudinal temperature distribution and thus on the current variations. We hence anticipate that the reduction of the excess air flow would alleviate the variations and the associated thermal stresses.