Page 108 - Introduction to Transfer Phenomena in PEM Fuel Cells

The mass fraction (w i) of the gas (i) is calculated from the molar fraction
(x i) and the molar mass of the gases as follows [NGU 10]:
 xM i Mass Transfer Phenomena 97
⋅
i
 w = N
i
  xM
⋅
 j j
 j1 = [3.29]
 N
  w = 1
 i
 i1 =
For a good description of mass transfer in the binary mixture at the anode
and ternary at the cathode, the system of coupled differential equations must
be solved.
The transfer is considered to be unidirectional according to (Ox), and that
the system is isobaric [RAM 05]; therefore:

– at the anode:
- the gaseous mixture is binary; the species involved are hydrogen and
water vapor, so the equation system to solve is written as:
 x + x a = 1
 H 2 H O

2
 dx H 1  ( a )  [3.30]
 2 = eff ⋅  x H 2 ⋅ N H O + N H 2 − N H 2 
⋅
2
  dx cD H,H O
2
2
- at the diffuser inlet, the relative humidities (RH) in the gaseous
mixture introduced into the bipolar plate channels are expressed as follows:
 ae p sat
 x HO = HR ⋅
a
 2 p
 [3.31]
 x e =− p sat
1 HR ⋅
 H 2 a p

The exponent “ e ” refers to the input supply conditions of the fuel cell;