Anisotropic heat conduction in composite rectangular fins: A theoretical analysis and optimal design

In pursuit of higher aero-engine performance, fins are designed to meet extremely high-temperature tolerance. With excellent properties including low density, high thermal resistance and corrosion resistance, ceramic matrix composites (CMCs) have been widely used as promising thermal structure materials. The presence of fiber angle in composites results in the directionality of thermal conductivity, which limits the application of analysis and optimization methods developed based on isotropic fins. The analysis considers heat conduction in both the fin height (H) and thickness (δ) directions involving the mixed partial derivatives of temperature in the differential equation. The boundary conditions take into account the heat convection between the fin and the fluid as well as the adiabatic fin tip. The equations are solved using the integral method and Taylor expansion to obtain the fin efficiency and temperature field. Good agreement is observed between our analytical and numerical results demonstrated with the maximum relative deviation of 7.03 % for the fin efficiency and − 12.26 % for the dimensionless excess temperature. According to the proposed solution, the equivalent thermal conductivity is derived to broaden the universality of the previous fin optimization formula, which lays solid foundations for a deep understanding of the heat conduction process in anisotropic fins.