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Title
Non-Fourier heat conduction : from phase-lag models to relativistic and quantum transport / Alexander I. Zhmakin.
ISBN
9783031259739 electronic book
3031259734 electronic book
9783031259722
3031259726
Published
Cham, Switzerland : Springer, [2023]
Language
English
Description
1 online resource (ix, 422 pages) : illustrations
Item Number
10.1007/978-3-031-25973-9 doi
Call Number
TA418.54 .Z46 2023
Dewey Decimal Classification
536/.2012
Summary
This book presents a broad and well-structured overview of various non-Fourier heat conduction models. The classical Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation becomes dominant and memory or non-local spatial effects become significant; e.g., during ultrafast heating, heat transfer at the nanoscale, in granular and porous materials, at extremely high values of the heat flux, or in heat transfer in biological tissues. The book looks at numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory, such as hereditary materials, including fractional hereditary materials, and/or spatial non-locality, i.e. materials with a non-homogeneous inner structure. Beginning with an introduction to classical transport theory, including phase-lag, phonon, and thermomass models, the book then looks at various aspects of relativistic and quantum transport, including approaches based on the Landauer formalism as well as the Green-Kubo theory of linear response. Featuring an appendix that provides an introduction to methods in fractional calculus, this book is a valuable resource for any researcher interested in theoretical and numerical aspects of complex, non-trivial heat conduction problems.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from digital title page (viewed on July 25, 2023).
1. Introduction
2. Phase-Lag Models
3. Phonon Models
4. Thermomass Model
5. Mesoscopic Moment Equations
6. Micro-Temperature & Micromorphic Temperature Models
7. Thermodynamic Models
8. Fractional Derivative Models
9. Fractional Boltzmann and Fokker-Planck equations
10. Elasticity and thermal expansion coupling
11. Some Exact Solutions
12. Relativistic Brownian Motion
13. Relativistic Boltzmann Equation
14. Variational Models
15. Relativistic Thermodynamics
16. Landauer approach
17. Green-Kubo approach
18. Coherent Phonon Transport
19. Conclusions.
