# Mathematical Modeling of Alkaline Anion Exchange Membrane Fuel Cells

Chapter
Part of the Lecture Notes in Energy book series (LNEN, volume 63)

## Abstract

The modeling work on the alkaline anion exchange membrane (AEM) fuel cell has been greatly facilitated by the rapid development of AEM fuel cell in recent years. Mathematical modeling has been widely recognized as a powerful tool to quantify the physical and electrochemical processes inside the fuel cells. In this study, modeling researches on the AEM fuel cell fed by various fuels have been summarized and discussed. General modeling formulation for AEM fuel cell has been comprehensively introduced. The relevant modeling results with various cell design parameters and operational conditions are revealed and analyzed accordingly. Moreover, the comparison of the operating characteristics of AEM fuel cells fueled by hydrogen (H) and liquid alcohols is also carried out in this study.

## .

a

Water activity, anode

Anode

Anode

A

Geometric area of the fuel cell (m2)

c

Mole concentration (mol m−3), cathode

Cathode

Cathode

D

Diffusion coefficient (m2 s−1)

E

Voltage (V)

EW

Equivalent weight of membrane

F

G

Free energy (J mol−1)

h

Latent heat, J kg−1

J

Current density (A cm−2)

J0

Volumetric exchange current density (A m−3)

k

Electrical conductivity (S m−1)

K

Permeability (m2)

m

Membrane

M

Relative mole mass (kg mol−1)

n

Moles of electrons production per mole of reactants consumption

$$n_{d}$$

Electroosmosis coefficient (H2O/ OH)

N

The change of moles of gas (mol), the flux of the liquid water in the fuel cell component (mol m−2 s−1)

p

Pressure (Pa)

poro

Porous media

r

ri

Order of the reaction

R

Ideal gas constant (8.314 J K−1 mol−1) internal resistance of cell $$\left( {{\Omega} \,{\text{m}}^{2} } \right)$$ electrochemical reaction rate (A m−3)

Re

Reynolds number

RH

Relative humidity

s

Volume fraction

S

Entropy (J mol−1 K−1), Source term (kg m−3 s−1, mol m−3 s−1)

ST

Stoichiometric ratio

T

Temperature (K)

$$\overrightarrow {u}$$

Velocity (m s−1)

x, y, z

Coordinate position (m)

X

Mole fraction

Y

Mass fraction

## Greek symbols

α

Apparent transfer coefficient

β

Liquid water volume fraction supplied for cathode inlet

γ

Activity coefficient, water phase change rate (s−1)

δ

Thickness (m)

ε

Porosity

ζ

Water transfer rate (s−1)

η

Internal resistance of cell $$\left( {{\Omega} \,{\text{m}}^{2} } \right)$$, voltage loss

θ

Contact angle (°)

ι

Interfacial drag coefficient

λ

Water content in polymer exchange membrane

μ

Dynamic viscosity (kg m−1 s−1)

ρ

Mass density (kg m−3) electrical resistivity (Ω m)

σ

Conductivity (S m−1)

φ

Potential (V)

ω

Volume fraction of ionomer in catalyst layer

## Superscript and subscripts

0

Proper value standard condition

a

Anode

act

Activation loss parameter

aver

Average

AAEM-CL

Interface between the membrane and catalyst layer

c

Cathode,capillary pressure

ch

Flow channel

CL

Catalyst layer

e

Electrode

eff

Effective parameter

equi

Equilibrium

evap

Evaporation

EOD

Electro-osmotic drag

g

Gas

GDL

Gas diffusion layer

H2

Hydrogen

H2O

Water

i

The composition of the gas mixture

lh

Latent heat

lq

Liquid water

ion

Electrical

m

Membrane

me

Methanol

mw

Membrane water

mv

Methanol vapor

m-l

Membrane water to liquid (vice versa)

ohm

Ohmic parameter

O2

Oxygen

P

Plate

r

Reversible

ref

Reference condition

s

Electrode

sat

Saturation state

total

Total

vap

Water vapor

v-l

Vapor to liquid (vice versa)

## Notes

### Acknowledgements

This work is supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 51622606), and the Key Program of Natural Science Foundation of Tianjin (China) (Grant No. 16JCZDJC30800).

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