Title: Transformation heat transfer and thermo-hydrodynamic cloaks for creeping flows: Manipulating heat fluxes and fluid flows simultaneously

Abstract

Although the subject of thermal cloaking has attracted extensive academic attention, most pioneering studies have so far focused on thermal conduction systems or thermal convection in the porous media, which prevents the object from moving. Here, we have discovered that Stokes equations and the energy transport equation do abide by the coordinate-transformation invariant theory if the former is replaced with the pressure Laplace equation. This discovery enables us to rightfully take advantage of the merit of this theory and to analytically design metamaterial thermo-hydrodynamic cloaks. More importantly, since our designed cloaks depend on the viscosity and the thermal conductivity of background flows as well as geometries of cloaks only, but not on boundary conditions of background flows, they can be continuously utilized when objects travel in the media under realistic flow conditions. Besides, we also suggest experimental demonstrations to show the feasibility of our design. Finally, it is our hope that numerical data obtained in the proposed study can (1) facilitate the realization of lab experiments as well as help them identify characteristic flow and thermal parameters, and (2) serve as a stepping stone to further explore other thermo-hydrodynamic metamaterial devices.