Thermal‐composite design optimization for heat flux shielding, focusing, and reversal

The optimization of thermal‐composite structural designs for heat flux shielding, focusing, and reversal is explained in this paper. Heat conduction in anisotropic solids is reviewed, and a detailed two‐phase material microstructure description for non‐symmetric inclusions embedded in a matrix medium is provided. Objective functions related to heat flux shielding and focusing are derived from a general energy formulation of thermal compliance by using information related to the magnitude of the thermal gradients. Additionally, a multi‐term objective function for heat flux reversal is developed based on the directionality of the thermal gradients. A computational optimization technique is then employed to examine the validity of these three design objectives in the context of an established benchmark example. The results of these numerical experiments are shown to be in good agreement with experimental results from the literature. Additionally, the optimization method is shown to be capable of handling structures with arbitrary geometry. Logical extensions of the method include the development of novel structural layouts for thermal circuits, thermal cloaks, and negative differential thermal resistance materials.