Purpose: Dimensional tolerances in the flow-channel height of metallic interconnects are unavoidable during the manufacturing and assembly of solid oxide cell (SOC) stacks. Such tolerances can lead to non-uniform internal flow distribution and may threaten cell performance and long-term stability. This study aims to evaluate the effects of flow-channel height tolerance on the coupled electrical, flow, and mass-transfer behavior in single-layer and three-layer SOC stacks, and to provide a theoretical basis for rational tolerance specification. 

Methods: A coupled thermal–mass–electrical–chemical multiphysics model was developed for SOC stacks. The model integrates an electrochemical model with momentum, species, and energy conservation equations, allowing analysis of current density, gas-flow distribution, pressure drop, and temperature. For the single-layer stack, four flow-channel height profiles were considered: uniform height, random height, height decreasing toward both sides, and height increasing toward both sides. For the three-layer stack, two comparative cases were further examined: consistent layer heights (DN1) and inconsistent layer heights (DN2). All simulations were performed under constant-voltage operation at 0.8 V. Macroscopic and interfacial current-density distributions, gas distribution, fuel-channel pressure drop, interlayer voltage variation, and the coefficient of variation (CV) of gas flow were systematically compared. 

Results: For the single-layer stack, the difference in macroscopic current density among the four flow-channel height profiles was less than 0.5%, and the maximum relative deviation of the standard deviation of the interfacial current density was only 0.18%. This indicates that the current distribution was insensitive to flow-channel height tolerance within the studied range. However, further analysis of flow and mass transfer revealed hidden non-uniformity. Under all height-deviation scenarios, the fuel-side channel pressure drop increased by approximately 28.6% compared with the uniform case, indicating that the flow field was far more sensitive to height tolerance than the electrical performance. For the three-layer stack, the layer voltages in DN1 were nearly identical, with an interlayer voltage error of only 0.4% and a gas-flow CV of 1.8%, indicating excellent gas-distribution uniformity. In contrast, in DN2, complete hydrogen depletion occurred in the rear region of the top-layer flow channel, concentration polarization intensified, and the voltage decreased continuously; the interlayer voltage error reached 6.7%, and the gas-flow CV was 18.7%, indicating a highly non-uniform gas distribution. These results show that although the current distribution in a single cell is relatively tolerant of flow-channel height deviations, the flow and mass-transfer fields are strongly affected. In multilayer stacks, interlayer height inconsistency can lead to severe local fuel starvation and performance degradation. 

Conclusions: Within the range studied, the flow-channel height tolerance for single cells can be moderately relaxed to reduce manufacturing costs. However, interlayer dimensional consistency must be strictly controlled during stack assembly. The proposed coupled model and findings provide a theoretical basis for formulating reasonable manufacturing tolerances for SOC stacks.