Convective Cloak in Hele-Shaw Cells with Bilayer Structures: Hiding Objects from Heat and Fluid Motion Simultaneously

Abstract

Thermal convection is one of the three basic mechanisms of heat transfer, which profoundly influences the natural environment, social production, and our daily life. However, the high complexity of the governing equation, which describes the coupling of heat and mass transfer, makes it difficult to manipulate thermal convection at will in both theory and experiment. Here, we consider the heat transfer in Hele-Shaw cells, a widely used model of Stokes flow between two parallel plates with a small gap, and apply the scattering-cancellation technology to construct convective thermal materials with bilayer structures and homogeneous isotropic materials. By tailoring thermal conductivities and viscosities, we demonstrate cloaking devices that can hide obstacles from heat and fluid motion simultaneously, and verify their robustness under various thermal-convection environments by numerical simulations. Our results show that about 80% of the temperature and pressure disturbances in the background caused by obstacles can be eliminated by the cloak. The developed approach can be extended to control other convection-diffusion systems or even other multiphysics processes, and the results pave a promising path for designing various metadevices such as concentrators or sensors.