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Research Papers

# Temperature and Current Distribution Along the Air Channel in Planar SOFC Stack: Model and Asymptotic Solution

[+] Author and Article Information
A. A. Kulikovsky

Institute for Energy Research–Fuel Cells (IEF–3), Research Center “Jülich”, D-52425 Jülich, Germany; Research Computing Centre, Moscow State University, 119992 Moscow, Russia

Moreover, detailed calculations (4) show that the variation of the product $ρairv$ in SOFC air channel does not exceed 2%, although $ρair$ and $v$ exhibit variations on the order of 10%.

The characteristic length $lu$ of Nusselt number variation in Eq. 22 is usually small compared with a typical channel length ($lu≃0.3 cm$, while $L≳10 cm$). In numerical calculations, this allows us to put $fu=1$ in Eqs. 30,17 keeping, however, high value of inlet Nusselt number $N̂u0$ in the boundary condition 33.

Indeed, substituting

$∂2T̃∂x̃2=1ψ2∂f1∂x̃$
and Eq. 42 to Eq. 37 and equating the terms with $γ0$ we obtain
$1ψ2∂f1∂x̃+(ω2T̃air+φ2η̃0)η̃0R̃c(T̃air)=f1$
Parameter $ψ2$ is large (Table 2); this, in the leading order the term with the derivative $∂f1/∂x̃$ can be neglected and we come to 44.

J. Fuel Cell Sci. Technol 7(1), 011015 (Nov 10, 2009) (6 pages) doi:10.1115/1.3119060 History: Received November 26, 2007; Revised April 24, 2008; Published November 10, 2009; Online November 10, 2009

## Abstract

We report a model for coupled temperature and current distributions along the single channel in planar solid-oxide fuel cell stack. Approximate analytical solution to model equations is derived; the solution predicts that air and stack temperatures are close to each other and linearly increase with the distance along the channel. Maximal temperature at the channel outlet is proportional to the average stack current and inversely proportional to the air flow velocity. This means that temperature oscillations due to variable load can be compensated for by the respective variation in air flow velocity.

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## Figures

Figure 1

Sketch of the heat fluxes in a small box in the interconnect

Figure 2

Sketch of the stack element: the single linear air channel in the interconnect

Figure 3

Schematic of the heat fluxes onto the cathode and the anode sides of the interconnect. When stack temperature and current do not vary along the z-axis the situation in (a) is equivalent to the situation in (b), where the total flux falls onto one side of the plate while the other side is thermally insulated.

Figure 4

(a) Solid lines: numerical solution to a full system of Eqs. 30,17,33,34,36. Dashed lines: approximate analytical solution 54. The parameters for calculations are listed in Table 1. (b) Numerical and approximate interconnect temperatures for indicated values of voltage loss (V).

Figure 5

Local current density 29 calculated with the numerical shape of T(x) (solid curves) and with the analytical relation 53 (dashed curves). Indicated are the values of total voltage loss (V).

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