Analytical modelling of fuel cells / Andrei A. Kulikovsky.

Format:

Book

Author/Creator:

Kulikovsky, Andrei A., author.

Language:

English

Subjects (All):

Fuel cells--Mathematical models.

Fuel cells.

Physical Description:

1 online resource (384 pages)

Edition:

Second edition.

Place of Publication:

Amsterdam, Netherlands ; Kidlington, Oxford, England ; Cambridge, Massachusetts : Elsevier, [2019]

Summary:

Analytical Modelling of Fuel Cells, Second Edition, is devoted to the analytical models that help us understand the mechanisms of cell operation.The book contains equations for the rapid evaluation of various aspects of fuel cell performance, including cell potential, rate of electrochemical reactions, rate of transport processes in the cell, and.

Contents:

Front Cover

Analytical Modeling of Fuel Cells

Copyright

Contents

Preface to the First Edition

Preface to the Second Edition

Introduction

Dimensionless variables

Maple codes

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 open-circuit voltage

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

Fick's diffusion

Stefan-Maxwell diffusion

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 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

2.4.4 Small zeta

2.5 Optimal oxygen diffusion coef cient

2.5.1 Reduction of the full system.

2.5.2 Optimal oxygen diffusivity

2.6 Complete polarization curve of a PEMFC

2.6.1 Model equations

2.7 Gradient of catalyst loading

2.7.1 Model

2.7.2 Polarization curve

2.8 DMFC cathode and mixed potential

2.8.1 Model

Basic equations

Boundary conditions

First integral

2.8.2 Mixed potential

2.9 DMFC anode

2.9.1 The rate of methanol oxidation

2.9.2 Basic equations and the conservation law

2.9.3 The general form of the polarization curve

2.9.4 Small variation of overpotential in the active layer

2.9.5 Active layer of variable thickness

2.10 Heat balance in the catalyst layer

2.10.1 Heat transport equation in the CL

2.10.2 Reduction to boundary condition

2.10.3 Solution to the heat transport equation

2.11 Remarks on Chapter 2

3 One-dimensional model of a fuel cell

3.1 Voltage loss due to oxygen transport in the GDL

3.2 One-dimensional polarization curve of a cell

3.2.1 Fast oxygen transport in the CCL

3.2.2 General equation for the PEMFC polarization curve

Polarization curve tting

3.3 One-dimensional model of DMFC

3.3.1 Feed molecule concentration in the active layers

Methanol

Oxygen

3.3.2 One-dimensional polarization curve of DMFC

3.4 Heat transport in the MEA of a PEFC

3.4.1 General assumptions

3.4.2 Equations

3.4.3 Exact solutions

3.4.4 Temperature pro les

3.4.5 How to measure thermal conductivities of MEA layers

3.4.6 One-sided uxes from the MEA

3.4.7 Heat crossover through the membrane

4 Quasi-2D model of a fuel cell

4.1 Gas dynamics of channel ow

4.1.1 Momentum balance in the cathode ow

4.1.2 The limit of low ow velocity

4.2 A PEFC model

4.2.1 Oxygen concentration and local current along the channel

4.2.2 Cell polarization curve

4.2.3 Water crossover and the polarization curve.

4.2.4 Local polarization curves

4.3 Degradation wave

4.3.1 Model

4.3.2 Wave propagation

4.3.3 Cell potential

4.3.4 Two scenarios of cell performance degradation

4.4 A PEFC model with water management

4.4.1 Model and governing equations

4.4.2 Solution at constant ow velocity

4.4.3 Close to the limiting current density (Ẽ0 -&gt

8)

4.4.4 The general case ( nite Ẽ0)

4.4.5 Model validation

4.4.6 Limiting current, optimal feed composition

4.4.7 Constant oxygen stoichiometry

Modi cation of model equations

Condition of ideal membrane humidi cation

4.4.8 Accelerated testing of aging phenomena

4.5 Catalyst loading gradient along the oxygen channel

4.5.1 Low cell current

4.5.2 High cell current

4.5.3 The effect of transport loss in the GDL

4.6 Nonuniform aging of a PEM fuel cell

4.6.1 Are constant parameters along the channel optimal for the cell performance?

Constant parameters along the channel

Are the exponential shapes optimal?

Nonuniform oxygen diffusivity in the GDL

Nonuniform exchange current density

How to check if the shape of the local current is optimal?

4.6.2 Nonuniform catalyst degradation

4.6.3 Nonuniform GDL ooding

4.6.4 Combined case of aged catalyst and GDL

4.6.5 Remarks

4.7 A model of SOFC anode

4.7.1 Basic equations and the local polarization curve

4.7.2 Hydrogen concentration in the channel

4.7.3 Cell voltage

4.7.4 Low current: z-shapes

4.7.5 Low current: polarization curve

4.7.6 High current: z-shapes and polarization curve

4.7.7 Remarks

4.8 A DMFC model

4.8.1 Continuity equations in the feed channels

4.8.2 Solution for the case of equal oxygen and methanol stoichiometries

4.8.3 Cell depolarization at zero current

4.8.4 Cross-linked feeding.

4.8.5 Oxygen and methanol utilization, mean crossover current density

4.8.6 Remarks

4.9 DMFC: The general case of arbitrary stoichiometries

4.9.1 Equation for local current

4.9.2 Numerical solution

4.10 DMFC: large methanol stoichiometry, small current

4.10.1 The shape of the jumper

4.10.2 Plateau

4.10.3 Critical air ow rate

4.10.4 Experimental veri cation

5 Modeling of fuel cell stacks

5.1 Temperature eld in planar SOFC stack

5.1.1 General assumptions

5.1.2 The general equation for bipolar plate temperature

5.1.3 Heat balance in the air channel

5.1.4 Heat balance in the bipolar plate

5.1.5 Cell polarization curve and the heat transport equation

5.1.6 Boundary conditions

5.1.7 Method of asymptotic expansion

5.1.8 Asymptotic solution

5.1.9 Local current

5.1.10 Example: oxide-dominated stack resistivity

5.1.11 Remarks

5.2 Temperature gradient in SOFC stack

5.2.1 Stack and air temperatures

5.2.2 Temperature gradient

5.3 Thermal waves in SOFC stack

5.3.1 Basic equations

5.3.2 Stability analysis

5.3.3 Flow temperature is constant

5.3.4 Solution: the general case

5.3.5 Role of boundary conditions

5.3.6 Remarks

5.4 Heat effects in DMFC stack

5.4.1 General assumptions

5.4.2 Equations for stack and ow temperature

5.4.3 Asymptotic solution: the general case

5.4.4 Optimal stack temperature

5.5 Mirroring of current-free spots in a stack

5.5.1 Equation for bipolar plate potential

5.5.2 Incorporation of the cell polarization curve

5.5.3 Spot shape and numerical details

5.5.4 Numerical results

5.5.5 Analysis of equations: the length of mirroring

Equation for stack potential

The damping length of small-amplitude disturbance

5.5.6 Remarks

5.6 Hybrid 3D model of SOFC stack

5.6.1 Thermal model

5.6.2 Electric problem.

5.6.3 Numerical details

5.6.4 Numerical results

5.6.5 Analysis of governing equations

3D equation for stack temperature

The damping length

5.6.6 Temperature strati cation

5.6.7 The mechanism of anomalous heat transport

5.7 Power generated and lost in a stack

5.7.1 The nature of voltage loss in bipolar plates

5.7.2 Power dissipated in a bipolar plate

5.7.3 Power dissipated in a thin bipolar plate

5.7.4 Useful power generated by the individual cell

5.7.5 Illustration: a 1D case

5.8 Detection and localization of current-free spots in a fuel cell stack

5.8.1 Model

5.8.2 Numerical results

6 Applications of analytical models

6.1 Carbon corrosion in a PEMFC

6.1.1 Model

Currents: hydrogen on the anode

Currents: oxygen on the anode side

Currents: oxygen and carbon on the cathode side

Final form of the basic equation

6.1.2 Numerical results

6.2 Anode cracks, delaminated domains, and reference electrodes

6.2.1 Electrochemical model of a crack

6.2.2 Dead stripe

Inside the dead stripe

Outside the dead stripe

Matching conditions

Peak of the HOR current and the peak width

6.2.3 Single anode edge

Basic equation for F~ and solution

Peak of the HOR current density

Characteristic scale of membrane potential decay as x^-&gt

-8

Potential of the reference anode

6.2.4 Remarks

6.3 Reference electrode near curved anode edge

6.3.1 Model equations

6.3.2 Analytical solution

6.3.3 Positioning of a reference electrode

Shapes of overpotential for different anode radii

Debye screening

Positioning of the reference electrode

6.3.4 Remarks

6.3.5 The case of a nite cathode radius

6.3.6 Proof that the parameter A is bounded

7 Models for PEM fuel cell impedance

7.1 Introduction.

7.2 Basic model for impedance of the cathode catalyst layer in a PEMFC.

Notes:

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-444-64290-0

OCLC:

1100071216