Thermal Anisotropy and Heat Flux Deviation Degree of Composites

Abstract In numerous applications, particularly in aerospace (e.g., thermal protection systems), the research focuses on materials capable of thermal management, such as thermally insulating in one direction while conducting heat in its orthogonal direction. Anisotropic composite structures can meet such needs. This paper first defines two indices that quantify the thermal management performance of anisotropic structures: a thermal anisotropy degree (TAD), and a heat flux deviation degree (HFDD). Second, it compares several anisotropic composite structures: multilayer, fiber-reinforced composites, cross-shaped, and double cross-shaped. Effective thermal conductivities in the three principal directions were calculated for each structure using analytical and numerical homogenization techniques. Subsequently, the TAD, thermal anisotropy efficiency, and HFDD were determined. Calculations were repeated for varying filler fractions. The effect of the fiber shape was evaluated by repeating calculations with circular and square-shaped sections. For the square-shaped fiber, the influence of section rotation was also investigated. Moreover, the Monte Carlo optimization technique was applied solely to the cross-shaped structure to determine which angle between the two fibers maximizes the thermal anisotropy. Results demonstrated that the multilayer structure exhibits the highest anisotropy efficiency among all analyzed structures for each filler fraction; however, it has zero heat flux deviation degree. Thus, the multilayer structure is optimal for insulation; nevertheless, the surface exposed to flux would reach higher temperatures with respect to other structures. The cross-shaped structure shows the best compromise between the TAD (hence good insulation) and HFDD (thus good flow channeling capability and reduced exposed surface temperature due to the flux). For the fiber-reinforced and cross-shaped structures, it was observed that the fiber shape does not significantly influence the TAD. However, at the same filler fraction, the crossed square-shaped fiber exhibits a HFDD up to 10 times greater than the crossed circular-shaped one. Finally, the rotation of the square-shaped fiber has a minimal impact at low filler fractions but becomes more and more significant for filler fractions exceeding 20–30%.