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RESEARCH PAPERS

# Spectral Radiative Heat Transfer Analysis of the Planar SOFC

[+] Author and Article Information
David L. Damm

Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0405

Andrei G. Fedorov1

Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332-0405andrei.fedorov@me.gatech.edu

1

Corresponding author.

J. Fuel Cell Sci. Technol 2(4), 258-262 (Apr 05, 2005) (5 pages) doi:10.1115/1.2041667 History: Received November 18, 2004; Revised April 05, 2005

## Abstract

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.

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## Figures

Figure 1

Schematic of the planar, anode-supported unit cell model of SOFC (not to scale)

Figure 2

Definition of the spectral range of interest wherein 90% of radiative energy falls according to Planck’s law for blackbody emissive power (n=1.8) for the temperatures relevant to SOFCs

Figure 3

FTIR transmittance and reflectance data for a 330‐μm-thick sample of polycrystalline yttria-stabilized zirconia (YSZ)

Figure 4

Absorption coefficient of YSZ computed from transmittance and reflectance measurements showing strong spectral dependence

Figure 5

Comparison of the numerical predictions obtained using the spectral two-flux model with the analytical solution [Eq. 10] for the non-dimensional wall heat flux

Figure 6

A simple problem of radiation-conduction heat transfer in a 1D, plane-parallel medium bounded between two isothermal plates used for validation of the spectral two-flux radiation model

Figure 7

Comparison of results obtained using the two-flux and discrete ordinates (benchmark) methods for various optical thicknesses and gray optical properties [(a)–(c)], and spectrally varying absorption coefficient (d)

Figure 8

Temperature profile of the anode∕electrolyte and cathode∕electrolyte interfaces with and without radiation

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