Generalized Correlations for Heat Transfer through High Performance Fins

Analysis of heat transfer through different candidates for high performance fins is considered in this work. These candidates are: (A) fins of constant cross-sectional area, (B) fins of constant cross-sectional area gradient, and (C) radial fins with power-law cross-sectional area distribution. The types (A) and (B) fins are allowed having variable power-law profile distributions. The energy equation for each case is solved analytically, and closed form equations for various performance indicators including the fin efficiency are obtained. It is identified that high performance fins are those fins having larger tip and surface areas and smaller tip thickness than those of the straight fin. These effects tend to augment the fin heat transfer rate. One of the indicators of the type (A) fins is found to become dependent on the tip thickness when it is smaller than the base thickness and for thermal lengths larger than 1.5. The type (C) fins are found to transfer more thermal energy than the type (B) fins under same tip area and tip thickness. Finally, generalized correlations for the fin efficiency of high performance fins as function of base and tip areas and thicknesses and the thermal length are proposed and validated