Control of heat flux using computationally designed metamaterials

Abstract

To gain control over the diffusive heat flux in a given domain, one has to design metamaterials with a specifc distribution of the generally anisotropic thermal conductivity throughout the domain. Until now, the appropriate conductivity distribution was usually determined using transformation thermodynamics. By this way, only a few particular cases of heat flux control in simple domains having simple boundary conditions were studied. As a more general approach, we propose to define the heat control problem as an optimization problem where we minimize the error in guiding the heat flux in a given way, taking as design variables the parameters that define the variable microstructure of the metamaterial. Anisotropic conductivity is introduced by using a metamaterial made of layers of two materials with highly dfferent conductivities, the thickness of the layers and their orientation throughout the domain are the current design variables. As an application example we design a device that thermally shields the region it encloses, while it keeps unchanged the flux outside it.