Mesoscopic Theories of Heat Transport in Nanosystems (eBook)

David Jou (born in Sitges, Catalonia, Spain in 1953) is Full Professor of Physics of Condensed Matter at the Autonomous University of Barcelona, Spain. He has published 230 research papers on nonequilibrium thermodynamics and statistical mechanics as well as several books, including Extended Irreversible Thermodynamics (with J. Casas-Vázquez and G Lebon, Springer, now in its 4th edition, 2014), Thermodynamics of Fluids Under Flow (with J. Casas-Vázquez and M. Criado-Sancho, Springer, 2014), and Understanding Non-equilibrium Thermodynamics (with G. Lebon and J. Casas-Vázquez, Springer, 2008). Vito Antonio Cimmelli (born in Sarno, Italy in 1958) is a Full Professor of Mathematical Physics at the University of Basilicata, Potenza, Italy. His research interests are the mathematical methods of nonequilibrium thermodynamics, nonlocal constitutive theories, and heat conduction far from equilibrium. Professor Cimmelli is the author of around 90 research articles on these topics. Antonio Sellitto (born in Nocera Inferiore, Italy in 1978) is a fixed-term researcher in Mathematical Physics at the University of Salerno, Italy, and an adjunct professor at the University of Basilicata, Potenza, Italy. In 2012 he was awarded an INdAM-SIMAI prize for his PhD thesis on “Nonequilibrium Temperature and Heat Transport Equations in Nanosystems”. He has published several papers on nonequilibrium thermodynamics and heat transport in nanosystems.

Preface 8
Acknowledgements 10
About This Book 12
Contents 18
1 Nonequilibrium Thermodynamics and Heat Transport at Nanoscale 21
1.1 Memory Effects and Generalized Entropy 22
1.2 Second-Order Nonlocal Effects 26
1.3 Higher-Order Fluxes and Nonlinear Hierarchy of Transport Equations: Ballistic Heat Transport 28
1.4 Nonequilibrium Temperature and Heat Transport 31
1.4.1 Dynamical Temperature 32
1.4.2 Flux-Dependent Absolute Temperature 35
1.4.3 Comparison of Nonequilibrium Temperatures Through Heat Pulse Experiments 36
1.4.4 Propagation of Temperature Waves Along Cylindrical Nanowires 39
References 46
2 Linear and Nonlinear Heat-Transport Equations 51
2.1 The Maxwell-Cattaneo-Vernotte Equation and Heat Waves 52
2.2 The Guyer-Krumhansl Equation and Phonon Hydrodynamics 53
2.3 The Nonlinear MCV and GK Equations 55
2.3.1 Characteristic Dimensionless Numbers for Heat Transport: Approximated Heat-Transport Equation 58
2.4 Other Generalized Heat-Transport Equations 61
2.4.1 The Dual-Phase-Lag Model 61
2.4.2 The Thermomass Theory 63
2.4.3 Anisotropic Heat Transport 65
2.4.4 Two-Population Ballistic-Diffusive Model 66
2.4.5 Effective Medium Approach 68
References 68
3 Mesoscopic Description of Boundary Effects and Effective Thermal Conductivity in Nanosystems: Phonon Hydrodynamics 72
3.1 Phonon Slip Flow 74
3.2 Size Dependence of the Effective Thermal Conductivity 78
3.2.1 Nanowires with Circular Cross Sections 79
3.2.2 Nanowires with Elliptical Cross Sections 82
3.2.3 Core-Shell and Tubular Smooth-Walled Nanowires 84
3.2.4 Thin Layers and Nanowires with Rectangular Cross Sections 86
3.2.5 Thin Channels Filled with Superfluid Helium 88
3.3 Phonon Backscattering and Roughness Dependence of the Effective Thermal Conductivity 89
3.3.1 Roughness Dependence of the Wall Coefficients 91
3.3.2 Effective Phonon Mean-Free Path and Nonlocal Effects 93
3.3.3 Phonon Backscattering and Conductor-InsulatorTransition 95
3.3.4 A Qualitative Microscopic Interpretation of C and ? 98
3.4 Phonon-Wall Interactions and Frequency-Dependent Thermal Conductivity in Nanowires 102
References 104
4 Mesoscopic Description of Effective Thermal Conductivity in Porous Systems, Nanocomposites and Nanofluids 109
4.1 Pore-Size Dependence of the Effective Thermal Conductivity 109
4.1.1 Results from Classical Fluid-Dynamics: The Correction Factors 112
4.1.2 Theoretical Thermal Conductivity of Porous Silicon 113
4.1.3 An EIT Approach 117
4.1.4 Microporous Films 117
4.2 Nanocomposites, Superlattices and Nanofluids 118
4.2.1 Thermal Conductivity of Nanocomposites 119
4.2.2 Thermal Conductivity of Superlattices 120
4.2.3 Thermal Conductivity of Nanofluids 121
References 123
5 Weakly Nonlocal and Nonlinear Heat Transport 127
5.1 Flux Limiters and Effective Thermal Conductivity of Short Carbon Nanotubes 127
5.2 Thermal Rectification in Tronco-Conical Nanowires 132
5.3 Axial Heat Transport in Thin Layers and Graphene Sheets 136
5.3.1 Nonlocal Heat Transport and Steady-State Temperature Profile in Thin Layers 138
5.3.1.1 Silicon Thin Layers 139
5.3.1.2 Graphene Sheets 142
5.3.2 Thermodynamic Aspects: Second Law at the Mean-Free Path Scale 143
5.4 Stability of the Heat Flow in Nanowires 146
References 148
6 Heat Transport with Phonons and Electrons and Efficiency of Thermoelectric Generators 151
6.1 Two-Temperature Model for Thermoelectric Effects 154
6.1.1 Possible Estimations of the Phonon and Electron Temperature 158
6.1.2 Efficiency of a Thermoelectric Energy Generator in a Two-Temperature Model 160
6.1.3 Influence of the Electric-Charge Density on the Optimal Efficiency of a Thermoelectric Energy Generator 164
6.2 One-Temperature Models: Effects of Non-local and Non-linear Breakings of Onsager Symmetry 168
6.2.1 The Nonlocal Model 169
6.2.1.1 Cylindrical Nanowires with e< R<
6.2.1.2 Cylindrical Nanowires with e< p<
6.2.2 The Crossed-Effects Nonlocal Model 176
6.2.3 The Nonlinear Model 178
References 182
7 Perspectives 185
Index 187