Table Of Contents:
Preface v
Introduction xiii

1 Fuel cell basics 1(38)

1.1 Fuel cell thermodynamics 1(5)

1.1.1 The physics of the fuel cell effect 1(3)

1.1.2 Open-circuit voltage 4(1)

1.1.3 Nernst equation 4(2)

1.1.4 Temperature dependence of OCV 6(1)

1.2 Potentials in a fuel cell 6(3)

1.3 Rate of electrochemical reactions 9(7)

1.3.1 Butler-Volmer equation 9(4)

1.3.2 Butler-Volmer and Nernst equations 13(2)

1.3.3 Tafel equation 15(1)

1.4 Mass transport in fuel Cells 16(16)

1.4.1 Overview of mass transport processes 16(2)

1.4.2 Stoichiometry and utilization 18(1)

1.4.3 Quasi-2D approximation 19(1)

1.4.4 Mass conservation equation in the channel 20(2)

1.4.5 Flow velocity in the channel 22(2)

1.4.6 Mass transport in gas-diffusion/backing layers 24(3)

1.4.7 Mass transport in catalyst layers 27(1)

1.4.8 Proton and water transport in membranes 28(4)

1.5 Sources of heat in a fuel cell 32(2)

1.6 Types of cells considered in this book 34(5)

1.6.1 Polymer electrolyte fuel cells (PEFCs) 34(2)

1.6.2 Direct methanol fuel cells (DMFCs) 36(1)

1.6.3 Solid oxide fuel cells (SOFCs) 37(2)

2 Catalyst layer performance 39(44)

2.1 Basic equations 41(3)

2.1.1 The general case 41(3)

2.1.2 First integral 44(1)

2.2 Ideal oxygen and proton transport 44(1)

2.3 Ideal oxygen transport 45(8)

2.3.1 Basic equations 45(1)

2.3.2 Integral of motion 45(1)

2.3.3 Equation for proton current 46(1)

2.3.4 Low cell current 47(1)

2.3.5 High cell current 48(3)

2.3.6 The general polarization curve 51(2)

2.3.7 Condition of negligible oxygen transport loss 53(1)

2.4 Ideal proton transport 53(2)

2.4.1 Basic equations 53(1)

2.4.2 The x-shapes and polarization curve 53(1)

2.4.3 Large cell current (ζ >> 1) 54(1)

2.4.4 Small cell current (ζ << 1) 55(1)

2.5 Optimal oxygen diffusion coefficient 55(3)

2.5.1 Reduction of the full system 55(1)

2.5.2 Optimal oxygen diffusivity 56(2)

2.6 Gradient of catalyst loading 58(6)

2.6.1 Model 58(4)

2.6.2 Polarization curve 62(2)

2.7 DMFC anode 64(10)

2.7.1 The rate of methanol oxidation 64(1)

2.7.2 Basic equations and the conservation law 65(2)

2.7.3 The general form of the polarization curve 67(1)

2.7.4 Small variation of overpotential in the active layer 68(3)

2.7.5 Active layer of variable thickness 71(3)

2.8 Heat balance in the catalyst layer 74(5)

2.8.1 Heat transport equation in the CL 75(1)

2.8.2 Reduction to the boundary condition 76(1)

2.8.3 Solution to the heat transport equation 77(2)

2.9 Remarks on Chapter 2 79(4)

3 One-dimensional model of a fuel cell 83(34)

3.1 Voltage loss due to oxygen transport in the GDL 84(2)

3.2 1D polarization curve of a cell 86(1)

3.3 1D model of DMFC 87(6)

3.3.1 Feed molecule concentration in the active layers 88(4)

3.3.2 1D polarization curve of DMFC 92(1)

3.4 Heat transport in the MEA of a PEFC 93(12)

3.4.1 General assumptions 93(1)

3.4.2 Equations 94(3)

3.4.3 Exact solutions 97(1)

3.4.4 Temperature profiles 98(2)

3.4.5 How to measure thermal conductivities of MEA layers 100(2)

3.4.6 One-sided fluxes from the MEA 102(2)

3.4.7 Heat crossover through the membrane 104(1)

3.5 Heat transport in the MEA of a DMFC 105(12)

3.5.1 Assumptions 106(1)

3.5.2 Equations 107(3)

3.5.3 Heat transport under open-circuit conditions 110(1)

3.5.4 How to measure thermal conductivities of MEA layers 111(2)

3.5.5 Temperature profiles and discussion 113(1)

3.5.6 Exact solutions for finite current 114(3)

4 Quasi-2D model of a fuel cell 117(76)

4.1 Gas dynamics of channel flow 118(5)

4.1.1 Momentum balance in the cathode flow 119(1)

4.1.2 The limit of low flow velocity 120(3)

4.2 A model of PEFC 123(10)

4.2.1 Oxygen concentration and local current along the channel 124(3)

4.2.2 Cell polarization curve 127(1)

4.2.3 Water crossover and the polarization curve 128(3)

4.2.4 Local polarization curves 131(2)

4.3 A model of PEFC with water management 133(14)

4.3.1 Model and governing equations 134(2)

4.3.2 Solution at constant flow velocity 136(1)

4.3.3 Close to the limiting current density (Eo →∞) 137(3)

4.3.4 The general case (finite Eo) 140(1)

4.3.5 Model validation 141(1)

4.3.6 Limiting current and optimal feed composition 142(1)

4.3.7 Constant oxygen stoichiometry 143(4)

4.4 Degradation wave 147(9)

4.4.1 Model 147(2)

4.4.2 Wave propagation 149(2)

4.4.3 Cell potential 151(2)

4.4.4 Two scenarios of cell performance degradation 153(1)

4.4.5 Accelerated testing of ageing phenomena 154(2)

4.5 Gradient of catalyst loading along the oxygen channel 156(4)

4.5.1 Low cell current 157(1)

4.5.2 High cell current 158(2)

4.5.3 The effect of transport loss in the GDL 160(1)

4.6 A model of SOFC anode 160(12)

4.6.1 Basic equations and the local polarization curve 162(2)

4.6.2 Hydrogen concentration in the channel 164(1)

4.6.3 Cell voltage 165(1)

4.6.4 Low current: z-shapes 166(1)

4.6.5 Low current: Polarization curve 167(2)

4.6.6 High current: z-shapes and polarization curve 169(2)

4.6.7 Remarks 171(1)

4.7 A model of DMFC 172(12)

4.7.1 Continuity equations in the feed channels 173(3)

4.7.2 Solution for the case of λa = λc 176(2)

4.7.3 Cell depolarization at zero current: Mixed potential 178(3)

4.7.4 Cross-linked feeding 181(2)

4.7.5 Oxygen and methanol utilization, and mean crossover current density 183(1)

4.7.6 Remarks 184(1)

4.8 DMFC: The general case of arbitrary λa and λc 184(2)

4.8.1 Equation for local current 184(1)

4.8.2 Numerical solution 185(1)

4.9 DMFC: Large methanol stoichiometry and small current 186(7)

4.9.1 The shape of the jumper 186(3)

4.9.2 Plateau 189(1)

4.9.3 Critical air flow rate 190(1)

4.9.4 Experimental verification 191(2)

5 Modelling of fuel cell stacks 193(80)

5.1 Temperature field in planar SOFC stacks 195(15)

5.1.1 General assumptions 195(1)

5.1.2 The general equation for bipolar plate temperature 196(2)

5.1.3 Heat balance in the air channel 198(1)

5.1.4 Heat balance in the BP 199(2)

5.1.5 Cell polarization curve 201(1)

5.1.6 Boundary conditions 202(1)

5.1.7 Method of asymptotic expansion 203(1)

5.1.8 Asymptotic solution 204(2)

5.1.9 Local current 206(1)

5.1.10 Example: Oxide-dominated stack resistivity 207(1)

5.1.11 Remarks 208(2)

5.2 Temperature gradient in SOFC stack 210(4)

5.2.1 Stack and air temperatures 210(2)

5.2.2 Temperature gradient 212(2)

5.3 Thermal waves in SOFC stack 214(12)

5.3.1 Basic equations 214(2)

5.3.2 Stability analysis 216(1)

5.3.3 Flow temperature is constant 217(1)

5.3.4 Solution: The general case 218(4)

5.3.5 Role of boundary conditions 222(1)

5.3.6 Remarks 223(3)

5.4 Heat effects in DMFC stack 226(10)

5.4.1 General assumptions 226(1)

5.4.2 Equations for stack and flow temperature 227(4)

5.4.3 Asymptotic solution: The general case 231(3)

5.4.4 Optimal stack temperature 234(2)

5.5 Mirroring of current-free spots in a stack 236(13)

5.5.1 Equation for bipolar plate potential 237(2)

5.5.2 Cell polarization curve 239(1)

5.5.3 Spot shape and numerical details 240(1)

5.5.4 Numerical results 241(2)

5.5.5 Analysis of equations: The length of mirroring 243(5)

5.5.6 Remarks 248(1)

5.6 Hybrid 3D model of SOFC stack 249(13)

5.6.1 Thermal model 250(2)

5.6.2 Electric problem 252(1)

5.6.3 Numerical details 253(2)

5.6.4 Numerical results 255(1)

5.6.5 Analysis of governing equations 255(5)

5.6.6 Temperature stratification 260(1)

5.6.7 The mechanism of anomalous heat transport 261(1)

5.7 Power generated and lost in a stack 262(11)

5.7.1 The nature of voltage loss in bipolar plates 262(1)

5.7.2 Power dissipated in a bipolar plate 263(2)

5.7.3 Power dissipated in a thin bipolar plate 265(2)

5.7.4 Useful power generated by the individual cell 267(3)

5.7.5 Illustration: A 1D case 270(3)
Bibliography 273(10)
Abbreviations 283(2)
Nomenclature 285(8)
Index 293