Chapter 1, Problem 1.58P

Single fuel cells such as the one of Example 1.5 can be scaled up by arranging them into a fuel cell stack. A stack consists of multiple electrolytic membranes that are sandwiched between electrically conducting bipolar plates. Air and hydrogen are fed to each membrane through flow channels within each bipolar plate, as shown in the sketch. With this stack arrangement, the individual fuel cells are connected in series, electrically, producing a stack voltage of $E_{\text{stack}}=N\times E_c,$ where $E_c$ is the voltage produced across each membrane and N is the number of membranes in the stack. The electrical current is the same for each membrane. The cell voltage, $E_c,$ as well as the cell efficiency, increases with temperature (the air and hydrogen fed to the stack are humidified to allow operation at temperatures greater than in Example 1.5), but the membranes will fail at temperatures exceeding $T\approx 85°\text{C}\text{.}$ Consider $L\times w$ membranes, where $L=w=100\text{mm,}$ of thickness $t_m=0.43\text{mm,}$ that each produce $E_c=0.6\text{V}$ at $I=60\text{A},$ and ${\stackrel{.}{E}}_{c,g}=45\text{W}$ of thermal energy when operating at $T=80°\text{C}\text{.}$ The external surfaces of the stack are exposed to air at $T_{\infty }=25°\text{C}$ and surroundings at $T_{\text{sur}}=30°\text{C,}$ with $\epsilon =0.88$ and $h=150{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Find the electrical power produced by a stack that is $L_{\text{stack}}=200\text{mm}$ long, for bipolar plate thickness in the range $1\text{mm}<t_{bp}<10\text{mm}\text{.}$ Determine the total thermal energy generated by the stack.
2. Calculate the surface temperature and explain whether the stack needs to be internally heated or cooled to operate at the optimal internal temperature of $80°\text{C}$ for various bipolar plate thicknesses.
3. Identify how the internal stack operating temperature might be lowered or raised for a given bipolar plate thickness, and discuss design changes that would promote a more uniform temperature distribution within the stack. How would changes in the external air and surroundings temperature affect your answer? Which membrane in the stack is most likely to fail due to high operating temperature?