Fin efficiency of an annular fin composed of a substrate metallic fin and a coating layer

An analytical solution to a composite annular fin made of a substrate metallic fin and a coating layer has been carried out. Useful expressions for calculating temperature distribution and fin efficiency have been derived. Comparing the analytical results to those of numerical calculation, the premise for the expressions is also explored. Theoretical analyzing results show that fin efficiency of a coated fin decreases with an increase of the coating layer thickness if the thermal conductivity of coating layer is much less than that of the substrate metallic fin. Whereas, the reverse influence of the coating layer thickness on the fin efficiency appears the thermal conductivity of the coating layer is beyond the above range.