Physical processes taking place in micro/nanoscale strongly depend on the material types and can be very complicated. Known approaches include kinetic theory and quantum mechanics, non-equilibrium and irreversible thermodynamics, molecular dynamics, and/or fractal theory and fraction model. Due to innately different physical bases employed, different approaches may involve different physical properties in describing micro/nanoscale heat transport. In addition, the parameters involved in different approaches, may not be mutually inclusive. Macro- to Microscale Heat Transfer: The Lagging Behavior, Second Edition continues the well-received concept of thermal lagging through the revolutionary approach that focuses on the finite times required to complete the various physical processes in micro/nanoscale. Different physical processes in heat/mass transport imply different delay times, which are common regardless of the material type. The delay times, termed phase lags, are characteristics of materials. Therefore the dual-phase-lag model developed is able to describe eleven heat transfer models from macro to nanoscale in the same framework of thermal lagging. Recent extensions included are the lagging behavior in mass transport, as well as the nonlocal behavior in space, bearing the same merit of thermal lagging in time, in shrinking the ultrafast response down to the nanoscale. Key features: Takes a unified approach describing heat and mass transport from macro, micro to nanoscale Compares experimental results for model validation Includes easy to follow mathematical formulation Accompanied by a website hosting supporting material Macro- to Microscale Heat Transfer: The Lagging Behavior, Second Edition is a comprehensive reference for researchers and practitioners, and graduate students in mechanical, aerospace, biological and chemical engineering.

Stochastic Systems

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.

HEAT CONDUCTION Mechanical Engineering THE LONG-AWAITED REVISION OF THE BESTSELLER ON HEAT CONDUCTION Heat Conduction, Third Edition is an update of the classic text on heat conduction, replacing some of the coverage of numerical methods with content on micro- and nanoscale heat transfer. With an emphasis on the mathematics and underlying physics, this new edition has considerable depth and analytical rigor, providing a systematic framework for each solution scheme with attention to boundary conditions and energy conservation. Chapter coverage includes: Heat conduction fundamentals Orthogonal functions, boundary value problems, and the Fourier Series The separation of variables in the rectangular coordinate system The separation of variables in the cylindrical coordinate system The separation of variables in the spherical coordinate system Solution of the heat equation for semi-infinite and infinite domains The use of Duhamel’s theorem The use of Green’s function for solution of heat conduction The use of the Laplace transform One-dimensional composite medium Moving heat source problems Phase-change problems Approximate analytic methods Integral-transform technique Heat conduction in anisotropic solids Introduction to microscale heat conduction In addition, new capstone examples are included in this edition and extensive problems, cases, and examples have been thoroughly updated. A solutions manual is also available. Heat Conduction is appropriate reading for students in mainstream courses of conduction heat transfer, students in mechanical engineering, and engineers in research and design functions throughout industry.

Understanding non-equilibrium properties of classical and quantum many-particle systems is one of the goals of contemporary statistical mechanics. Besides its own interest for the theoretical foundations of irreversible thermodynamics(e.g. of the Fourier's law of heat conduction), this topic is also relevant to develop innovative ideas for nanoscale thermal management with possible future applications to nanotechnologies and effective energetic resources. The first part of the volume (Chapters 1-6) describes the basic models, the phenomenology and the various theoretical approaches to understand heat transport in low-dimensional lattices (1D e 2D). The methods described will include equilibrium and nonequilibrium molecular dynamics simulations, hydrodynamic and kinetic approaches and the solution of stochastic models. The second part (Chapters 7-10) deals with applications to nano and microscale heat transfer, as for instance phononic transport in carbon-based nanomaterials, including the prominent case of nanotubes and graphene. Possible future developments on heat flow control and thermoelectric energy conversion will be outlined. This volume aims at being the first step for graduate students and researchers entering the field as well as a reference for the community of scientists that, from different backgrounds (theoretical physics, mathematics, material sciences and engineering), has grown in the recent years around those themes.

Presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems, utilized in a wide range of heat transfer and industrial applications.

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

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 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.