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 1000 K 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 (Journal of Power Sources, Vol. 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 (YSZ) 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 (RTE) 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 3-D thermo-fluid model of a SOFC through the user-defined function utility in the commercial FLUENT CFD software. The results of sample calculations are reported and compared against the baseline cases when no radiation effects are included and when the spectrally gray approximation is used for treatment of radiative heat transfer.
Modulation and splitting of three-body radiative heat flux via graphene/SiC core-shell nanoparticles
