The Thermal Conductivity Coefficient of a Square Thermal Invisibility Cloak Cell and Its Application in Periodic Plate

Abstract

In this paper, the thermal conductivities of the square thermal invisibility cloak are constructed in two ways. One is the direct method, another is the rotation matrix method. The thermal conductivity coefficients obtained by the two methods are the same. The cloud map of thermal conductivity coefficient of the thermal cloak is drawn, which can help us understand more intuitively how the thermal invisibility cloak works. Besides, to manipulate heat flow in a larger area, the cloaks are arranged periodically by introducing the position parameters into the calculation of the thermal conductivity coefficient of the thermal invisibility cloak. The heat insulation function of both the single thermal cloak and the thermal cloak periodic plate are tested under different heat boundary conditions using COMSOL Multiphysics. For different heat boundary conditions, heat flux direction of the simulation result is given. The results show that both the single thermal cloak and the thermal cloak periodic plate have the function of avoiding heat flow under different heat boundary conditions. The heat fluxes travel around the inner domain with good thermal stealth effect.