Analytically Determined Fin-Tip Heat Transfer Coefficients

An analysis was performed to determine the fin-tip heat transfer coefficients for an array of straight longitudinal fins attached to a plane wall. The array is shrouded by an adiabatic surface positioned adjacent to the tips, with a clearance gap between the shroud and the tips. The analysis was carried out for hydrodynamically and thermally developed conditions and for laminar flow. Results were obtained from numerical solutions of the momentum and energy conservation equations for the fluid and the energy equation for the fin, with two-dimensional conduction being permitted in the fin. From the solution, the average fin-tip heat transfer coefficient was evaluated and compared with the average coefficient for a segment of the principal face of the fin that is adjacent to the tip, the segment length being half the tip width. These coefficients were found not to differ too greatly, with the largest deviations being on the order of twenty-five percent. When connective heat transfer at the fin tip was suppressed, the heat transfer coefficients on the tip-adjacent portion of the principal face increased markedly. Because of this compensating effect, the overall performance of the fin is about the same when the tip is either convectively active or adiabatic. In general, large variations of the fin heat transfer coefficient were encountered between the base and the tip, with the smallest values at the base and the largest values at the tip.