A Reverse Thermal Cloak Design Method Based on Inverse Problem Theory

A reverse thermal cloak design method is developed based on inverse problem theory. The design of thermal conductivity distribution within a cloak can be regarded as the density-based topology optimization with that penalization parameter equals to 1. The relative density is explored using conjugate gradient method with an adjoint equation (CGMAE). A prescribed objective function is used to evaluate the design result, and the function is no larger than 6.41×10⁻⁶. The maximum deviation between background temperature with and without cloak position is no larger than 0.9% for background with uniform gradient and no larger than 5% for background with non-uniform gradient. The dimension of a cloak can also be designed in case of known material thermal conductivity to avoid complex material synthesis process. Compared with coordinate transformation, the reverse design method is able to remove anisotropy of thermal conductivity and is appropriate for design of irregularly shaped cloak. It is easy to implement programming for proposed method and can boost the flexibility of cloak design. Thus, the proposed method offers a practicable scheme for thermal cloak design to control heat conduction at will.