Continuum Theory and Modeling of Thermoelectric Elements

Sound knowledge of the latest research results in the thermodynamics and design of thermoelectric devices, providing a solid foundation for thermoelectric element and module design in the technical development process and thus serving as an indispensable tool for any application development. The text is aimed mainly at the project developer in the field of thermoelectric technology, both in academia and industry, as well as at graduate and advanced undergraduate students. Some core sections address the specialist in the field of thermoelectric energy conversion, providing detailed discussion of key points with regard to optimization. The international team of authors with experience in thermoelectrics research represents such institutes as EnsiCaen Université de Paris, JPL, CalTech, and the German Aerospace Center.

Auteur
Christophe Goupil is professor at the Ecole Nationale Supérieure d'Ingénieurs in Caen, France. His research interest spans from experimental studies of vortices in the so-called high-Tc superconductors to theoretical thermodynamics. Professor Goupil has extensive experience in collaborative research with industrial partners, including major energy suppliers and companies of the automotive industry. He holds several patents. As expert in thermoelectric systems and thermodynamics of thermoelectricity, Professor Goupil currently pursues and develops his research activities at the Laboratoire Interdisciplinaire des Energies de demain at the Paris Interdisciplinary Energy Research Institute.

Contenu

List of Contributors XIII

Preface XV

List of Frequently Used Symbols XVII

Glossary XIX

1 Thermodynamics and Thermoelectricity 1
Christophe Goupil, Henni Ouerdane, Knud Zabrocki, Wolfgang Seifert, Nicki F. Hinsche, and Eckhard Müller

1.1 Milestones of Thermoelectricity 1

1.1.1 Discovery of the Seebeck Effect 2

1.1.2 Discovery of the Peltier Effect 8

1.1.3 Discovery of the Thomson Effect 9

1.1.4 Magnus' Law 10

1.1.5 Early Performance Calculation of Thermoelectric Devices 11

1.1.6 First Evaluation of the Performance of a Thermoelectric Device by E. Altenkirch 11

1.1.7 Benedicks' Effect 12

1.1.8 The Bridgman Effect 13

1.1.9 Semiconductors as Thermoelectric Materials 14

1.1.10 Thermoelectric Applications Excitement and Disappointment 19201970 15

1.1.11 Thermoelectric Industry Niche Applications 19702000 16

1.1.12 New Concepts in Thermoelectricity 2000-Present 17

1.2 Galvanomagnetic and Thermomagnetic Effects 17

1.2.1 The Hall Coefficient 21

1.2.2 The Nernst Coefficient 21

1.2.3 The Ettingshausen Coefficient 21

1.2.4 The RighiLeduc Coefficient 22

1.2.5 Devices Using Galvano- and Thermomagnetic Effects and the Corresponding Figure of Merit 22

1.3 Historical Notes on Thermodynamic Aspects 25

1.4 Basic Thermodynamic Engine 27

1.5 Thermodynamics of the Ideal Fermi Gas 28

1.5.1 The Ideal Fermi Gas 28

1.5.2 Electron Gas in a Thermoelectric Cell 29

1.5.3 Entropy Per Carrier 30

1.5.4 Equation of State of the Ideal Electron Gas 32

1.5.5 Temperature Dependence of the Chemical Potential c(T) 34

1.6 Linear Nonequilibrium Thermodynamics 35

1.6.1 Forces and Fluxes 35

1.6.2 Linear Response and Reciprocal Relations 36

1.7 Forces and Fluxes in Thermoelectric Systems 37

1.7.1 Thermoelectric Effects 37

1.7.2 Forces, Fluxes, and Kinetic Coefficients 38

1.7.3 Energy Flux and Heat Flux 39

1.7.4 Thermoelectric Coefficients 40

1.7.5 The Entropy Per Carrier 41

1.7.6 Kinetic Coefficients and Transport Parameters 42

1.7.7 The Dimensionless Figure of Merit zT 43

1.8 Heat and Entropy 44

1.8.1 Volumetric Heat Production 45

1.8.2 Entropy Production Density 45

1.8.3 Heat Flux and the PeltierThomson Coefficient 46

1.8.4 The PeltierThomson Term 46

1.8.5 Local Energy Balance 47

1.9 The Thermoelectric Engine and Its Applications 48

1.10 Thermodynamics and Thermoelectric Potential 50

1.10.1 Relative Current, Dissipation Ratio, and Thermoelectric Potential 51

1.10.2 Local Reduced Efficiency and Thermoelectric Potential of TEG, TEC, and TEH 53

1.10.3 Thermoelectric Potential and Nonequilibrium Thermodynamics 56

2 Continuum Theory of TE Elements 75
Knud Zabrocki, Christophe Goupil, Henni Ouerdane, Yann Apertet, Wolfgang Seifert, and Eckhard Müller

2.1 Domenicali's Heat Balance Equation 75

2.1.1 Tensorial Character of Material Properties 75

2.1.2 Heat Balance and Source Terms 76

2.1.3 Spatial and Temperature Averaging of the Material Properties 79

2.2 Transferred Heat Balance 80

2.3 Ioffe's Description and Performance Parameters of CPM Devices 81

2.3.1 Single-Element Device 82

2.3.2 Performance Parameters of a Thermoelectric Element with Constant Material Properties 84

2.3.3 Inverse Performance Equations and Effective Device Figure of Merit 91

2.4 Maximum Power and Efficiency of a Thermogenerator Element 93

2.4.1 Load Resistance as Design Parameter for a Thermogenerator 96

2.4.2 Efficiency versus Power Approach 97

2.4.3 Constant Heat Input (CHI) Model 100

2.5 Temperature-Dependent MaterialsAnalytic Calculations 102

2.5.1 Inverse Temperature Dependence of the Thermal Conductivity 103 2.5.2 Inverse Temperature Dependence of the T...