Losses in Fuel Cells
Fuel Cell Charge Transport
Mass Transport
Convection dominant in flow channels Diffusion dominant in electrode
Concentration Drop
i i
v v
p p nF
E RT E
Reactants Product
0 ln
Π
− Π
= ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
= ⎟⎠
⎜ ⎞
⎝
⎛ −
⎟ −
⎠
⎜ ⎞
⎝
⎛
RT nF
P RT P
nF
R
R e
C e C
C j C j
η α η
α (1 )
0 0 0
Diffusion In Electrode
Limiting Current Density
- To increase jL
Q: Are 1 & 2 are easy?
Q: Does anode has larger jL?
Diffusivity & Effective Diffusivity
Diffusivity from kinetic theory
Effective diffusivity
Nernst Effect
Concentration Effect
B-V for high current density
Mass Transportation Loss
Adding two losses
Pictorial View
Theoretical EMF or ideal voltage
Cell Voltage (V)
Current Density (A/cm2)
j ηact
N’
ηconc,1
ηconc,1 A
V
A’
N
Pictorial View
Theoretical EMF or ideal voltage
Cell Voltage (V)
Current Density (A/cm2) j
ηact ηconc,1
ηconc,1
ηconc,2
V
N’
A
A’
N
A*
A Very3 Tricky Example
PEMFC with or without temperature control
0 50 100 150 200 250 300 350 400 450 0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Voltage
Power density
Current density (mA/cm2) Voltage (V)
0 50 100 150 200 250
Power density (mW/cm
2)
Convection
Viscosity
Temperature effect or
Mixture
Viscosity: Example
Viscosity: Example
Viscosity: Example
In general, flow in fuel cell is laminar.
Pressure Drop In Flow Channels
Convective Mass Transport
Convective Mass Transport in PEMFC
5. Flow velocity in the channel is constant.
Convective Mass Transport in PEMFC
Convective Mass Transport in PEMFC
Convective Mass Transport in PEMFC
A More Realistic Alternative Solution
) ) (
(
) (
) (
x dx Bj
x dC
nF u
x j dx
d
nF dx x j u dx
u
in in in
−
=
−
=
⎟ =
⎠
⎜ ⎞
⎝
⎛ +
− ρ
ρ ρ ρ
ρuin
dx
(ρ+ρ/dx)uin j/nF
A More Realistic Alternative Solution
If constant Voltage instead of constant current is assumed
ax in
ax
RT nF
Ke x
j
A c
c
Ae x
c
x ac c e
x Bj c
x dx Bj
x dc
−
−
=
=
=
=
=
−
=
−
=
) (
) 0 (
) (
) ) (
) ( ) (
( /
0 0
0
η α
•Current drop Exponentially
•Concentration also drop exponentially
•HW 5.10
Flow Channel Design
PEMFC Flow Channel Design
PEMFC Flow Channel Design
Toyota Metal Mesh Flow Field