Analytical Investigation on Heat Conduction Performance of Anisotropic Annular Fin

Fin structures fabricated from Ceramic Matrix Composites (CMC) are increasingly employed in advanced aircraft cooling systems due to their low density, high thermal resistance and corrosion resistance. However, due to the inherent anisotropy and directionality in heat conduction, theoretical solutions for such CMC fin structures remain challenging, which limits their design and optimization for practical applications. Therefore, this paper proposes an analytical solution for the heat transfer rate and efficiency of anisotropic annular fins. A mathematical model was developed, yielding the governing dimensionless numbers based on the differential equations and boundary conditions. Solution methods included variable separation, Taylor expansion, and integral averaging. Derived analytical correlations were numerically verified. The numerical validation demonstrated that within the ranges of Bi_r = 0.005, Bi_z = 0.01 ~ 0.05, Bi_φ = 0.01 ~ 0.05, β_R = 10, r^* = 0.1, and α = 0 ~ 90°, the deviation in fin efficiency predicted by the proposed formula did not exceed 1.56% compared to numerical methods. Since circumferential thermal resistance does not influence fin efficiency, rotation of principal thermal axes in the rOφ and φOz planes under λ_rz = 0 enhances fin efficiency by exclusively reducing either radial or axial thermal resistance. Additionally, when λ_rz ≠ 0, thermal principal axes rotate in the rOz. Higher Bi_r/Bi_z values accelerate the decline in fin efficiency as α increases. The proposed method and results provide new insights into anisotropic heat transfer problems and lay a solid foundation for the design and optimization of the anisotropic fins.