4.1 Introduction

Fuel cell technology, a core component in a hydrogen-based energy economy, has the advantages of high energy conversion efficiency, low pollution, and no dependency on depleting fossil resources. Significant progress has been made in the state-of-the-art in materials, design, and fabrication, however, the widespread commercialization of most fuel cells is still limited by issues such as high cost and low durability ^{[1] [2] [3] [4]}. Mathematical models are effective tools in understanding and optimization of various transport and electrochemical processes, leading to cost reduction and improved performance and durability. The purpose of this chapter is to summarize the current status of fundamental models for fuel cells that have been actively studied in the past decade.

A typical fuel cell can be schematically represented by the layered structure in Figure 4.1, where an electrolyte is placed between an anode and a cathode backing layer, or gas diffusion layer (GDL). A thin catalyst layer exists between the anode (or cathode) GDL and the electrolyte, referred to as the anode (or cathode) catalyst layer. The anode-electrolyte-cathode assembly is clamped between two bipolar plates, which house the flow channels for fuel and oxidant feed. Based on the charge carriers in the electrolytes, i.e., proton ( H ⁺), hydroxide ( OH ^?), carbonate ( CO ^2? ₃), and oxide ( o ^2?), fuel cells may be classified into four categories: acid fuel cell, alkaline fuel cell (AFC), molten carbonate fuel cell (MCFC),...