A Simple Thermal Model

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A Simple Thermal Model of PEM Fuel Cell Stacks
Brian Wetton, Atife Caglar
Keith Promislow
Mathematics, UBC www.math.ubc.ca/wetton
Mathematics, MSU

• 11 D Performance Model
• Single Cell Thermal Model
• Stack Thermal Model
• Stack Tool (In Progress)

Financial support MITACS, Ballard Power, NSERC,
NSF
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11 D Models

• Straight Channels (Ballard Mk9)
• Averaged over width (x)
• Through MEA (z) transport decouples from channel
  flow (y)
• Steady State

Not new Fuller and Newman 1991, Yi and Nyguyen
1998, Freunberger et al. 2003.
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Sources of Heat
Performance Model Output

• Condensation
• Overpotential
• Membrane Resistivity

• Cell Voltage
• Overpotential
• Water flux
• Membrane Resistivity
• Current density

Approximations to these quantities are obtained
from a 11 D performance model Berg et al 2003
Voltage losses
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Unit Cell Coolant Temperature T(y)
Assume heat is only removed through the coolant
stream
One step of an iterative procedure to determine
consistent T(y)
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Unit Cell Through MEA profile

• Further Assumptions
• Condensation is uniform in the cathode electrode
• Ohmic heating is uniform in the membrane
• Thermal Transfer to the coolant can be described
  by Nusselt number

We obtain a linear system for each y for
Describes one cell in a uniform stack
is piecewise linear/quadratic
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Unit Cell Through MEA profile
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Stack Model
Anomalous cell has quadrupled resistivity
(systematic vs anomalous sensitivities)
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Stack Model (cont)
Local (y) unknowns
Implicit solve 6N by 6N unknowns at each channel
grid point.
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Stack Tool (In progress)
These thermal models are part of a larger
programme to build a computational Stack
Modelling Tool.

• Header flow sharing can be neglected.
• Remaining stack effects are electrical and
  thermal
• A preliminary stack tool has been developed with
  these effects.

• Unit Cell Improvements (In Progress)
• 1D MEA transport including liquid water
• Parametric effects of liquid water in channels
• 2D MEA transport models