The Efficiency of Composite Fins

The fin efficiency, defined as the ratio of the average temperature of the surface of the fin to the temperature at its base, is derived for flat and for circular fins composed of two or more materials (such as copper clad with stainless steel), for the usual conditions of constant heat transfer coefficient h and uniform ambient temperature. The exact solution is in the form of an infinite series, but the terms beyond the first are usually negligible. For most cases of interest, the fin efficiency η is shown to be approximated closely by the familiar equation η = (tanh αL)/αL, where α = and L, P, and A are, respectively, the length, perimeter, and cross-sectional area of the fin, and is the volumetric average thermal conductivity of the fin, = Σ k_iA_i/A where k_i and A_i are the conductivity and cross-sectional area of the region i.