Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage

Gaole Dai, Jin Shang, and Jiping Huang
Phys. Rev. E 97, 022129 – Published 20 February 2018

Abstract

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.

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  • Received 31 May 2017
  • Revised 8 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.022129

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gaole Dai, Jin Shang, and Jiping Huang*

  • 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

  • *jphuang@fudan.edu.cn

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Issue

Vol. 97, Iss. 2 — February 2018

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