This book introduces the fundamental concepts of thermal cloaking based on transformation theory and bilayer theory, under the conduction and convection heat transfer modes. It focuses on thermal cloaking with detailed explanations of the underlying theoretical bases leading to the primary thermal cloaking results in open literature, from an engineering perspective, and with practical application in mind. Also, the authors strive to present the materials with an emphasis on the related physical phenomena and interpretation, to the extent possible. Through this book, engineering students can grasp the fundamental ideas of thermal cloaking and the associated mathematics, thus being better able to initiate their own research and explore new ideas in thermal cloaking.
While not intended to be a general reference in the vast field of thermal cloaking research, this book is a unique monograph addressing the theoretical and analytical aspects of thermal cloaking within the scope mentioned above. This book also contains many independent analytical solutions to thermal cloaking problems that are not available in open literature. It is suitable for a three-credit graduate or advanced undergraduate course in engineering science.
Author(s): Woon-Shing Yeung, Ruey-Jen Yang
Publisher: Springer
Year: 2021
Language: English
Pages: 276
City: Singapore
Preface I
Preface II
Acknowledgements
Contents
About the Authors
1 Introduction
1.1 What Is a Thermal Cloak?
1.2 Historical Perspective: General Cloaking
1.3 Historical Perspective: Thermal Cloaking
1.4 Book Organization
References
2 Review of Curvilinear Coordinates
2.1 Introduction
2.2 Scale Factors
2.3 Relationships of Unit Base Vectors
2.4 Relationship to Jacobian
2.5 Gradient and Divergence in Curvilinear Coordinates
2.6 Summary
Reference
3 Review of Heat Conduction
3.1 Introduction
3.2 Matrix Representation of Heat Conduction Equation
3.3 Heat Conduction in Anisotropic Media
3.4 Summary
References
4 Transformation Theory for Conduction Thermal Cloaking
4.1 Introduction
4.2 Fundamental Theory
4.2.1 Homogenization of Metamaterials
4.2.2 Arbitrary Two-Dimensional Shape
4.3 Numerical and Experimental Verification
4.4 Temperature Distribution Within Cloak
4.4.1 Arbitrary Shape
4.4.2 Nonlinear Background Temperature Distribution
4.5 Summary
References
5 Bilayer Theory for Conduction Thermal Cloaking
5.1 Introduction
5.2 Basic Bilayer Theory
5.3 Does a 1D Bilayer Thermal Cloak Exist?
5.4 General Remarks on Bilayer Thermal Cloak
5.5 Temperature Distribution in a Circular Bilayer Cloak
5.6 Elliptical Bilayer
5.7 Trilayer Thermal Cloak
5.7.1 Trilayer Theory
5.7.2 Temperature Distribution in a Trilayer Cloak
5.7.3 Spherical Trilayer
5.8 Effect of Thermal Contact Resistance
5.9 Nonlinear Background Temperature Distribution
5.9.1 Examples of Specific Background Temperature Distributions
5.9.2 Inner Layer Temperature Distribution
5.9.3 Section Summary
5.10 Summary
References
6 General Consideration of Bilayer Thermal Cloaks
6.1 Introduction
6.2 Cloaked Sensor
6.2.1 Circular Cloaked Sensor
6.2.2 Elliptical Cloaked Sensor
6.3 Bilayer with Conducting Inner Layer
6.3.1 General Circular Bilayer
6.3.2 General Elliptical Bilayer
6.4 Application to Bilayer Cloak Design
6.5 Bilayer Versus Metamaterials
6.6 Inverse Problem: Bilayer Cloak of Arbitrary Shape
6.6.1 Uniqueness and Existence of Solution for the Inverse Formulation
6.7 Summary
References
7 Transformation Theory for Convection Thermal Cloaking
7.1 Introduction
7.2 Flow in Porous Media
7.2.1 Anisotropic Porous Media
7.2.2 Section Summary
7.3 Transformation Theory
7.3.1 Hydrodynamic Cloak
7.3.2 Convection Cloak
7.3.3 Analytical Results for the Convection Cloak
7.4 Summary
References
8 Bilayer Theory for Convection Thermal Cloaking
8.1 Introduction
8.2 Theory
8.3 Two-Dimensional Systems: Planar Cloaks
8.3.1 Flow in x Direction
8.3.2 Flow in y Direction
8.4 Three-Dimensional Systems: Spherical Cloaks
8.5 Analytical Results
8.5.1 Analytical Results for Spherical Cloaks
8.6 Numerical Simulation
8.6.1 Simulation Results for Spherical Cloaks
8.7 Summary
References
9 Transient Thermal Cloaking
9.1 Introduction
9.2 Transient Transformation Theory for Conduction
9.2.1 Initial Temperature Distribution in Cloak
9.2.2 Analytical Example
9.2.3 Practical Example
9.2.4 Realization of Transient Thermal Cloaks
9.3 Transient Behavior of Bilayer Thermal Cloaks for Conduction
9.3.1 Simulation and Experimental Studies of Transient Bilayer Cloaks
9.3.2 Effect of Volumetric Heat Capacity
9.4 Transient Transformation Theory for Convection Cloaks
9.5 Transient Bilayer Theory for Convection Cloaks
9.6 Summary
References
10 Numerical Simulations and Experiments
10.1 Introduction
10.2 Numerical Simulations
10.2.1 Numerical Procedures
10.2.2 Overview of COMSOL
10.2.3 Examples: Application of COMSOL
10.3 Experimental Study
10.3.1 Common Apparatus in Thermal Cloaking Experiments
10.3.2 Example: Experimental Investigation of a Quadrilateral Bi-Material Thermal Cloak
10.4 Summary
References
11 Potential Engineering Applications and Future Prospects
11.1 Introductory Remarks
11.2 Potential Applications
11.3 Thermal Metamaterials Research
11.3.1 Metamaterials for Multi-field Applications
11.4 Concluding Remarks: Future Prospects and Outlook
References
Appendix A Derivation of Principal Conductivities in Spherical Coordinates
Appendix B Derivation of Principal Conductivities in Polar Coordinates
Appendix C Direct Solution Path to Eq. 4.4.9摥映數爠eflinklinearTcloak4.4.94
Appendix D Step-by-Step COMSOL Execution for Example 3
References
