A multi-criteria assessment to show the superiority of time-dependent heat flux over constant heat flux during direct heating of solid oxide fuel cell

Although the high operating temperature of solid oxide fuel cells (SOFCs) provides several advantages, it extends the heating time. Accelerating the heating process can lead to severe temperature gradients and consequent structural issues. Therefore, making a balance between the time and temperature gradient is crucial for SOFC’s practical development. Previous studies have considered constant heat flux for the direct heating process of SOFCs. This study, however, numerically assesses the benefits of employing time-dependent heat flux and identifies the best time-dependent heat flux function, using a multi-criteria approach. In this regard, various polynomial functions, including linear, quadratic, cubic, and quartic, along with their rotated forms are examined. The findings indicate that the variable heat flux function is superior to the constant one from a multi-criteria perspective (i.e., when heating time and temperature gradient are considered simultaneously). Among the examined functions, the linear rise function with a heat flux rise coefficient of 1 W s⁻¹, which results in a heating time of 628 s and a maximum temperature gradient of 6.18 K cm⁻¹, is identified as the optimal trade-off solution. The obtained results highlight the desirable potential of time-dependent heat flux functions in achieving a balance between temperature gradients and heating duration.