  Predicting flashback represents a pivotal challenge in the development of
innovative perforated burners for household appliances, especially for
substituting natural gas with hydrogen as fuel. Most existing numerical studies
have utilized two-dimensional (2D) simulations to investigate flashback in
these burners, primarily to reduce computational costs. However, the inherent
complexity of flashback phenomena suggests that 2D models may inadequately
capture the flame dynamics, potentially leading to inaccurate estimations of
flashback limits. In this study, three-dimensional (3D) simulations are
employed to examine the impact of the actual slit shapes on the flashback
velocities of hydrogen-premixed flames. Steady-state simulations are conducted
to compute flashback velocities for three equivalence ratios ($\phi=0.6$,
$0.8$, and $1.0$), investigating slits with fixed width and varying lengths.
Additionally, transient simulations are performed to investigate the flashback
dynamics. The results are compared with those from 2D configurations to assess
the reliability of the infinite slit approximation. For stable flames, 2D
simulations underpredict the burner plate temperature compared to slits with
lengths typical of practical devices but match the 3D results as $L\to\infty$.
Conversely, flashback velocities are consistently underpredicted in 2D
simulations compared to 3D simulations, even as $L\to\infty$. This is due to
the critical role of the slit ends in flashback dynamics, where preferential
diffusion effects and enhanced heat transfer trigger the initiation of
flashback in those regions. These findings underscore the necessity of
employing 3D simulations to estimate the flashback velocities in domestic
perforated burners accurately.
