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Research Papers

# Resistive Spot in a Fuel Cell Stack: Exact Solutions

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

Institute for Energy Research-Fuel Cells (IEF-3), Research Center “Jülich”, D-52425 Jülich, Germany

This is justified provided that the mean current density in a stack is not small, $J̃0≲1$. From practical point of view, this is the most interesting case.

J. Fuel Cell Sci. Technol 6(1), 011024 (Nov 26, 2008) (6 pages) doi:10.1115/1.2972168 History: Received June 28, 2007; Revised October 24, 2007; Published November 26, 2008

## Abstract

We report the analytical solution to a problem of voltage and current distribution in a two-cell stack with the small amplitude resistive spot in one of the cells. Voltage disturbance in the defective cell increases almost linearly with the characteristic spot radius. The general expression for voltage loss due to a spot in an $N$-cell stack is obtained; it is stack current density times peak spot resistivity times square of the characteristic spot radius. Based on the solutions derived, a method for spot detection in a stack is discussed.

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## Figures

Figure 1

Sketch of a two-cell stack with the resistive spot in the cell α. The arrows indicate the current lines. Part of the current is transported through the spot and the rest part bypasses the spot moving in plane in the bipolar plate.

Figure 2

(a) Spot resistivity R̃α1 and (b) dimensionless disturbance of voltage of the cell Ṽα1 due to the spot. Indicated are the characteristic spot radii s̃.

Figure 3

Voltage disturbance in the spot center Ṽα1(0) as a function of spot radius s̃

Figure 4

Function F(0)=qexp(q)Ei(1,q)

Figure 5

Current of the cell α for indicated spot radii s̃.

Figure 6

(a) Voltage and (b) current of the cells α and β. Spot radius is s̃=0.1; other parameters are listed in Table 1.

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