Equivalent Thermal Conductivity of Topology-Optimized Composite Structure for Three Typical Conductive Heat Transfer Models

Composite materials and structural optimization are important research topics in heat transfer enhancement. The current evaluation parameter for the conductive heat transfer capability of composites is effective thermal conductivity (ETC); however, this parameter has not been studied or analyzed for its applicability to different heat transfer models and composite structures. In addition, the optimized composite structures of a specific object will vary when different optimization methods and criteria are employed. Therefore, it is necessary to investigate a suitable method and parameter for evaluating the heat transfer capability of optimized composites under different heat transfer models. Therefore, this study analyzes and summarizes three typical conductive heat transfer models: surface-to-surface (S-to-S), volume-to-surface (V-to-S), and volume-to-volume (V-to-V) models. The equivalent thermal conductivity ( k eq ) is proposed to evaluate the conductive heat transfer capability of topology-optimized composite structures under the three models. A validated simulation method is used to obtain the key parameters for calculating k eq . The influences of the interfacial thermal resistance and size effect on k eq are considered. The results show that the composite structure optimized for the V-to-S and V-to-V models has a k eq value of only 79.4 W m −1 K −1 under the S-to-S model. However, the k eq values are 233.4 W m −1 K −1 and 240.3 W m −1 K −1 under the V-to-S and V-to-V models, respectively, which are approximately 41% greater than those of the in-parallel structure. It can be demonstrated that k eq is more suitable than the ETC for evaluating the V-to-S and V-to-V heat transfer capabilities of composite structures. The proposed k eq can serve as a characteristic parameter that is beneficial for heat transfer analysis and composite structural optimization.