The Zoo of Non-Fourier Heat Conduction Models

The Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation or time lags become dominant and the memory or/and spatial non-local effects significant -- in ultrafast heating (pulsed laser heating and melting), rapid solidification of liquid metals, processes in glassy polymers near the glass transition temperature, in heat transfer at nanoscale, in heat transfer in a solid state laser medium at the high pump density or under the ultra-short pulse duration, in granular and porous materials including polysilicon, at extremely high values of the heat flux, in heat transfer in biological tissues. In common materials the relaxation time ranges from $10^{-8}$ to $10^{-14}$ sec, however, it could be as high as 1 sec in the degenerate cores of aged stars and its reported values in granular and biological objects varies up to 30 sec. The paper considers numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory (hereditary materials, including fractional hereditary materials) or/and spatial non-locality, i.e. materials with non-homogeneous inner structure

Gradient Preserved And Artificial Neural Network Method For Solving Heat Conduction Equations In Double Layered Structures

Layered structures have appeared in many engineering systems such as biological tissues, micro-electronic devices, thin  lms, thermal coating, metal oxide semiconductors, and DNA origami. In particular, the multi-layered metal thin  lms, gold-coated metal mirrors for example, are often used in high-powered infrared-laser systems to avoid thermal damage at the front surface of a single layer  lm caused by the high-power laser energy. With the development of new materials, functionally graded materials are becoming of more paramount importance than materials having uniform structures. For instance, in semiconductor engineering, structures can be synthesized from di erent polymers, which result in various values of conductivity. Analyzing heat transfer in layered structure is crucial for the optimization of thermal processing of such multi-layered materials. There are many numerical methods dealing with heat conduction in layered structures such as the Immersed Interface Method, the Matched Interface Method, and the Boundary Method. However, development of higher-order accurate stable nite di erence schemes using three grid points across the interface between layers for variable coe cient case is mathematically challenging. Having three grid points ensures that the nite di erence scheme leads to a tridiagonal matrix that can be solved easily using the Thomas Algorithm. But extension of such methods to higher dimensions is very tedious. Recently there have been some solution to such complex systems with the use of neural networks, that can be easily extended to higher dimensions. For the above purposes, in this dissertation, we  rst develop a gradient preserved method for solving heat conduction equations with variable coe cients in double layers. To this end, higher-order compact  nite di erence schemes based on three grid points are developed. The  rst-order spatial derivative is preserved across the interface. Unconditional stability and convergence with O(  2 + h4) are analyzed using the discrete energy method, where   and h are the time step and grid size, respectively. Numerical error and convergence rates are tested in an example. We then present an arti cial neural network (ANN) method for solving the parabolic two-step heat conduction equations in double-layered thin  lms exposed to ultrashort-pulsed lasers. Convergence of the ANN solution to the analytical solution is theoretically analyzed using the energy method. Finally, both developed methods are applied for predicting electron and lattice temperature of a solid thin  lm padding on a chromium  lm exposed to the ultrashort-pulsed lasers. Compared with the existing results, both methods provide accurate solutions that are promising

Heat equations beyond Fourier: from heat waves to thermal metamaterials

In the past decades, numerous heat conduction models beyond Fourier have been developed to account for the large gradients, fast phenomena, wave propagation, or heterogeneous material structure, such as being typical for biological systems, superlattices, or thermal metamaterials. It became a challenge to orient among the models, mainly due to their various thermodynamic backgrounds and possible compatibility issues. Additionally, in light of the recent findings on the field of non-Fourier heat conduction, it is not even straightforward how to interpret and utilize a non-Fourier heat equation, primarily when one aims to thermally design the material structure to construct the new generation of thermal metamaterials. Adding that numerous modeling strategies can be found in the literature accompanying different interpretations even for the same heat equation makes it even more difficult to orient ourselves and find a comprehensive picture of this field of research. Therefore, this review aims to ease the orientation among advanced heat equations beyond Fourier by discussing properties concerning their possible practical applications in light of experiments. We start from the simplest model with basic principles and notions, then proceed toward the more complex models related to coupled phenomena such as ballistic heat conduction. We do not enter the often complicated technical details of each thermodynamic framework but do not aim to compare each approach. However, we still briefly present their background to highlight their origin and the limitations acting on the models. Additionally, the field of non-Fourier heat conduction has become quite segmented, and that paper also aims to provide a common ground, a comprehensive mutual understanding of the basics of each model, together with what phenomenon they can be applied to

Models of Delay Differential Equations

This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineerin

Heat Transfer

Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Metamaterial

In-depth analysis of the theory, properties and description of the most potential technological applications of metamaterials for the realization of novel devices such as subwavelength lenses, invisibility cloaks, dipole and reflector antennas, high frequency telecommunications, new designs of bandpass filters, absorbers and concentrators of EM waves etc. In order to create a new devices it is necessary to know the main electrodynamical characteristics of metamaterial structures on the basis of which the device is supposed to be created. The electromagnetic wave scattering surfaces built with metamaterials are primarily based on the ability of metamaterials to control the surrounded electromagnetic fields by varying their permeability and permittivity characteristics. The book covers some solutions for microwave wavelength scales as well as exploitation of nanoscale EM wavelength such as visible specter using recent advances of nanotechnology, for instance in the field of nanowires, nanopolymers, carbon nanotubes and graphene. Metamaterial is suitable for scholars from extremely large scientific domain and therefore given to engineers, scientists, graduates and other interested professionals from photonics to nanoscience and from material science to antenna engineering as a comprehensive reference on this artificial materials of tomorrow

Magnetic Nanomaterials

The constant search for innovative magnetic materials increasingly leads to the creation of highly engineered systems built in different forms (films, wires, particles), structured on the nanoscale in at least one spatial direction, and often characterized by the coexistence of two or more phases that are magnetically and/or structurally different. In magnetic systems, the nanometric structural characteristics of the constituent elements, together with the type and strength of the magnetic interactions between them, determine the overall magnetic behavior and can lead to the appearance of unexpected and amazing magnetic phenomena. Indeed, the study of the magnetic properties of nanomaterials continues to arouse great interest for their intriguing fundamental properties and prospective technological applications. This Special Issue contributes to broadening the knowledge on magnetic nanomaterials, demonstrating the breadth and richness of this research field as well as the growing need to address it through an interdisciplinary approach. The papers collected in this book (two reviews and eight regular articles) report cutting-edge studies on the production and characterization of a variety of novel magnetic nanomaterials (nanoparticles, nanocomposites, thin films and multilayers), which have the potential to play a key role in different technologically advanced sectors, such as biotechnology, nanomedicine, energy, spintronics, data storage, and sensors