Preface

Abstract

What you do not know always determines what you know. Unfortunately, what you know often hinders you from knowing what you do not know yet. In this sense, it is valuable for inheritance and innovation to systematize the existing scattered knowledge.

1.1 Traditional Thermodynamics Versus Theoretical Thermotics

What you do not know always determines what you know. Unfortunately, what you know often hinders you from knowing what you do not know yet. In this sense, it is valuable for inheritance and innovation to systematize the existing scattered knowledge. We believe now is the time to present “theoretical thermotics” as a new discipline with systematic knowledge constructed by transformation thermotics and its extended theories. See Fig. 1.1. Here, transformation thermotics is known to originate from transformation optics [7], but the latter always handles wave systems rather than diffusion systems (that serve as a focus of transformation thermotics).

If you want to be a big tree, compare yourself with other big trees, rather than grass. Let us compare “theoretical thermotics” with “traditional thermodynamics”. As shown in Table 1.1, theoretical thermotics distinctly differs from traditional thermodynamics. Certainly, as one of the most fundamental theoretical frameworks for describing nature, traditional thermodynamics must also work for all the artificial systems studied by theoretical thermotics. Nevertheless, theoretical thermotics has its purposes, systems, and frameworks, thus distinguishing it from traditional thermodynamics (Table 1.1).

Fig. 1.1

The new discipline of “theoretical thermotics” is constructed by the theory of transformation thermotics and its extended theories with different levels. All these theories are connected with functions/properties/behaviors. For example, “theory of transformation thermotics for steady state” [1, 2] $\Longrightarrow$ “thermal cloaking (Function 1)” [1, 2] $\Longleftarrow$ “scattering cancellation (Extended Theory A)” [3, 4] $\Longrightarrow$ “thermal camouflage (Function 2)” [5] $\Longleftarrow$ “effective medium theory (Extended Theory B)” [6] $\Longrightarrow$ $\cdots$

Table 1.1 Traditional thermodynamics versus theoretical thermotics. Here, the phrase “passive description” means that people cannot change the heat phenomena of natural systems but understand them according to the four thermodynamic laws. In contrast, the phrase “active control” represents that people can change the heat phenomena at will by designing artificial systems based on transformation thermotics and its extended theories. These theories also make theoretical thermotics different from the existing heat transfer theory (which is much more familiar to engineering thermophysicists than physicists). Adapted from Ref. [8]

Though the word “thermotics” is not commonly used, I choose it for the new discipline, “theoretical thermotics”. Here, “thermotics” can always be translated into “heat transfer (heat transfer theory)” and sometimes into ”thermodynamics”. But, the reason why I do not choose to use “theoretical heat transfer” is two-folded: I hope to add new concepts (say, those from condensed matter physics, optics, statistical physics, etc.) to “thermotics”, which goes beyond traditional heat transfer; I do not hope the existing knowledge of conventional “heat transfer” affects the understanding of the connotation of “theoretical thermotics”. These two reasons also hold for another name, “theoretical thermodynamics”. If a name can be easily followed without confusion, work can be accomplished, one of Confucius’s sayings. Anyway, the future name is up to others, but what we can do now is up to us.

For transformation thermotics, the starting point of theoretical thermotics, its foundations could be summarized as “four properties” in the following.

A. Invariance: Thermal equations have form invariance. Many thermal equations, including those describing heat conduction, have the same form in different coordinate systems;

B. Anisotropy: Thermophysical quantities can be anisotropic. The physical properties can be anisotropic, which are described by anisotropic thermophysical quantities like thermal conductivity;

C. Inhomogeneity: Thermophysical quantities can be inhomogeneous. The physical properties can be non-uniformly distributed in space, which are described by inhomogeneous thermophysical quantities like thermal conductivity;

D. Effectiveness: Thermophysical quantities have effective properties. The thermophysical quantities described in B and C above can be equivalent to the composite of isotropic homogeneous materials.

Based on the above A, we can deduce B and C, and the prior existence of B and C also ensures the necessity of A’s existence. Therefore, A, B, and C lie in the same column, supporting and guarding each other. More importantly, B and C make the existence of D indispensable. Otherwise, the experiment cannot easily verify the theoretical prediction based on A-C, thus blocking the engineering application.

The four foundations (A-D) help construct the whole discipline of theoretical thermotics by starting from transformation thermotics.

1.2 Theoretical Thermotics Meets Metamaterials: Inside Versus Outside Metamaterials

Theoretical thermotics is interdisciplinary with three first-class disciplines, i.e., physics, engineering thermophysics, and materials science; see Fig. 1.2. On the other hand, the mature discipline of metamaterials is also interdisciplinary with many disciplines, say, optics, electromagnetics, acoustics, classical mechanics, quantum mechanics, etc. When theoretical thermotics meets metamaterials, what will happen? They give birth to a new direction, thermal metamaterials [9]; see Fig. 1.3. The first monograph on thermal metamaterials was published in 2020 [10]. Thanks to Ref. [9], the name “thermal metamaterials” was first used to cover the five works on thermal cloaks for controlling thermal conduction [1, 2, 11,12,13]. The first monograph on thermal cloaks was published in 2022 [14]. The connotation of thermal metamaterials has been extended significantly from thermal conduction to convection and radiation. As a result, so far, theoretical thermotics has been studied and developed from pure science to technology and engineering; see Fig. 1.4. The biennial International Conference on Thermodynamics and Thermal Metamaterials has been organized since 2020 to promote the development; see Fig. 1.5.

Fig. 1.2

Theoretical thermotics is interdisciplinary with three first-class disciplines, namely, physics (thermodynamics and statistical physics), engineering thermophysics (heat transfer), and materials science (material thermodynamics). A huge number of articles have appeared in the professional journals corresponding to these three disciplines (such as Physical Review Letters, Physical Review E, Physical Review Applied, and Applied Physics Letters for physics; International Journal of Heat and Mass Transfer for engineering thermophysics; and Advanced Materials for materials science), besides those interdisciplinary journals (say, Science, Nature, and Proceedings of the National Academy of Sciences of the United States of America)

Fig. 1.3

Theoretical thermotics (an interdisciplinary subject) meets metamaterials (another interdisciplinary subject), yielding a new central branch of thermal metamaterials. Metamaterials have a characteristic length larger or much larger than the construction unit

Fig. 1.4

Theoretical thermotics contains the research on the whole chain from science (from zero to one) to technology (from virtual to real) and engineering (from useless to useful). This book focuses on the part of science. The parts of technology and engineering exist in Ref. [15,16,17,18,19]

Fig. 1.5

Group photo: 2020 International Conference on Thermodynamics and Thermal Metamaterials, held on August 7–9, 2020, in Zoom (Online)

The key factor for treating an artificial structural material as a metamaterial is that the construction unit should have a characteristic length. The concept of effective media helps to understand the novel properties associated with metamaterials. For example, the characteristic length of electromagnetic metamaterials is the incident wavelength, that of thermal conduction metamaterials is the diffusion length, that of thermal convection metamaterials is the migration length of fluids, and that of thermal radiation metamaterials is the radiation wavelength.

Metamaterials can be classified in diverse ways: wave metamaterials versus diffusion metamaterials, programmable metamaterials versus unprogrammable metamaterials, bulk metamaterials versus metasurfaces, and so on. Figure 1.3 displays that theoretical thermotics can be classified as “inside metamaterials” and “outside metamaterials”. Currently, the part of “inside metamaterials” has received much attention [8, 10, 20,21,22,23,24,25]. In the meantime, the part of “outside metamaterials” is rapidly developing as well [26,27,28].

1.3 Acknowledgment and Some Additional Notes

Liu-Jun Xu, the first author of this monograph, would like to thank Prof. Ji-Ping Huang for involving him in this book writing. Supervised by Prof. Huang, Liu-Jun came into contact with and immersed in theoretical thermotics, making his five-year Ph.D. career fulfilling and rewarding. Liu-Jun also appreciates Prof. Cheng-Wei Qiu’s careful guidance when Liu-Jun spent one year at the National University of Singapore. He has received a doctoral degree from the Department of Physics, Fudan University, Shanghai, China, in June 2022. (Notes: Liu-Jun Xu wrote this paragraph in the third person.)

The content of this book mainly comes from the articles published by my group. We add “Exercise and Solution” because we hope this book could be a monograph for experts to read and a textbook for newcomers to practice (so that they could engage in this new field as soon as possible). Incidentally, each chapter in the book has its symbols to facilitate reading. In this sense, to read this book, the reader may start with any chapter.

I am also grateful to my family members, especially my wife (Yan-Jiao Zhao) and my two daughters (Ji-Yan Huang with the nickname of Qian-Qian and Ji-Yang Huang with the nickname of Yue-Yue), for bringing me great happiness. Qian-Qian also helped polish Figs. 1.1, 1.2, 1.3 and 1.4 in this preface. I have stayed at home or the residential area due to COVID-19 between April 1, 2022 and May 31, 2022.

When writing this preface, I refer to my previous book Ref. [10].

Last, we acknowledge financial support from the National Natural Science Foundation of China under Grants No. 11725521 and No. 12035004 and the Science and Technology Commission of Shanghai Municipality under Grant No. 20JC1414700.

Shanghai, China Ji-Ping Huang

June 17, 2022