Losses in Fuel Cells
Fuel Cell Charge Transport
Mass Transport
Convection dominant in flow channels Convection dominant in flow channels Diffusion dominant in electrode
Concentration Drop
vi
p
RT P d t
0 l Π ⎜⎛ ⎜⎝⎛ ⎟⎠⎞ −⎜⎝⎛ −RT ⎟⎠⎞ ⎟⎞
nF RT P
nF
R C
C α η (1 α) η
vi
p p nF
E RT E
Reactants Product
0 ln
Π
− Π
= ⎟⎟
⎜ ⎠
⎜
⎝
−
= ⎝ ⎠ ⎝ RT ⎠
P RT P
R
R e
C e C
C j C
j 0 0 0
Diffusion In Electrode
Limiting Current Density
- To increase j - 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
Pictorial View
Pictorial View
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 u j
u ⎟⎞ =
⎜⎛ +
− ρ ρ
ρ
) (x j d
nF dx u dx
uin in
−
=
⎟ =
⎜ ⎠
⎝ +
− ρ
ρ ρ
) ) (
( Bj x
d x dC
nF u
dx in
−
= j( ) dx
A More Realistic Alternative Solution
If constant Voltage instead of constant current is assumed
RT
x nF
B c x B
dc ( ) ( )
) ) (
( 0 α η/
ax
RT nF
A
x ac c e
x Bj c
x dx Bj
x dc
−
=
−
=
−
= )
(
) ) (
) ( ) (
( /
0 0
0
η α
in ax
A c
c
Ae x
c
=
=
= ) 0 (
) (
Ke ax
x
j( ) = −
•Current drop ExponentiallyCurrent drop Exponentially
•Concentration also drop exponentially
•HW 5.10
Flow Channel Design
PEMFC Flow Channel Design
PEMFC Flow Channel Design
Flow Visualization (Neutron Radiography)
PEMFC serpentine cathode channels Dark area is liquid filled PEMFC serpentine cathode channels. Dark area is liquid filled.
DMFC parallel anode channels. Bright area is CO2
filled filled
Flow Visualization
