Control Of The Heat Transfer Path For The Thermal Conduction

The topic of the heat flux stealth is another emerging field after the rapid development of the magnetic wave and acoustic wave invisible problems. Because of the thermal diffusion equation has the same property of the form-invariability as the Maxwell equation, so inspired by the electromagnetic wave cloak, transformation optics is successfully extended to the field of thermodynamics, and the corresponding thermal invisibility cloak was designed and fabricated successfully. After that the term "transformation thermodynamics" emerged soon. Because of the qualitative difference between the transient heat conduction problems and the transient electromagnetic wave propagation problems: the former is not a wave motion, so the study of thermal invisibility need not consider the size of the coated target, that is to say, the heat flux stealth problem can be applied to any situaiton which need management the high temperature, whether it is micro(such as microelectronics) or macro level. On the other hand, the hot issues range from our daily life to the country’s leading technology and national defense security, which prompts the scientific researchers make more profound, system and abundant investigations on the control of heat flow. And the heat flux stealth problem as an emerging field is undoubtedly a new research direction in this problem, therefore this paper will research the thermal invisible problem systematically based on the coordinate transformation and the idea of the neutral inclusion.At present, the traditional heat cloak acquainted by people can only keep the temperature field inside the cloak be uniform without disturbing the outside field, but can not control the temperature value of the uniform field, and the material parameters in the cloak will be of infinite value, which will bring difficulty to the actual preparation system. In order to widen the application range of the thermal cloak and abound it, this dissertation not only proposed the design scheme for arbitrarily shaped two-dimensional non singular opening heat cloak based on the transformation thermodynamics, but also successfully derived the precise expression of the open cloak in each region and carried out the numerical verification.In view of the fact the practical problems mostly is three-dimensional(3D), the two-dimensional(2D) thermal invisibility problem was extended into three dimensional domain based on the coordinate transformation method. The design and numerical validation problem of the heat flow invisble cloak has been studied in-depth. General design method of the 3D thermal concentrator, 3D thermal invisibility cloak, 3D thermal shrinker, 3D thermal amplifier and the 3D thermal reshaper is given by the design procedure the 3D thermal reshaper. Not only give out the general expression of material parameters of the thermal illusion tools, but also analyse the specific circumstance for various thermal invisble devices. In additon, the effectiveness of each kind of the stealth tools are verified numerically through the finite element simulation.Although the theorecical principle of the coordinate transformation of the above work has the advantages of simple design, convenient operation, and can be used to design cloaks with arbitrary shape, the material parameters of the thermal cloak designed by the coordinate transformation are inhomogeneous anisotropic, thus material paremeters should be simplified based on the equivalent medium theory in the actual fabrication, which will increase the workload and difficulty. In consideration of the above problems, this paper will introduce the neutral inclusion theory in the micromechanics into the heat flux stealth, and focuses on the thermal invisble devices with the regular shape(cylinder, sphere and ellipsoid). Various rules given by Milton for the equivalent thermal conductivity of regular coated inclusions are used to derive relationships between the geometry and material parameters of the neutral inclusions. Based on these equations, the coating thickness and material parameters can be obtained conveniently and adjusted according to different required demand. Because a neutral inclusion with special properties not interfere the field of the matrix, so a neutral inclusion in the matrix can also achieve the stealthy aim. In addition, when neutral inclusions and other impurities present in the substrate at the same time, the thermal signal in the matrix only reflects the existence of non-neutral inclusions, which will make neutral inclusions camouflage and achieve thermal illusion of the neutral inclusions.In order to make the content more full and complete, after the completion of the theoretical level work in this paper, preliminary exploration is made from the experimental angle. This paper uses the materials obtained based a method totally different from the method of coordinate transformation and chose a new scheme to reproduce experiment of the 2D circular non-singular thermal cloak, which is a preliminary attempt and basic study of the experimental fabrication. The experimental results show that the fabricatoin of the prepared thermal cloak in this paper can realize the heat stealthy aim effectively.