Lin Jun-Hong, Chen Tungyang
Department of Civil Engineering, Chung Yuan Christian University, Zhongli Dist., Taoyuan City 320314, Taiwan.
Department of Civil Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
Materials (Basel). 2023 Mar 13;16(6):2297. doi: 10.3390/ma16062297.
In this paper, analytic modeling for the design of a transient thermal invisibility cloak with imperfect interfaces is presented together with numerical simulations. In contrast to steady-state conditions, it is shown that an object can only be made partially invisible under a transient-state condition with either ideal or imperfect interfaces. The thermal visibility of an object to the external region can be optimally suppressed under certain conditions referred to as the "weak invisibility conditions" for the transient response, which are different from the "strong invisibility conditions" that can completely conceal an object in a steady state. In the formulation, a homogeneous metamaterial with constant volumetric heat capacity and constant anisotropic conductivity tensor is employed. It can be demonstrated that the interface's bonding conditions will have a significant effect on the design of metamaterials. Two typical types of imperfect interfaces, referred to as low-conductivity- and high-conductivity-type interfaces, are considered. Conditions, that render an object mostly undetectable, are analytically found and expressed in simple forms under quasi-static approximations. Within the quasi-static limit, the thermal localization in the target region can be tuned with the anisotropy of the conductivity tensor. Thermal shielding or concentrating effects in the target region are exemplified based on finite element simulations to demonstrate the manipulation of heat flux in the target region. The present findings make new advances in theoretical fundamentals and numerical simulations on the effect of the imperfect interface in the transient regime and can serve as guidelines in the design of thermal metamaterials through the entire conduction process.
本文提出了一种具有不完善界面的瞬态热隐身斗篷设计的解析模型，并进行了数值模拟。与稳态情况不同，结果表明，在具有理想或不完善界面的瞬态条件下，物体只能部分不可见。在某些被称为瞬态响应的“弱隐身条件”下，物体对外部区域的热可见性可以得到最佳抑制，这些条件不同于能在稳态下完全隐藏物体的“强隐身条件”。在公式推导中，采用了具有恒定体积热容和恒定各向异性电导率张量的均匀超材料。可以证明，界面的结合条件对超材料的设计有显著影响。考虑了两种典型的不完善界面，即低电导率型和高电导率型界面。在准静态近似下，通过解析找到了使物体基本不可检测的条件，并以简单形式表示。在准静态极限范围内，目标区域的热局域化可以通过电导率张量的各向异性进行调整。基于有限元模拟举例说明了目标区域的热屏蔽或集中效应，以展示目标区域内热通量的操控。本研究结果在瞬态情况下不完善界面效应的理论基础和数值模拟方面取得了新进展，并可为热超材料在整个传导过程中的设计提供指导。
