Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200433, China and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China.
Phys Rev E. 2018 Feb;97(2-1):022129. doi: 10.1103/PhysRevE.97.022129.
Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.
热量可以通过热传导、热辐射和热对流进行传递。现有的相变热学和光学理论分别可以处理热传导和热辐射。不幸的是，由于缺乏合适的理论，相变理论很少涉及热对流，从而限制了与通过流体（液体或气体）传热相关的应用。在这里，我们通过考虑对流-扩散方程、连续性方程和达西定律，发展了一种相变热对流理论。通过引入多孔介质，我们得到了一组在坐标变换下保持其形式的方程。作为模型应用，该理论有助于展示隐身、聚焦和伪装的效果。我们的有限元模拟证实了理论发现。这项工作为热对流提供了一种相变理论，从而揭示了与潜在应用相关的新行为；它不仅为如何通过结合热传导、热对流和热辐射来控制传热提供了不同的启示，而且还使质量扩散和其他包含一组方程并需要同时变换速度的相关领域受益。
