Spectral Radiative Heat Transfer Analysis of the Planar SOFC

Thermo-mechanical failure of components in planar-type solid oxide fuel cells (SOFCs) depends strongly on the local temperature gradients at the interfaces of different materials. Therefore, it is of paramount importance to accurately predict the temperature fields within the stack, especially near the interfaces. Because of elevated operating temperatures (of the order of $1000K$ or even higher), radiation heat transfer could become a dominant mode of heat transfer in the SOFCs. In this study, we extend our recent work on radiative effects in solid oxide fuel cells [J. Power Sources, 124, No. 2, pp. 453–458] by accounting for the spectral dependence of the radiative properties of the electrolyte material. The measurements of spectral radiative properties of the polycrystalline yttria-stabilized zirconia electrolyte we performed indicate that an optically thin approximation can be used for treatment of radiative heat transfer. To this end, the Schuster–Schwartzchild two-flux approximation is used to solve the radiative transfer equation for the spectral radiative heat flux, which is then integrated over the entire spectrum using an $N$-band approximation to obtain the total heat flux due to thermal radiation. The divergence of the total radiative heat flux is then incorporated as a heat sink into a three-dimensional thermo-fluid model of a SOFC through the user-defined function utility in the commercial FLUENT computational fluid dynamics software. The results of sample calculations are reported and compared against the base line cases when no radiation effects are included and when the spectrally gray approximation is used for treatment of radiative heat transfer.