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PEM Fuel Cells: Modeling

  • Reference work entry
  • First Online:
Fuel Cells and Hydrogen Production
  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Sustainability Science and Technology, © Springer Science+Business Media LLC 2017

Glossary

Proton exchange membrane fuel cells (PEMFCs):

are energy conversion devices that transform chemical energy in a fuel directly to electricity by means of two electrochemical reactions divided by a proton conductive membrane.

Mathematical modeling:

is the development of partial differential equations for describing the physical and electrochemical processes that govern a physicochemical system, in this entry, a PEMFC.

Numerical modeling:

is the development of numerical analysis and software tools to solve the partial differential equations that describe a physicochemical system, in this entry, a PEMFC.

Gas diffusion layers (GDL):

are porous, electrically conductive layers made of carbon fibers, a binder, and usually coated with PTFE that are placed between a fuel cell gas channel and the catalyst layer.

Catalyst layers (CLs):

are porous, electronically and ionically conductive composite layers made of ionomer and supported catalysts. They are the heart of the fuel cell as it is...

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Abbreviations

\( {\overline{C}}_p \) :

Molar specific heat, [J mol−1K−1]

\( \overline{H} \) :

Enthalpy, [J]

\( \dot{W} \) :

Rate of work done by the system, [W cm−3]

g :

Gravity vector field, [cm s−2]]

\( {\widehat{C}}_p \) :

Specific heat, [J g−1K−1]

\( \widehat{h} \) :

Specific enthalpy, [J g−1]

\( \widehat{u} \) :

Specific internal energy, [J g−1]

\( \widehat{\boldsymbol{N}} \) :

Mass flux, [g cm−2 s−1]

\( \mathcal{D} \) :

Maxwell-Stefan diffusion coefficient, [ cm2 s−1]

N :

Molar flux, [mol cm−2 s−1]

q :

Molecular heat flux, [W cm−2 K−1]

n :

Outward normal vector

\( \widehat{\boldsymbol{K}} \) :

Permeability tensor, [cm2]

v :

Velocity, [cm s−1]

A v :

Active area of Pt per unit volume of catalyst layer, [cm2 cm−3]

a w :

Water activity

a lv :

Liquid-gas interfacial surface area per unit volume, [cm2 cm−3]

c :

Molar concentration, [mol cm−3]

C k :

Volume fraction of fluid k

D :

Fick’s diffusion coefficient, [cm2 s−1]

D K :

Knudsen diffusion coefficient, [cm2 s−1]

D T :

Thermo-osmotic diffusion coefficient, [mol cm−1s−1K−1]

E :

Half-cell voltage, [V]

EW :

Equivalent weight of the ionomer, [g mol−1]

F :

Faraday’s constant, [C mol−1]

h :

Convective heat transfer coefficient, [W cm−2K−1]

H g,  N :

Henry’s constant, [Pa cm3 mol−1]

i :

Volumetric current density, [A cm−3]

j :

Current density, [A cm−2]

\( {j}_0^{ref} \) :

Exchange current density, [A cm−2]

k :

Equilibrium rate constant, [cm s−1 (cm3mol−1)(α − 1)]

k e/ c :

Evaporation or condensation rate per unit of liquid-gas interfacial surface area, [mol cm−2 s−1]

K i,  j :

Frictional interaction coefficient between species i and j,  [N s cm−4]

k r :

Effective permeability, [cm2]

L :

Characteristic length, [cm]

M :

Molar mass, [g mol−1]

n d :

Electroosmotic drag coefficient

p :

Pressure, [g cm−1s−2]

R :

Universal gas constant, [J mol−1 K−1]

r p :

Pore radius, [cm]

S heat :

Volumetric heat source, [W cm−3]

T :

Absolute temperature, [K]

t :

Time, [s]

u i,  k :

Mobility of species i in phase k,  [cm2 mol J−1 s−1]

x :

Molar fraction

z i :

Valence (or charge number) of species i

BPP:

Bipolar plate

CL:

Catalyst layer

CSF:

Continuum surface force

CSS:

Continuum surface stress

ECSA:

Electrochemically active surface area

FEP:

Fluorinated ethylene propylene

GDL:

Gas diffusion layer

ICCP:

Ionomer covered catalyst particle

LS:

Level set

MEA:

Membrane electrode assembly

MPL:

Microporous layer

PEM:

Proton exchange membrane

PEMFC:

Proton exchange membrane fuel cell

PFSA:

Perfluorosulfonic acid

PLIC:

Piecewise linear interface calculation

PTFE:

Polytetrafluoroethylene

VOF:

Volume of fluid

α i :

Transfer coefficient for reaction i

\( \overline{\kappa} \) :

Partial viscosity, [g cm−1 s−1]

\( \overline{\nu} \) :

Specific volume, [cm3 g−1]

β :

Transfer coefficient for cathodic reaction

\( \widehat{\boldsymbol{\tau}} \) :

Cauchy stress tensor, [g cm−1 s−2]

Λ :

Collision diameter, [cm]

\( \widehat{\kappa} \) :

Surface curvature, [cm−1]

η :

Overpotential, [V]

\( \widehat{\boldsymbol{\beta}} \) :

Forchheimer correction tensor, [cm]

γ :

Surface tension coefficient, [g s−2]

γ i :

Order of reaction for reaction i

γ ads :

Potential range constant for adsorption isotherm

\( {\widehat{\mu}}_i \) :

Electrochemical potential of species i,  [J mol−1]

\( \widehat{\rho} \) :

Charge density, [C cm−3]

κ :

Thermal conductivity coefficient, [W cm−2 K−1]

λ :

Sorbed water content in the membrane

λ b :

Bulk viscosity, [g cm−1 s−1]

λ eq :

Equilibrium sorbed water content in the membrane

μ :

Dynamic viscosity, [g cm−1 s−1]

ν :

Rate of reaction, [mol cm−2s−1]

ω :

Mass fraction

ϕ k :

Electrostatic potential of phase k,  [V]

ψ :

Fraction of active platinum sites available

ρ :

Density, [g cm−3]

τ :

Shear stress tensor, [g cm−1 s−2]

σ :

Conductivity, [S cm−1]

τ :

Tortuosity

θ :

Coverage of intermediate reaction species

ε :

Volume fraction

∇:

Gradient

∇s:

Symmetric gradient

⊗:

Tensor product

Θ(x):

Heaviside step function

DA :

Dissociative adsorption reaction

g :

Gas mixture

H :

Heyrovsky reaction

i,  j:

Species indexes

k :

Phase index

m :

Electrolyte phase

p :

Percolation threshold

RA :

Reductive adsorption reaction

RD :

Reductive desorption reaction

RT :

Reductive transition reaction

s :

Solid phase

T :

Tafel reaction

V :

Volmer reaction

v :

Void phase

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    1. Energy Systems Design Laboratory, Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada

      M. Secanell, A. Jarauta, A. Kosakian, M. Sabharwal & J. Zhou

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      Adam Z. Weber

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    Secanell, M., Jarauta, A., Kosakian, A., Sabharwal, M., Zhou, J. (2019). PEM Fuel Cells: Modeling. In: Lipman, T., Weber, A. (eds) Fuel Cells and Hydrogen Production. Encyclopedia of Sustainability Science and Technology Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7789-5_1019

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