Hydrogen membrane fuel cell with electrode assembly

The fuel cell of claim 10, wherein a ratio of length to thickness

• (
• w
• h
• )
• of the GDL ranges from about 10:1 to 100:1.

The fuel cell of claim 10, wherein a ratio of length to thickness

• (
• ℓ
• h
• )
• of the GDL ranges from about 10:1 to 100:1.

The fuel cell of claim 10, wherein a ratio of length to thickness

• (
• ℓ
• h
• )
• of the GDL ranges from about 50:1 to 70:1.

A fuel cell with a membrane electrode assembly comprising:

• a catalyst layer (“CL”),
• a cathode gas diffusion layer (“GDL”), and
• hardware comprising a channel which has an inlet and outlet through which the oxygen can flow;
• wherein the GDL has a length (x-axis, ), thickness (y-axis, h) and width (z-axis, w) and is adjacent the channel in the fuel cell,
• wherein a porosity of the GDL increases along the length of the GDL, wherein the length of the GDL is measured from an end of the GDL nearest the inlet, and wherein a porosity is defined as an amount of unit surface area of the GDL occupied by pores,
• wherein the GDL has a porosity gradient to permit flow of oxygen through the GDL such that an oxygen mass fraction along the length or x-axis of the GDL meets boundary condition (6):
• p
• _
• g
• =
• _
• p
• _
• in
• +
• _
• p
• _
• out
• -
• _
• p
• _
• in
• ℓ
• ⁢
• x
• _
• ,
• _
• c
• _
• o
• =
• _
• ε
• _
• (
• x
• _
• )
• ⁢
• (
• c
• _
• in
• +
• _
• c
• _
• out
• -
• _
• c
• _
• in
• ℓ
• _
• ⁢
• x
• _
• )
• ,
• _
• (
• 6
• )
• _
• where pg is gas density, pin is inlet pressure, pout is outlet pressure, and x is a space variable;
• where co is the oxygen mass fraction, wherein E is the porosity of the GDL, x is a space variable, cin is inlet oxygen mass fraction, and cout is outlet oxygen mass fraction;
• the porosity of the GDL along the length ε=ε(x) is obtained by minimizing cost functional E.
• E
• _
• (
• _
• ε
• ;
• _
• ⁢
• c
• _
• o
• )
• _
• :=
• _
• 1
• _
• 2
• _
• ⁢
• a
• _
• ⁢
• ∫
• _
• M
• ⁢
• (
• c
• _
• o
• -
• _
• 1
• _
• ❘
• "\[LeftBracketingBar]"
• _
• M
• _
• ❘
• "\[RightBracketingBar]"
• _
• ⁢
• ∫
• _
• M
• ⁢
• c
• _
• o
• )
• -
• 2
• -
• _
• b
• _
• ⁢
• ∫
• _
• M
• ⁢
• c
• _
• o
• 2
• ,
• _
• (
• 7
• )
• wherein co is obtained from solution of boundary condition (6), and a and b are scalar and M is the catalyst layer;
• wherein the GDL meets the condition:
• E(ε*;
• U*)=min E(ε;
• U),
• subject to
• A(ε;
• U)=0.
• wherein the solution is a minimizer of Lagrangian L, defined as
• (ε, W, Λ):=E(ε, W)+ΛA(ε;
• W);
• and
• wherein εn is represented by εn+1=εn−δn∂nE(εn, Un),
• wherein a local minimizer (ε*, U*, Λ*) of the Lagrangian L that satisfies
• ∇L(ε*, U*, Λ*)=0;
• meets the conditions:
• ∂εL(ε*, U*, Λ*)=∂ε(ε*;
• U*)+Λ*∂εA(ε*;
• U*)=0;
• ∂WL(ε*, U*, Λ*)=∂W(ε*;
• U*)+Λ*∂WA(ε*;
• U*)=0;
• and
• ∂ΛL(ε*, U*, Λ*)=A(ε*;
• U*)=0,
• wherein the porosity εn is in a range of from 0.4 to 0.8 and parameter δn is selected to keep porosity within this range,
• wherein a ratio of width to thickness
• (
• w
• _
• h
• _
• )
• of the GDL is in a range of from 10:1 to 100:1, and
• wherein a ratio of length to thickness
• (
• ℓ
• _
• h
• _
• )
• of the GDL is in a range of from 50:1 to 70:1.