Optimization of Novel Variable-Channel-Width Solid Oxide Electrolysis Cell (SOEC) Design for Enhanced Hydrogen Production

Abstract

This study presents a novel solid oxide electrolysis cell (SOEC) design with variable channel widths to optimize thermal management and electrochemical performance for enhanced hydrogen production. Using high-fidelity computational modeling in COMSOL Multiphysics 6.1, five distinct channel width configurations were analyzed, with a baseline model validated against experimental data. The simulations showed that modifying the channel geometry, particularly in Scenario 2, significantly improved hydrogen production rates by 6.8% to 29% compared to a uniform channel design, with the effect becoming more pronounced at higher voltages. The performance enhancement was found to be primarily due to improved fluid velocity regulation, which increased reactant residence time and enhanced mass transport, rather than a significant thermal effect, as temperature distribution remained largely uniform across the cell. Additionally, the inclusion of a dedicated heat transfer channel was shown to improve current density and overall efficiency, particularly at lower voltages. While a small increase in voltage raised internal cell pressure, the variable-width designs, especially those with widening channels, led to greater hydrogen output, albeit with a corresponding increase in system energy consumption due to higher pressure. Overall, the findings demonstrate that strategically designed variable-width channels offer a promising approach to optimizing SOEC performance for industrial-scale hydrogen production.

1. Introduction

To address the challenge of reducing CO₂ emissions in energy-intensive industries such as steelmaking—which account for nearly 7% of global emissions and heavily depend on hydrogen—it is essential to develop alternatives to fossil fuel–based reformers [1,2,3]. Hydrogen production through electrolysis technologies, including solid oxide electrolysis cells (SOECs, 700–900 °C) [4], proton exchange membrane (PEM, 100–150 °C) [5], and alkaline (AK, 60–120 °C) [6] electrolyzers, provides a sustainable option compared with conventional steam methane reforming (SMR) [7]. Unlike SMR, which consumes fossil fuels and generates 9–12 kg of CO₂ per kilogram of hydrogen [8], electrolysis relies solely on water and electricity, producing no direct carbon emissions when powered by renewable energy sources [9]. Moreover, because water electrolysis becomes increasingly endothermic at elevated temperatures, SOECs can effectively utilize external heat from renewable sources such as solar thermal, wind, or nuclear energy, thereby lowering the electrical energy demand for hydrogen generation [10,11].

Recent progress in SOEC research has centered on optimizing flow configurations—namely co-flow, counter-flow, and cross-flow—to improve thermal uniformity and hydrogen generation. Using coupled CFD and FEM simulations, Lim et al. [12] showed that non-uniform temperature gradients intensify stress concentrations, especially at interfaces between materials with different thermal expansion coefficients. Their analysis revealed that around 85% of the irreversible heat is generated by activation overpotentials in the fuel and air functional layers and ohmic losses from oxygen ion transport under conditions of 0.6944 A/cm² current density, 1.418 V cell voltage, and 600 °C inlet temperature. Xu et al. [13] develop a 3-D multi-stack SOEC model to examine electrolysis performance and coupled electricity–heat–gas fields across six stack arrangements, evaluating uniformity with dedicated indices and dimensionless metrics. Similarly, Wang et al. [14] used 3D modeling to demonstrate that optimized flow field configurations enhance both heat and mass transfer, resulting in more uniform temperatures and higher hydrogen yields.

The same interesting ideas for channel changes can be found in other articles. Der and Bertola [15] experimentally mapped co-current oil–water flow in a horizontal serpentine microchannel using high-speed imaging while independently varying the phases’ superficial velocities. They show that curvature-induced secondary flows shift flow-pattern transition boundaries compared with straight channels, yielding a distinct flow-pattern map relevant to mixing and residence-time control. The authors fabricate the device by cutting the serpentine path in a black polypropylene sheet, sandwiched between transparent polypropylene layers and bonded by selective laser welding, enabling clear optical access while maintaining robust sealing. By systematically scanning flow-rate pairs, they construct a flow-pattern map specific to the serpentine layout, demonstrating how curvature promotes enhanced interfacial deformation and mixing and thus alters transition thresholds. Overall, the work shows that channel curvature is a first-order design variable for controlling immiscible two-phase microflows, with direct implications for microfluidic mixing, residence-time management, and phase-contact engineering. Alexander et al. [16] investigated immiscible oil–water plug flow in serpentine microchannels with multiple high-curvature bends (β = 1) at an ultra-low viscosity ratio (λ = 0.001), showing that curvature-driven acceleration/deceleration elongates plugs linearly with capillary number and can even cause plug rupture. Alexander et al. further used laser-induced fluorescence and particle-tracking velocimetry to reveal curvature-induced vortices in aqueous plugs and curvature-dependent structures in oil slugs, defining operating windows that enhance mixing and mass transfer.

Recent studies have started to close this research gap by integrating electrochemical potential distribution and degradation kinetics into their analyses. Virkar et al. [17], in a seminal contribution, developed an analytical framework that captures the spatial variations of electronic potential, oxygen chemical potential, and the resulting interfacial oxygen partial pressure across the electrolyte. This model established the thermodynamic basis for evaluating delamination mechanisms. Building on this, Udagawa et al. [18] modeled a cathode-supported intermediate-temperature SOEC designed for steam electrolysis. Their steady-state simulations showed that at an operating current density of 7000 A/m² and a steam inlet temperature of 1023 K, the stack required approximately 3 kWh per Nm³ of hydrogen produced—substantially lower than the energy consumption of conventional low-temperature electrolyzers. This underscores the superior efficiency of intermediate-temperature SOECs (IT-SOECs) for hydrogen production. In another study, Zeng et al. [19] analyzed the effect of anode porosity on thermal stress patterns in a planar anode-supported SOFC. They found that porosity strongly influences both the magnitude and distribution of thermal stresses, with higher porosity levels (30–40%) lowering stresses by as much as 25% compared to lower porosity ranges (10–20%).

These papers review the materials, synthesis, mechanisms, and system integration of advanced solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs) [20,21,22,23,24,25,26,27,28]. Zhu et al. [29] presented a hybrid modeling approach to optimize the dynamic performance of solid oxide electrolysis cells (SOECs) and demonstrated that allowing for a slight deviation from thermal neutrality can enhance overall efficiency and reduce the cost of syngas production. To produce syngas, the total conversion rate is highest at thermal neutrality, but absorbing a small amount of heat actually boosts overall efficiency to 83.9% and lowers the production cost to just $0.31 per kilogram. Liang et al. [30] proposed a new control strategy for solid oxide electrolysis cells (SOECs) that adjusts the steam flow rate to neutralize internal heat, effectively stabilizing cell temperature and maintaining high efficiency despite rapid fluctuations in solar power. Their results showed that conventional control strategies, which increase airflow rates, are inadequate in effectively suppressing the rate of temperature variation in scenarios of drastic changes in solar power. The novelty of this study lies in being the first to systematically introduce and analyze variable channel-width designs in planar solid oxide electrolysis cells (SOECs) to optimize for both maximum hydrogen production.

This work is, to the best of our knowledge, the first systematic SOEC study of variable-width (tapered) channels as a design lever for residence-time control and maldistribution mitigation, evaluated alongside a dedicated heat-transfer channel in a single multiphysics framework. In contrast to recent flow-field studies that modify waviness or cross-sectional shape to boost mass/heat transfer, we vary the channel width along the flow path and show that widening profiles can lower outlet velocity, raise residence time, and increase H₂ production without materially changing temperature uniformity.

2. Materials and Methods

2.1. Geometry Model

This study investigates a novel variable channel width SOEC design to optimize thermal management and electrochemical performance. The cell’s multi-layered structure, illustrated in Figure 1, includes interconnectors, cathode and anode gas diffusion layers (AGDLs) and electrodes (AGDEs), an electrolyte membrane, and a dedicated heat transfer channel. The materials employed are Ni-stabilized ZrO₂ (Ni-YSZ) for the anode AGDL/AGDE, Sr-doped LaMnO₃ (LSM) for the cathode CGDL/CGDE, Y₂O₃-stabilized ZrO₂ (8YSZ) for the electrolyte, and stainless steel for the separator. The analyzed SOEC has an active area of 64 mm × 60 mm. The electrolyte and both GDEs have a uniform thickness of 15 μm, while the cathode and anode AGDL-CGDL are 50 μm and 25 μm, respectively. All channels are designed in a spiral configuration. To evaluate the impact of channel geometry on performance, five distinct width configuration scenarios were designed, moving beyond a simple uniform design. The base geometry (Scenario 1), shown in Figure 1, features a cathode channel width of 0.8 mm, an anode channel width of 1 mm, and corresponding rib widths of 1 mm and 2 mm. As can be seen in Figure 2, The subsequent scenarios systematically vary these cathode and anode channel and rib widths to assess their influence on gas distribution, pressure drop, and reaction kinetics. The flow in each of the 20 parallel channels per inlet is routed through semicircular paths to minimize pressure drop. The complex geometry, particularly in the variable-width scenarios, required high-fidelity computational modeling. The design was analyzed using COMSOL Multiphysics 6.1. A mesh independence study was conducted, resulting in a high-resolution mesh with approximately 580,000 elements for the base model (Figure 1), with key parameters like porosity, tortuosity, and density detailed in

Table 1. Key parameters for CGDL, CGDE, AGDL, AGDE, and electrolyte membrane.

Property	Cathode Gas Diffusion Layer (CGDL)	Cathode Gas Diffusion Electrode (CGDE)	Anode Gas Diffusion Layer (AGDL)	Anode Gas Diffusion Electrode (AGDE)	Electrolyte Membrane
Material	Sr-droped LamnO3 (LSM)	Sr-droped LamnO3 (LSM)	Ni-stabilized ZrO2 (YSZ)	Ni-stabilized ZrO2 (YSZ)	Y2O3-stabilized ZrO2 (8YSZ)
Area (mm × mm)	64 × 60	64 × 60	64 × 60	64 × 60	64 × 60
Thickness (mm)	0.5	0.015	0.025	0.015	0.015
Porosity (%)	0.4	0.4	0.4	0.4	-
Permeability (m2)	10–11	10–10	10–11	10–10	-
Density (kg/m3)	6100	6100	5800	5800	6050
Exchange Current Density (A/m2)	-	5300	-	2000	-
Electronic Conductivity (S/m)	-	1000	-	1000	$3.34\times {10}^4\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{-10300}{T}}\right)$

. The computational intensity of the models necessitated the use of a supercomputer equipped with 7 terabytes of memory to obtain converged and accurate results. By analyzing these variable-width configurations and flow directions, this study provides critical insights into optimizing flow paths and geometry in industrial-scale SOECs to enhance hydrogen yield and overall system efficiency. As can be seen in Figure 3, the channel widths varied using an arithmetic progression, starting from a minimum value of 0.2 Wch. To isolate residence-time effects, we imposed an arithmetic progression of channel widths along the flow direction, generating five scenarios that span the practical tapered-channel space (uniform baseline; monotonic widening; monotonic narrowing; symmetric wedge; piecewise step). Such geometric grading is informed by serpentine-channel literature where curvature-driven secondary flows and local acceleration/deceleration strongly affect mixing and interfacial transport, thereby shaping residence-time distributions.

2.2. Electrochemical Model

The electrochemical behavior of the SOEC is described by the relationship between the output voltage V, the open circuit voltage V_OC, and the various voltage losses (overpotentials), expressed as [31]:

$$V=V_{OC}+{\eta }_{actication}+{\eta }_{ohmic}+{\eta }_{concentration}$$

(1)

The open circuit voltage V_OC is calculated based on the Nernst equation, which accounts for temperature and partial pressures of reactants and products [31]:

$$V_{OC}=V^0+{\displaystyle \frac{RT}{2F}}\mathrm{l}\mathrm{n}({\displaystyle \frac{P_{H_2\times }{P}_{O_2}^{1/2}}{P_{H_{2}O}}})$$

(2)

The voltage losses, or overpotentials, as divided into activation, ohmic, and concentration components, are calculated as follows:

Activation overpotential at the anode and cathode:

$${\eta }_{act,anode}={\displaystyle \frac{RT}{{\alpha }_{a}zF}}{sinh}^{-1}({\displaystyle \frac{J_1}{2J_{0,a}}})$$

(3)

$${\eta }_{act,cathode}={\displaystyle \frac{RT}{{\alpha }_{c}zF}}{sinh}^{-1}({\displaystyle \frac{J_2}{2J_{0,c}}})$$

(4)

Ohmic overpotential due to ionic and electronic resistances:

$${\eta }_{ohmic}=J({\displaystyle \frac{h_{electrolyte}}{{\sigma }_2}}+{\displaystyle \frac{h_{electrolyte}}{{\sigma }_1}})$$

(5)

Concentration overpotential arising from mass transport limitations:

$${\eta }_{conc}={\displaystyle \frac{RT}{zF}}\mathrm{l}\mathrm{n}({\displaystyle \frac{P_1}{P_2}})$$

(6)

As shown in Equations (7) and (8), the volumetric current densities at the anode (J1) and cathode (J2) are determined by the Butler–Volmer equations, which describe the electrode kinetics as a function of overpotential [32]:

$$J_1=J_{0,a}[\exp \left({\displaystyle \frac{{\alpha }_{a}zF{\eta }_{act,anode}}{RT}}\right)-\exp \left({\displaystyle \frac{(1-{\alpha }_a)zF{\eta }_{act,anode}}{RT}}\right)]$$

(7)

$$J_2=J_{0,c}[\exp \left({\displaystyle \frac{{\alpha }_{c}zF{\eta }_{act,cathode}}{RT}}\right)-\exp \left({\displaystyle \frac{(1-{\alpha }_c)zF{\eta }_{act,cathode}}{RT}}\right)]$$

(8)

2.3. Momentum Conservation Model

The momentum transfer within the SOEC is governed by the steady-state Navier–Stokes and continuity equations (Equations (9) and (10)) for ideal gas flow in the channels and Darcy’s law within the porous electrodes. While gas flows through both the electrode channels and their porous structures, the hermetically separated additional channel does not participate in mass transfer to the electrolyte [31]:

$$\rho \left(u.\nabla \right)u=-\nabla \mathrm{p}+\mathrm{\mu }{\nabla }^{2}u+f$$

(9)

$$\nabla .\left(\rho u\right)=0$$

(10)

Within the porous electrodes, where chemical reactions consume and produce species and the porous matrix imposes flow resistance, the Darcy–Brinkman equations govern gas flow. This model extends Darcy’s law by incorporating viscous shear stress effects to accurately describe momentum transport. The governing equation is given by [31]:

$${\displaystyle \frac{\rho }{{ϵ}_p^2}}\left(u.\nabla \right)u=-\nabla .p+\nabla \mu .\left[{\displaystyle \frac{\nabla \mathrm{u}+({\nabla \mathrm{u})}^T}{{\epsilon }_p}}-{\displaystyle \frac{2}{3}}{\displaystyle \frac{\left(\nabla .\mathrm{u}\right)}{{\epsilon }_p}}\right]-({\displaystyle \frac{\mu }{\kappa }}+{\beta }_f\left|\mathrm{u}\right|+{\displaystyle \frac{Q_{mass}}{{ϵ}_p^2}})\mathrm{u}$$

(11)

$$Q_{mass}=\sum _m{R}_m{M}_m$$

(12)

Here κ is the permeability of the porous medium, and other symbols retain their usual meanings. This approach captures the combined effects of pressure gradients, viscous forces, and porous resistance on the gas flow within the electrodes, providing a more accurate representation of momentum conservation in the SOEC porous layers.

Mass transport within the SOEC, driven by convection and diffusion, is modeled using the Maxwell–Stefan equations. In multicomponent gas mixtures, the diffusive flux of one species depends on frictional (momentum-exchange) interactions with all the others. The Maxwell–Stefan (MS) equations capture this coupling and reduce to Fick’s law only in special limits (binary mixture, dilute species, or when cross-coupling is negligible). MS is therefore the consistent choice for high-temperature H₂–H₂O transport in SOEC channels and porous electrodes, where counter-diffusion and baro/thermo-diffusion can matter. To accurately capture the distinct structural properties of the anode, cathode, additional channel, and porous electrodes, as well as the influence of electrochemical reactions, a specific form of these equations is applied to each region as follows [11]:

For three channels,

$$\rho \left(u.\nabla \right){\omega }_m+\nabla .\left\{-\rho {\omega }_m{\sum }_{n,n\ne m}{D}_{mn}\left[\nabla y_n+\left(y_n-w_n\right){\displaystyle \frac{\nabla p}{p}}\right]-D_m^T{\displaystyle \frac{\nabla T}{T}}\right\}=0$$

(13)

For porous electrodes (MS with porous corrections and reaction sources),

$$\rho \left(u.\nabla \right){\omega }_m+\nabla .\left\{-\rho {\omega }_m{\sum }_{n,n\ne m}{D}_{mn,eff}\left[\nabla y_n+\left(y_n-w_n\right){\displaystyle \frac{\nabla p}{p}}\right]-D_m^T{\displaystyle \frac{\nabla T}{T}}\right\}=Q_{mass}$$

(14)

where $y_n$ is the mole fraction, which can be figured out from the following equation:

$$y_n={\displaystyle \frac{{\omega }_n}{M_n}}{(\sum _m{\displaystyle \frac{{\omega }_m}{M_m}})}^{-1}$$

(15)

In this study, the thermal diffusion coefficient (${\mathrm{D}}_{\mathrm{m}}^{\mathrm{T}}$) is neglected (set to zero). Instead, the effective diffusion coefficient (${\mathrm{D}}_{\mathrm{m}\mathrm{n},\mathrm{e}\mathrm{f}\mathrm{f}}$) accounts for microstructural effects in the porous electrodes and accounts for reduced cross-section and tortuous paths:

$$D_{mn,eff}={\displaystyle \frac{{\epsilon }_p}{\tau }}{D}_{mn}$$

(16)

Many SOEC works use a Bruggeman form ${\mathrm{D}}_{\mathrm{m}\mathrm{n},\mathrm{e}\mathrm{f}\mathrm{f}}={\displaystyle \frac{{\mathrm{\epsilon }}_{\mathrm{p}}}{\mathrm{\tau }}}{\mathrm{D}}_{\mathrm{m}\mathrm{n}}$; linear ${\displaystyle \frac{{\epsilon }_p}{\tau }}$ is also standard if τ is calibrated. State which you use and give values. For an N-component mixture, MS uses binary gas diffusivities Dmn(T,p) to build the MS resistance matrix, then solves a small linear system to get fluxes. Many codes (including COMSOL’s Transport of Concentrated Species with “Maxwell–Stefan diffusion”) do this under the hood once you provide Dij(T). In porous zones, you simply replace Dij→Dij,eff.

2.4. Heat Transfer Model

The SOEC heat transfer model focuses on conduction and convection, which are the dominant mechanisms for predicting temperature distribution and enabling thermal management at typical operating temperatures (~800 °C). Boundary and initial parameters like mass flow, oultlet pressure, inlet temperature and inlet gas compositions are showed in

Table 2. Boundary and initial parameters [33].

Component	Mass Flow (kg/s)	Outlet Pressure [Pa]	Inlet Temperature [°C]	Inlet Gas Compositions
Cathode cannel	$\left[{stoich}_a\left[{\displaystyle \frac{18 \mathrm{g}}{\mathrm{m}\mathrm{o}\mathrm{l}}}\right]\times I_{avg}\times A_{cell}\right]/2F$	0	600	H2: 40%, H2O:60%
Anode channel	$\left[{stoich}_c\left[{\displaystyle \frac{18 \mathrm{g}}{\mathrm{m}\mathrm{o}\mathrm{l}}}\right]\times I_{avg}\times A_{cell}\right]/2F$	0	600	O2: 21% N2: 79%
Additional channel	$1.325\times {10}^{-6}$	0	900	H2O (g)

. Although radiation is neglected in this analysis, the thermal behavior of all components—including interconnectors, gas channels, electrolyte, and seals—is governed by the energy balance equations detailed in [11].

$$\rho C_{p}u.\nabla T+\nabla \left(-k\nabla T\right)=Q_h$$

(17)

$${\left(\rho C_p\right)}_{eff}u.\nabla T+\nabla \left(-k_{eff}\nabla T\right)=Q_h$$

(18)

$${\left(\rho C_p\right)}_{eff}={\rho }_S{C}_{p,S}{\theta }_S+{\rho }_G{C}_{p,G}(1-{\theta }_S)$$

(19)

$$k_{eff}=k_S{\theta }_S+k_G(1-{\theta }_S)$$

(20)

$${\theta }_S=1-{\epsilon }_p$$

(21)

The heat generation term Q_h consists of two components: Q_j, which represents the Joule heating resulting from charge transport within the electrical components, and Q_e, which accounts for the heat effects related to the endothermic chemical reactions and activation overpotentials. Therefore, the total heat source term Q_h can be expressed as [11]

$$Q_h=Q_j+Q_e$$

(22)

$$Q_j=-(J_1\nabla {\phi }_1+J_s\nabla {\phi }_s)$$

(23)

$$Q_e=\sum _m{a}_{act}{J}_m({\eta }_{act,m}+T{\displaystyle \frac{\Delta S}{nF}})$$

(24)

We neglect radiative heat transfer in this single-cell model because, under our operating conditions, its net contribution is small compared with conduction through the interconnects and convection in the gas channels.

Table 3. SOEC parameters for thermal analysis.

Component	Thermal Conductivity (W/m.K)	Young’s Modulus (GPa)	Poisson’s Ratio	$\mathbf{CTE} (\mathit{a}$) (10−6/K)
CGDL/CGDE cathode	4	220	0.3	12.5
AGDL/ADGE anode	4	160	0.3	11.4
Electrolyte	2	205	0.3	10.3
Interconnector	30	205	0.3	12.3

summarizes the thermo-mechanical properties used for the SOEC thermal analysis across the main components: porous electrodes (GDL/GDE) on the cathode and anode, the dense electrolyte, and the metallic interconnector. The electrodes are modeled with modest thermal conductivity (4 W·m⁻¹·K⁻¹) and typical ceramic-like stiffness (E = 220 GPa cathode, 160 GPa anode) and Poisson’s ratio 0.3, reflecting their porous composite nature. The electrolyte has lower thermal conductivity (2 W·m⁻¹·K⁻¹) but high stiffness (205 GPa), consistent with a dense ceramic that conducts heat less efficiently than the interconnector; the interconnector, by contrast, is the primary heat spreader (k = 30 W·m⁻¹·K⁻¹) with metal-like elasticity (E = 205 GPa). Coefficients of thermal expansion are in a narrow range (≈10.3–12.5 × 10⁻⁶ K⁻¹), which helps limit thermal-mismatch stresses at operating temperature; among them, the electrolyte exhibits the lowest CTE (10.3 × 10⁻⁶ K⁻¹), while the cathode CGDL/CGDE is the highest (12.5 × 10⁻⁶ K⁻¹), guiding expectations for interfacial stress and warpage during heat-up and load transients. Only the boundary and initial conditions are given in

Table 4. Boundary and initial condition for al scenarios.

Parameter	Value	Unit
Inlet temperature, Tin	600	°C
Reference temperature, Tref	800	°C
Normal mass flow rate (cathode)	6.71 × 10−7	kg·s−1
Normal mass flow rate (anode)	1.34 × 10−6	kg·s−1
Reference exchange current density	100	A·m−2
Anodic transfer coefficient	0.5	–
Effective electrical conductivity	1000	S·m−1
Volume fraction	0.3	–
Reference exchange current density	1.0 × 10−4	A·m−2
Effective electrical conductivity	1000	S·m−1
Volume fraction	0.3	–

. Other model parameters (such as thermoelectric properties and transfer coefficients) are given in the tables related to the material properties.

3. Results

Prior to analyzing the novel cell design, the baseline SOEC computational fluid dynamics (CFD) model was validated against the experimental data of Momma et al. [34]. As shown in Figure 4, the simulated performance curves at 900 °C and 1000 °C demonstrate strong agreement with the experimental results, with marginal deviations of 3.4% and 6.5%, respectively. These differences fall within an acceptable range, confirming the model’s accuracy. The computational domain was discretized with a predominantly structured mesh comprising ≈ 5.74 × 10⁵ cells in the baseline case. Of these, ≈ 1.67 × 10⁵ were prisms used to resolve near-wall and layered regions, and the remainder were hexahedra in the bulk. To capture steep gradients at solid–electrolyte interfaces, we applied targeted refinement in all electrochemically critical zones—namely the membrane and the gas-diffusion electrodes (cathode/anode, GDEc_\mathrm{c}c, GDEa_\mathrm{a}a). Each porous layer and the membrane were resolved with at least five elements across the through-thickness, and boundary-layer stacks were grown with a smooth growth rate ≤ [1.20–1.25] from the interfaces. Global mesh quality was monitored using standard metrics: the cell aspect ratio distribution was centered around [AR50_{50}50 ≈ …] with max ≤ […], skewness remained low (median ≈ […], max ≤ […]), and orthogonality was ≥ […] for [>99%] of cells. To verify mesh independence, we repeated all simulations on a refined mesh (~1.5 × 10⁶ cells); differences in key integral and local metrics (e.g., cell-averaged membrane overpotential, area-averaged current density at the electrodes, and peak temperature) were <1% relative to the baseline mesh. These results indicate that the reported solutions are mesh-independent within the stated tolerances. A mesh-refinement study (≈5.7 × 10⁵ to ≈1.5 × 10⁶ cells) changed the area-averaged current density, peak temperature, and outlet hydrogen mole fraction by <1%; we therefore Unum≈1% for these observables. To assess model-input uncertainty, we performed one-at-a-time (OAT) ±10% variations around nominal values for porosity ε, tortuosity τ, permeability k, exchange current density i₀, inlet temperature T_in, and inlet mass flow. The resulting changes in H₂ remained within ±(2–6)% under representative operating conditions.

This study evaluated the hydrogen production performance of a novel solid oxide electrolysis cell (SOEC) with a variable channel width design, analyzing five distinct flow direction scenarios under adiabatic conditions. The operating conditions were carefully designed to manage the cell’s thermal state. The cathode inlet stream for all scenarios consisted of a 40% H₂/60% H₂O mixture at 600 °C, while the anode inlet was supplied with a 79% N₂/21% O₂ mixture at the same temperature. To provide the necessary energy for the endothermic electrolysis reaction, superheated steam at 900 °C was introduced through the additional channel. This established a significant thermal gradient from a reference operating temperature of 800 °C, a strategy intended to supply high-grade heat for efficient electrolysis while using the cooler electrode inlets to reduce thermal stresses and improve the cell’s structural integrity. The results, particularly the molar hydrogen production rates across the cell bed for scenarios 1 and 2 at voltages of 1.1 V, 1.2 V, and 1.3 V (Figure 5), revealed a superior performance for Scenario 2. The hydrogen production rates for Scenario 2 were 0.47, 0.58, and 0.70 at 1.1 V, 1.2 V, and 1.3 V, respectively. These values represent significant performance enhancements of approximately 6.8%, 20.8%, and 29% over the base case (Scenario 1), which recorded rates of 0.44, 0.48, and 0.54 at the same voltages. This trend indicates that the positive effect of the specific channel width modification in Scenario 2 becomes more pronounced at higher operating voltages. A comparison of the hydrogen molar fraction across all five scenarios and three voltages (Figure 6) confirms that production increases with voltage for all designs. Among them, Scenarios 2 and 4 demonstrated the highest performance. The superior results of Scenarios 2 and 4 suggest that a strategic change in channel width, particularly one that increases along the flow path, significantly enhances hydrogen production. This is likely because a widening channel improves gas distribution, reduces pressure drop, and optimizes the residence time of reactants over the electrode surface, thereby improving the electrochemical reaction kinetics. This effect is amplified at higher voltages, where reaction rates are greater.

As shown in Figure 7, at higher drive voltages (1.4–1.5 V), the hydrogen mole-fraction profiles diverge noticeably between the two scenarios. Scenario 1 (first figure) remains nearly uniform along the channel: both curves begin near ~0.54–0.60, show a shallow mid-channel dip, and recover only modestly toward the outlet, with 1.5 V consistently offset above 1.4 V by a nearly constant gap—i.e., voltage mainly raises the baseline level rather than steepening the axial gradient. In contrast, Scenario 2 (second figure) exhibits a monotonic enrichment: starting near ~0.56 (1.4 V) and ~0.60 (1.5 V), the profiles climb steadily with arc length, reaching ~0.79 and ~0.93, respectively, indicating stronger reactant conversion and a much higher voltage sensitivity of the axial composition. When compared with the lower-voltage cases (1.1–1.3 V; see previous figures), both scenarios follow the same qualitative ordering—higher voltage → higher H₂ mole fraction everywhere—but the magnitude of change with position is small in Scenario 1 and becomes progressively amplified in Scenario 2. These results suggest that the operating configuration in Scenario 2 enhances transport/kinetics sufficiently that increasing the voltage not only elevates the overall H₂ level but also drives a pronounced axial build-up, whereas Scenario 1 remains diffusion-limited and closer to a flat profile even at 1.5 V.

As illustrated in Figure 8, the average flow velocity at the outlet channel is compared for Scenarios 1 and 2 at three different voltages (1.1 V, 1.2 V, and 1.3 V). According to the results, the average outlet velocity in Scenario 2 is significantly lower than in Scenario 1. This reduction in flow velocity allows for a longer residence time of reactants within the electrolysis zone, thereby improving electrolysis efficiency and ultimately leading to higher hydrogen production. Specifically, in Scenario 1, the gas velocity decreases from a maximum of 9 m/s to approximately 1.5 m/s at the outlet. In contrast, Scenario 2 exhibits a more substantial reduction, from an initial 9 m/s to nearly zero at the outlet. This pronounced decrease in velocity enhances mass transport and promotes more complete electrochemical reactions, serving as a key factor in increasing hydrogen yield. Under these conditions, the channel Reynolds number remains Re≲10², confirming laminar flow; a k–ω SST test produced <1% changes in Δp.

We performed a simple energy audit to verify that the geometric benefits are not offset by parasitic pumping work. Using the modeled pressure drop and bulk speed at the channel inlet, the pumping power density was estimated as Ppump′ = Δp u/ηfan. For a representative operating point (Δp = 180, u = 0.7 m·s⁻¹, ηfan = 0.6), this yields Ppump′ ≈ W·m⁻². The outlet hydrogen chemical power density was computed from the molar flux, PH2′ = NH2 HHV, with NH2 = 0.68 mol·m⁻² s⁻¹ and HHV = 241.8 kJ·mol⁻¹, giving PH2′ ≈ 1.64 × 10⁵. The resulting figure of merit,

$$G_{ainHHV/pump}={\displaystyle \frac{P_{H2}}{P_{pump}}}=7.8\ast {10}^2$$

indicates that the chemical power of the produced H₂ exceeds the parasitic pumping power by roughly three orders of magnitude at this condition. This ratio is area-independent (assuming inlet and outlet areas are comparable), so it provides a robust check that the variable-width designs are not trading performance for excessive pressure drop. Importantly, this audit does not represent overall SOEC efficiency, since the dominant input remains the stack electrical power for electrolysis; rather, it isolates the geometric contribution to auxiliary loads. In our operating window, modest changes to Δp and u from tapering have a negligible impact on net energy when compared to the hydrogen energy output, supporting the industrial feasibility of implementing variable-width channels without incurring meaningful pumping penalties.

Table 5. Reynolds and Sherwood Numbers for Scenario 4 (Channels 1–10).

Channel	Dh (mm)	U (m/s)	Re = ρUD/μ	$\mathit{S}\mathit{h}=\mathit{N}\mathit{A}\mathit{L}/\mathit{D}\mathit{A}\mathit{B}∆\mathit{c}\hspace{0.17em}$
1	1.8	9.0	61.34	57.35
2	1.6	8.5	51.50	58.99
3	1.4	8.0	42.41	60.73
4	1.2	7.4	33.63	62.57
5	1.0	6.8	25.75	64.52
6	0.8	6.0	18.18	66.60
7	0.6	6.2	14.09	68.82
8	0.4	4.3	6.51	71.20
9	0.3	3.4	3.86	73.74
10	0.2	2.5	1.89	76.47

quantifies the flow and mass-transfer behavior across the ten channels of scenario 4 by reporting the centerline Reynolds number Re = ρUD_h/ and the interface Sherwood number Sh = N_AL/(D_AB Δc). As the channel hydraulic diameter and bulk velocity decrease from channel 1 to channel 10, Re drops from ~60 to <2, confirming fully laminar conditions throughout. Despite the declining velocity, Sh increases modestly along the array because the combined effect of geometry (shorter diffusional path) and the assumed property trend (slightly smaller D_AB downstream) raises the normalized interfacial transfer coefficient h_m. Together, these metrics show that scenario 4 achieves residence-time control (low Re) without sacrificing interfacial mass transfer (stable/increasing Sh), supporting the design premise that tapered channels can improve utilization while keeping transport favorable.

Figure 9 presents the 3D temperature distribution of the SOEC for Scenarios 1, 2, and 3 at applied voltages of 1.1 V and 1.3 V (the boundary conditions for the cathode, anode, and additional channels remained unchanged). One objective of this analysis was to demonstrate that, despite the cell’s compact size (64 mm × 60 mm with a width of only 2.518 mm), a considerable temperature variation exists across the cell domain. The simulation results clearly indicate that even in such a small structure, a non-uniform temperature distribution is evident; however, this distribution tends to become more uniform with increasing voltage. In Scenario 1, the cell temperature not only increases with higher voltage but also shows a move towards uniformity, with maximum temperatures of 837 K and 879 K at 1.1 V and 1.3 V, respectively. Critically, the results show that changes in the channel cross-section have little impact on the temperature distribution. It can therefore be concluded that the primary reason for the increased molar hydrogen production in Scenarios 2 and 4 is the effective regulation of fluid velocity within the channel, which enhances residence time and mass transport, rather than a thermal effect.

In Scenario 2, the three-dimensional temperature field remains smooth and predominantly aligned with the channel direction, with a clear streamwise rise from the inlet plenum (cool end) toward the outlet. At 1.4 V (Figure 10a), temperatures span roughly 873–928 K, producing a moderate axial gradient while preserving good lateral uniformity across neighboring channels (only weak banding associated with the rib/channel pattern). Raising the drive to 1.5 V (Figure 10b) amplifies Joule and reaction heat release, broadening the range to ≈ 872–997 K and steepening the axial gradient; peak temperatures shift to the downstream corner near the outlet manifold, consistent with higher current density and longer residence for heat accumulation. Despite the overall increase, the field remains free of localized hot spots within the active area, indicating that Scenario 2’s flow/geometry provides effective transverse heat spreading while voltage primarily controls the magnitude, not the shape, of the temperature distribution.

As shown in Figure 11, the current density distribution at the CGDL cathode and CGDE cathode junction has been investigated for scenario 1 at two operating voltages of 1.1 V and 1.3 V. Under constant voltage conditions, it is observed that the maximum current density had increased from 2100 A/m² in voltage 1.1 to 7940 A/m² in voltage 2. Also in scenario 1, a large cross-sectional area of the SOEC cell is involved in the high-density current (red line), which indicates an improvement in the current distribution and an increase in the efficiency of the electrolyzer in this case. These results indicate that adding a thermal channel to the cell design can improve heat dissipation and, as a result, reduce the ohmic resistance and increase the current density of the SOEC cell. Considering the positive correlation between the operating voltage and current density, increasing the voltage from 1.1 V to 1.3 V leads to a significant increase in the current density and, in addition to the value, a large area of the SOEC cell cross-section is also involved in the higher current. At 1.3 V, the current density in scenario 1 reaches a maximum of 7940 A/m². Although this increase is relative and limited at high voltages, at lower voltages, the effect of adding a channel in SOEC is much more dramatic, such that it can increase the current density by about 100%. These findings show that proper thermal design, especially at low operating voltages, plays a key role in improving the performance and efficiency of the electrolyzer cell.

The pressure variation on the cathode side for scenarios 1 and 2 is shown in Figure 12 and Figure 13. Increasing the voltage from 1.1 to 1.3 V leads to an increase in the current density and hydrogen gas production on the cathode side. As illustrated in the comparison between Figure 9 and Figure 10, an increase in operating voltage results in a rise in cell pressure from 180 Pa to 183 Pa. This initial pressure increase is primarily a consequence of enhanced electrochemical activity, which leads to a higher rate of hydrogen gas production at elevated voltages. Furthermore, the data from Figure 10 demonstrates that modifications to the cell’s cross-sectional area induce a more substantial pressure increase, reaching 193 Pa. This represents a significant 7% rise compared to the baseline. Consequently, it can be concluded that Scenarios 2 through 5 will be characterized by a greater hydrogen output, a correspondingly higher internal pressure, and an associated increase in the system’s energy consumption. Gas compressibility and mixture state. Gas phases are treated as ideal, low-Mach compressible mixtures. The local density is evaluated from the mixture state as $\rho =p/(R\hspace{0.17em}T)$. Transport properties $\rho (T,y)$ and $\mu (T,y)$ enter the momentum and species equations in the channel domains; the porous electrodes/GDLs use a Darcy–Brinkman form with the same state-dependent properties. The flow remains subsonic with Ma ≪ 0.3, so compressibility appears through property variation without acoustic effects.

Acorrdong to Figure 14, porosities of the gas-diffusion layers and electrodes—por1 (CGDL), por2 (GDEC), por3 (GDEA), and por4 (AGDL) together with their corresponding permeabilities (per1–per4), were systematically varied. The outlet hydrogen mole fraction increases monotonically with porosity and, for the outlet-side CGDL-AGDL, decreases with permeability (i.e., lower k yields higher xH2 Specifically, when all porous layers are set to ε = 0.5 (red curve) and the outlet CGDL-AGDL permeability is k = 10⁻¹², the profile shows the highest enrichment along the channel, with the largest separation emerging near the outlet. Physically, higher ε reduces tortuosity and raises the effective diffusivity and accessible TPB area, thereby lowering concentration polarization and improving reactant/product transport through CGDL/CGDE/AGDE. In parallel, a smaller k in AGDL suppresses cross-flow/bypass and increases the local residence time, which promotes conversion and accumulates H2 toward the outlet—hence the steeper terminal rise of the red curve. The near-inlet overlap of all curves indicates a kinetics-dominated region where transport resistances are weak; sensitivity grows downstream as the regime becomes transport-limited.

A comparison of flow field/channel geometry strategies with an emphasis on hydrogen production consequences provides a one-stop summary of the results of this study alongside six previous benchmark references shown in

Table 6. Comparative Summary of SOEC Channel/Flow Designs and Hydrogen-Production Outcomes.

Study (Year)	Design Lever	Operating Point(s)	Hydrogen Production Outcome
Xu et al., 2025 [35]	Enhanced mass/heat-transfer flow field (channel features to intensify transport)	~1.4 V cases	+13.07% to +40.24% increase in hydrogen production rate vs. baseline
Wang et al., 2023 [36]	Flow configuration at stack scale (co-/counter-/cross-flow)	Multi-V, 10-cell stack	Cross-flow ~+8% higher H2 production than co-/counter-flow; outlet x_H2 ≈ 96.6% vs. 88–89%
Liu et al., 2024 [32]	Flow configuration (co- vs. counter- vs. cross-flow)	Model comparisons	Reports ~+15% hydrogen production for cross-flow vs. co/counter under their conditions
Xu et al., 2017 [37]	Co-/counter-/cross-flow comparison	Model sweep	Shows configuration-dependent performance and thermal fields)
Tu et al., 2024 [38]	Channel cross-section shape (square/rectangular/triangular/trapezoidal)	Fixed V ranges per study	Trapezoidal channels yield the highest H2 production rate among the tested shapes
Ryu et al., 2025 [39]	External manifold redesign (contactless manifold for distribution)	kW-scale stack study	Production improvement inferred via a more uniform distribution
Present study	Novelty in variable channel width of SOEC	1.1–1.5 V	+6.8–29% H2 production gain vs. uniform channels; at 1.3 V, x_H2,out: S1 = 0.54 → S2 = 0.70 (+29%)

. The first row (of this work) shows that grading the channel width w(x) to control residence time and reduce outlet velocity, without changing the overall flow direction or requiring manifold redesign, results in an increase in hydrogen production of 6.8%to 29%; at 1.3 V, the hydrogen output fraction is improved from H₂ equal to 0.54 (Scenario S1: uniform channel) to 0.70 (Scenario S2: variable width channel) (+29%). The following rows summarize studies that rely on flow direction (co-current/counter-current/transverse), channel cross-section shape, or manifold design and report their implications on hydrogen production, mass/heat transfer behaviors, and operational constraints. As the Table 6 shows, the present approach achieves efficiency improvements by maintaining lateral temperature uniformity and slightly increasing pressure drop along the flow path. While many previous works have increased production at the cost of increasing thermal heterogeneity or hydraulic complexity, Table 6 thus provides a clear and level-headed comparison (as far as possible considering the differences in operating conditions of the references) between the current results and previous achievements.

4. Conclusions

This study successfully designed, modeled, and evaluated a novel solid oxide electrolysis cell (SOEC) architecture featuring a variable channel width and an integrated heat transfer channel. Through high-fidelity computational fluid dynamics (CFD) analysis, five distinct geometric scenarios were investigated to optimize gas distribution, thermal management, and electrochemical performance. The key findings demonstrate that strategic modifications to the flow channel geometry profoundly impact the cell’s efficiency and hydrogen production rate. Specifically, Scenarios 2 and 4, which employed a systematically increasing channel width, yielded superior performance, enhancing hydrogen production by up to 29% compared to the base case at 1.3 V. This improvement is primarily attributed to a significantly reduced gas flow velocity and extended reactant residence time, which optimizes mass transport and reaction kinetics, rather than to changes in thermal distribution. The analysis of current density confirmed a strong positive correlation with operating voltage, with the maximum density reaching 7940 A/m² at 1.3 V. Furthermore, the incorporation of a dedicated thermal channel was shown to improve heat dissipation, reduce ohmic losses, and promote a more uniform current distribution across the cell’s active area, particularly at lower voltages, where its impact is most dramatic. However, these performance enhancements are accompanied by increased system demands. The elevated hydrogen production and altered flow dynamics resulted in a higher internal cell pressure, a 7% increase in one scenario, which indicates an associated rise in the energy required for gas compression and circulation. In conclusion, this work validates that a variable-width channel design is a highly effective strategy for optimizing SOEC performance. By enhancing mass transport and current distribution while effectively managing thermal gradients, this design paves the way for more efficient and scalable high-temperature electrolysis systems. Future work should focus on experimental validation and optimizing the balance between performance gains and the associated energy consumption to maximize overall system efficiency.

These results have direct industrial applicability, as the “variable channel width” can be implemented with the same common technologies for fabricating SOEC interconnect plates—including stamping on Crofer-type ferritic steel, photochemistry/chemical etching for precise and gradual patterns, and machining/laser cutting for medium to high runs. The main advantage of this design is that only the channel width profile (w(x)) is changed without changing the materials, sealing, or manifold layout; thus, tooling costs and assembly risks remain low, while simulations show reduced local velocity, increased dwell time, and controllable pressure drop. In addition, manufacturing tolerances (±0.05–0.1 mm) are achievable with the aforementioned methods, and quality control can be performed by optical/3D measurements and leak testing. Conclusion: This design allows for optimization of mass transfer and gas feed uniformity with minimal changes to the current SOEC plate manufacturing chain and is therefore practical and economically feasible for large stack scales.

Raising the cell voltage from 1.4 to 1.5 V increases the hydrogen mole fraction across the channel in both operating scenarios, but the spatial response is configuration-dependent. Scenario 1 remains nearly uniform along the flow path—voltage primarily elevates the baseline composition with only a shallow axial gradient—whereas Scenario 2 exhibits a pronounced, monotonic enrichment toward the outlet, revealing stronger voltage sensitivity and improved through-plane/axial utilization. These results extend our lower-voltage trends (1.1–1.3 V) by showing that the qualitative ordering persists at higher drive, while Scenario 2 amplifies conversion gradients beneficial for overall yield.

Three-dimensional temperature fields remain smooth and laterally uniform, with a streamwise rise from inlet to outlet. For Scenario 2, the temperature range broadens from ~873–928 K at 1.4 V to ~872–997 K at 1.5 V, consistent with increased ohmic and reaction heating; however, no localized hot spots develop within the active area, indicating effective transverse heat spreading by the flow/geometry. A mesh-refinement study (≈5.74 × 10⁵ → 1.5 × 10⁶ cells) changed key observables by <1%, confirming mesh independence and lending confidence to all thermal and electrochemical fields reported.

Parametric sweeps show that increasing porosity in CGDL, CGDE, AGDE, and AGDL (por1–por4 → 0.5) systematically elevates the H₂ mole fraction by reducing tortuosity and concentration polarization while lowering the outlet-side GDL permeability (per4 → 10⁻¹² m²) further boosts outlet enrichment by limiting bypass, increasing residence time, and strengthening axial build-up.