Analytical Modelling of Fuel Cells

1st Edition

Authors: Andrei Kulikovsky
Hardcover ISBN: 9780444535603
eBook ISBN: 9780444535610
Imprint: Elsevier
Published Date: 29th June 2010
Page Count: 312
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In fuel cell research, the gap between fundamental electrochemical processes and the engineering of fuel cell systems is bridged by the physical modelling of fuel cells. This relatively new discipline aims to understand the basic transport and kinetic phenomena in a real cell and stack environment, paving the way for improved design and performance. The author brings his unique approach to the analytical modeling of fuel cells to this essential reference for energy technologists.

Key Features

  • Covers recent advances and analytical solutions to a range of problems faced by energy technologists, from catalyst layer performance to thermal stability
  • Provides detailed graphs, charts and other tools (glossary, index) to maximize R&D output while minimizing costs and time spent on dead-end research
  • Presents Kulikovsky’s signature approach (and the data to support it)—which uses "simplified" models based on idealized systems, basic geometries, and minimal assumptions—enabling qualitative understanding of the causes and effects of phenomena


Professionals working in the energy market (transportation, residential, industrial, military,and aerospace segments), chemical engineers, mechanical engineers, and organic chemists

Table of Contents

1 Fuel cell basics
1.1 Fuel cell thermodynamics
1.1.1 The physics of the fuel cell effect
1.1.2 Open-circuit voltage
1.1.3 Nernst equation
1.1.4 Temperature dependence of OCV
1.2 Potentials in a fuel cell
1.3 Rate of electrochemical reactions
1.3.1 Butler-Volmer equation
1.3.2 Butler-Volmer and Nernst equations
1.3.3 Tafel equation
1.4 Mass transport in fuel cells
1.4.1 Overview of mass transport processes
1.4.2 Stoichiometry and utilization
1.4.3 Quasi-2D approximation
1.4.4 Mass conservation equation in the channel
1.4.5 Flow velocity in the channel
1.4.6 Mass transport in gas diffusion/backing layers
1.4.7 Mass transport in catalyst layers
1.4.8 Proton and water transport in membrane
1.5 Sources of heat in a fuel cell
1.6 Types of cells considered in this book
1.6.1 Polymer electrolyte fuel cells (PEFCs)
1.6.2 Direct methanol fuel cells (DMFCs)
1.6.3 Solid oxide fuel cells (SOFCs)
2 Catalyst layer performance
2.1 Basic equations
2.1.1 The general case
2.1.2 First integral
2.2 Ideal oxygen and proton transport
2.3 Ideal oxygen transport
2.3.1 Basic equations
2.3.2 Integral of motion
2.3.3 Equation for proton current
2.3.4 Low cell current
2.3.5 High cell current
2.3.6 The general polarization curve
2.3.7 Condition of negligible oxygen transport loss
2.4 Ideal proton transport
2.4.1 Basic equations
2.4.2 The x-shapes and polarization curve
2.4.3 Large zeta (zeta greater than 1)
2.4.4 Small zeta (zeta less than 1)
2.5 Optimal oxygen diffusion coe±cient
2.5.1 Reduction of the full system
2.5.2 Optimal oxygen diffusivity
2.6 Gradient of catalyst loading
2.6.1 Model
2.6.2 Polarization curve
2.7 DMFC anode
2.7.1 The rate of methanol oxidation
2.7.2 Basic equations and the conservation law
2.7.3 The general form of the polarization curve
2.7.4 Small variation of overpotenti


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About the Author

Andrei Kulikovsky

Affiliations and Expertise

Research Centre Julich, Julich, Germany


"This is a well-written introduction to the modeling of fuel cells that the reader will no doubt want to supplement by referring to published research articles (a comprehensive bibliography is included).  It is written by a physicist, but is clearly influenced by engineering rather than science…It uses ‘simplified’ models based on idealized systems, basic geometries and minimal assumptions, enabling the qualitative understanding of the causes and effects of the system phenomena. In this way it shows how analytical modeling can be applied to real fuel cell systems." --Energy News