Non Fourier Heat Conduction

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.

This is the first single volume monograph that systematically summarizes the recent progress in using non-Fourier heat conduction theories to deal with the multiphysical behaviour of smart materials and structures. The book contains six chapters and starts with a brief introduction to Fourier and non-Fourier heat conduction theories. Non-Fourier heat conduction theories include Cattaneo-Vernotte, dual-phase-lag (DPL), three-phase-lag (TPL), fractional phase-lag, and nonlocal phase-lag heat theories. Then, the fundamentals of thermal wave characteristics are introduced through reviewing the methods for solving non-Fourier heat conduction theories and by presenting transient heat transport in representative homogeneous and advanced heterogeneous materials. The book provides the fundamentals of smart materials and structures, including the background, application, and governing equations. In particular, functionally-graded smart structures made of piezoelectric, piezomagnetic, and magnetoelectroelastic materials are introduced as they represent the recent development in the industry. A series of uncoupled thermal stress analyses on one-dimensional structures are also included. The volume ends with coupled thermal stress analyses of one-dimensional homogenous and heterogeneous smart piezoelectric structures considering different coupled thermopiezoelectric theories. Last but not least, fracture behavior of smart structures under thermal disturbance is investigated and the authors propose directions for future research on the topic of multiphysical analysis of smart materials.

This book mainly focuses on the theoretical and experimental study of non-Fourier heat conduction behavior. A novel thermomass theory is used as the theoretical basis, which provides a general heat conduction equation for the accurate prediction of non-Fourier heat conduction. In order to prove the validity of this thermomass theory, a large current was used to heat the metallic nanofilm at the minimum temperature of 3 K. The measured average temperature of the nanofilm was notably higher than the prediction of Fourier’s heat diffusion equation, while matching well with the general heat conduction equation. This is the first time that steady non-Fourier heat conduction has been observed. Moreover, this book concerns the role of electron-phonon interaction in metallic nanofilms, which involves the breakdown of the Wiedemann-Franz law at low temperatures and interfacial thermal resistance at femtosecond timescales. Readers will find useful information on non-Fourier heat conduction and the latest advances in the study of charge and heat transport in metallic nanofilms.

This thesis studies the general heat conduction law, irreversible thermodynamics and the size effect of thermal conductivity exhibited in nanosystems from the perspective of recently developed thermomass theory. The derivation bridges the microscopic phonon Boltzmann equation and macroscopic continuum mechanics. Key concepts such as entropy production, temperature and the Onsager reciprocal relation are revisited in the case of non-Fourier heat conduction. Lastly, useful expressions are extracted from the picture of phonon gas dynamics and are used to successfully predict effective thermal conductivity in nanosystems.

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.

Nearly thirty years since its first publication, the highly anticipated fourth edition of Heat Conduction upholds its reputation as an instrumental textbook and reference for graduate students and practicing engineers in mechanical engineering and thermal sciences. Written to suit a one-semester graduate course, the text begins with fundamental concepts, introducing the governing equation of heat conduction as derived from the First law of Thermodynamics. Solutions for one-dimensional conduction follow, then orthogonal functions, Fourier series and transforms, and multi-dimensional problems. Later sections focus on a series of specialized techniques, including integral equations, Laplace transforms, finite difference numerical methods, and variational formulations. Two new chapters (9 and 11) have been added to cover heat conduction with local heat sources and heat conduction involving phase change. Applications of Fourier transforms in the semi-infinite and infinite regions have been added to Chapter 7 and Chapter 10 has been expanded to include solutions by the similarity method. Also new to the fourth edition are additional problems at the end of each chapter.

This book provides a detailed yet comprehensive presentation of the theory of periodic conjugate heat transfer. It contains an analytical approach to the effects of thermophysical and geometrical properties of a solid body on the experimentally determined heat transfer coefficient. The main objective of the book is a simplified description of the interaction between a solid body and a fluid as a boundary value problem of the heat conduction equation.This third and extended edition covers Wall's thermal effect on Landau stability, gas bubbles pulsations in fluids, and also the interplay between periodic conjugate heat transfer and non-Fourier heat conduction. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students in engineering.

Many phenomena in social, natural and engineering fields are governed by wave, potential, parabolic heat-conduction, hyperbolic heat-conduction and dual-phase-lagging heat-conduction equations. This monograph examines these equations: their solution structures, methods of finding their solutions under various supplementary conditions, as well as the physical implication and applications of their solutions.