Cloaking: Controlling thermal and hydrodynamic fields simultaneously

Hydrodynamic and thermal cloaking effects have attracted interest among researchers using metamaterials. This paper explores an analytical solution using only isotropic materials to achieve cloaking under forced convective heat transfer. It is shown that, under a background of uniform flow and linearly varying temperature, a circular bilayer cloak with an inner layer made of impenetrable and insulated material and an outer layer made of a porous medium having a constant permeability and effective conductivity does not disturb the external flow and temperature fields. Moreover, the cloaked region is shielded from the external flow and temperature fields. Analytical temperature and velocity distributions within the porous outer layer are presented to demonstrate both the hydrodynamic and thermal cloaking effects of such a bilayer. Finally, numerical results, based on practically attainable material properties, are given to confirm the analytical model.