Acknowledgments ................................................ ix
1 An Introduction to Fuel Cells ................................ 1
1.1 Introduction ............................................ 1
1.2 What Is a Fuel Cell? .................................... 2
1.3 Why Do We Need Fuel Cells? .............................. 4
1.4 History of Fuel Cells ................................... 6
1.5 Mathematical Models in the Literature ................... 8
1.6 Creating Mathematical Models ........................... 12
Chapter Summary ............................................. 13
Problems .................................................... 14
Bibliography ................................................ 14
2 Fuel Cell Thermodynamics .................................... 15
2.1 Introduction ........................................... 15
2.2 Enthalpy ............................................... 16
2.3 Specific Heats ......................................... 18
2.4 Entropy ................................................ 27
2.5 Free Energy Change of a Chemical Reaction .............. 33
2.6 Fuel Cell Reversible and Net Output Voltage ............ 44
2.7 Theoretical Fuel Cell Efficiency ....................... 44
Chapter Summary ............................................. 47
Problems .................................................... 47
Bibliography ................................................ 47
3 Fuel Cell Electrochemistry .................................. 49
3.1 Introduction ........................................... 49
3.2 Basic Electrokinetics Concepts ......................... 49
3.3 Charge Transfer ........................................ 51
3.4 Activation Polarization for Charge Transfer
Reactions .............................................. 53
3.5 Electrode Kinetics ..................................... 54
3.6 Voltage Losses ......................................... 64
3.7 Internal Currents and Crossover Currents ............... 74
Chapter Summary ............................................. 75
Problems .................................................... 75
Bibliography ................................................ 76
4 Fuel Cell Charge Transport .................................. 77
4.1 Introduction ........................................... 77
4.2 Voltage Loss Due to Charge Transport ................... 77
4.3 Electron Conductivity of Metals ........................ 88
4.4 Ionic Conductivity of Polymer Electrolytes ............. 89
Chapter Summary ............................................. 94
Problems .................................................... 96
Bibliography ................................................ 96
5 Fuel Cell Mass Transport .................................... 97
5.1 Introduction ........................................... 97
5.2 Fuel Cell Mass Balances ................................ 98
5.3 Convective Mass Transport from Flow Channels
to Electrode .......................................... 108
5.4 Diffusive Mass Transport in Electrodes ................ 110
5.5 Convective Mass Transport in Flow Field Plates ........ 114
5.6 Mass Transport Equations in the Literature ............ 120
Chapter Summary ............................................ 124
Problems ................................................... 124
Bibliography ............................................... 125
6 Heat Transfer .............................................. 127
6.1 Introduction .......................................... 127
6.2 Basics of Heat Transfer ............................... 128
6.3 Fuel Cell Energy Balances ............................. 132
6.4 Fuel Cell Heat Management ............................. 156
Chapter Summary ............................................ 164
Problems ................................................... 164
Bibliography ............................................... 165
7 Modeling the Proton Exchange Structure ..................... 167
7.1 Introduction .......................................... 167
7.2 Physical Description of the Proton Exchange
Membrane .............................................. 168
7.3 Types of Models ....................................... 171
7.4 Proton Exchange Membrane Modeling Example ............. 177
Chapter Summary ............................................ 192
Problems ................................................... 193
Bibliography ............................................... 193
8 Modeling the Gas Diffusion Layers .......................... 197
8.1 Introduction .......................................... 197
8.2 Physical Description of the Gas Diffusion Layer ....... 198
8.3 Basics of Modeling Porous Media ....................... 199
8.4 Modes of Transport in Porous Media .................... 202
8.5 Types of Models ....................................... 210
8.6 GDL Modeling Example .................................. 215
Chapter Summary ............................................ 236
Problems ................................................... 236
Bibliography ............................................... 239
9 Modeling the Catalyst Layers ............................... 243
9.1 Introduction .......................................... 243
9.2 Physical Description of the РЕМ Fuel Cell Catalyst
Layers ................................................ 245
9.3 General Equations ..................................... 246
9.4 Types of Models ....................................... 248
9.5 Heat Transport in the Catalyst Layers ................. 255
Chapter Summary ............................................ 262
Problems ................................................... 265
Bibliography ............................................... 265
10 Modeling the Flow Field Plates ............................. 269
10.1 Introduction .......................................... 269
10.2 Flow Field Plate Materials ............................ 271
10.3 Flow Field Design ..................................... 272
10.4 Channel Shape, Dimensions, and Spacing ................ 275
10.5 Pressure Drop in Flow Channels ........................ 276
10.6 Heat Transfer from the Plate Channels to the Gas ...... 283
Chapter Summary ............................................ 296
Problems ................................................... 296
Bibliography ............................................... 297
11 Modeling Micro Fuel Cells .................................. 299
11.1 Introduction .......................................... 299
11.2 Micro РЕМ Fuel Cells in the Literature ................ 301
11.3 Microfluidics ......................................... 307
11.4 Flow Rates and Pressures .............................. 313
11.5 Bubbles and Particles ................................. 314
11.6 Capillary Effects ..................................... 315
11.7 Single-and Two-Phase Pressure Drop .................... 316
11.8 Velocity in Microchannels ............................. 318
Chapter Summary ............................................ 330
Problems ................................................... 330
Bibliography ............................................... 332
12 Modeling Fuel Cell Stacks .................................. 335
12.1 Introduction .......................................... 335
12.2 Fuel Cell Stack Sizing ................................ 335
12.3 Number of Cells ....................................... 337
12.4 Stack Configuration ................................... 338
12.5 Distribution of Fuel and Oxidants to the Cells ........ 340
12.6 Stack Clamping ........................................ 346
Chapter Summary ............................................ 359
Problems ................................................... 360
Bibliography ............................................... 360
13 Fuel Cell System Design .................................... 365
13.1 Introduction .......................................... 365
13.2 Fuel Subsystem ........................................ 366
Chapter Summary ............................................ 390
Problems ................................................... 390
Bibliography ............................................... 391
14 Model Validation ........................................... 393
14.1 Introduction .......................................... 393
14.2 Residuals ............................................. 393
14.3 Normal Distribution of Normal Random Errors ........... 398
14.4 Missing Terms in the Functional Part of the Model ..... 401
14.5 Unnecessary Terms in the Model ........................ 405
Chapter Summary ............................................ 407
Problems ................................................... 408
Bibliography ............................................... 408
Appendix A .................................................... 409
Appendix В .................................................... 411
Appendix С .................................................... 413
Appendix D .................................................... 415
Appendix E .................................................... 417
Appendix F .................................................... 419
Appendix G .................................................... 427
Appendix H .................................................... 429
Appendix I .................................................... 431
Appendix J .................................................... 433
Index ......................................................... 485
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