Dai Gaole, Wang Jun
School of Sciences, Nantong University, Nantong 226019, China.
School of Physics, East China University of Science and Technology, Shanghai 200237, China.
Materials (Basel). 2022 Dec 30;16(1):376. doi: 10.3390/ma16010376.
Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier-Stokes equations or their simplified forms under coordinate transformations, which determines whether the transformation operations can be executed on thermal convection to simultaneously regulate the flow and thermal fields. In this work, we show that thermal convection in two-dimensional Hele-Shaw cells keeps form-invariance, while its counterpart in general creeping flows or general laminar flows does not. This conclusion is numerically verified by checking the performances of invisible devices made of transformation media in convective environments. We further exploit multilayered structures constituted of isotropic homogeneous natural materials to realize the anisotropic inhomogeneous properties required for transformation media. Our results clarify the long-term confusion about the validation of the transformation method in thermal convection and provide a rigorous foundation and classical paradigm on inspiring various fascinating metadevices in both thermal and flow fields.
在过去二十年中，对诸如光场或声场等物理场的有效控制极大地受益于变换介质。这些快速发展的研究领域之一是变换热学，尤其体现在热传导和热辐射模式中。另一方面，由于涉及流体运动和传热项的复杂控制方程，热对流中的变换介质很少被研究。困难在于纳维 - 斯托克斯方程或其简化形式在坐标变换下形式不变性的稳健性，这决定了变换操作是否可以应用于热对流以同时调节流场和温度场。在这项工作中，我们表明二维赫勒 - 肖槽中的热对流保持形式不变性，而在一般的蠕动流或一般层流中的热对流则不然。通过检查由变换介质制成的隐形装置在对流环境中的性能，这一结论得到了数值验证。我们进一步利用由各向同性均匀天然材料构成的多层结构来实现变换介质所需的各向异性非均匀特性。我们的结果澄清了长期以来关于热对流中变换方法有效性的困惑，并为激发热场和流场中各种引人入胜的元器件提供了严格的基础和经典范例。
