Hydrogen fuel cells (HFCs) are devices used to generate electricity from the electrochemical reaction between air and the fuel (hydrogen gas). An attractive advantage of these devices is that their by-product is water vapour, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, and optimizing their operating conditions.

In this talk, we consider the cathode part of the fuel cell. Our Objective is to improve the HFC’s efficiency through optimizing the classical geometry of the cathode air channel.

To tackle this problem, we first introduce and validate a mathematical model describing the physics taking place in the cathode part. The cathode involves the air channel, gas diffusion layer (GDL, a porous medium) and catalyst layer (modeled as an interface). The mathematical model is based on conservation laws of mass, momentum and electrical charges. We assume the system to be a single gas-phase, isothermal, and at steady state.

Next, we introduce a shape optimization problem, which is defined as minimization of a cost functional subjected to the state equations. The cost functional concerns about the following three efficiency objectives:

· maximizing the total the current density over the catalyst layer

· minimizing the total variance of the current density over the catalyst layer

· minimizing the pressure drop used to deliver the air in the air channel

We present optimal shape designs for the cathode air channel to meet the individual and mixed objectives, and discuss the numerical methods as well as the existence and uniqueness of the solution.