要約

It is generally understood that heat transfer of a fin increases with its length. In cases where the fin tip experiences significantly higher convective coefficients, a situation exists where the heat transfer decreases with its length. Applications of this situation may exist in air conditioning, refrigeration, and electronics cooling. Analytical results for one-dimensional temperature distribution and heat transfer rate are presented for such a pin fin. A critical tip-to-surface coefficient ratio h(= h_crit) depending only on the transverse Biot number Bi exists, for which the heat transfer is independent of length. For "subcritical" conditions (h < h_crit), fin heat transfer increases with length, as is commonly known. In this case, long fins will be necessary for maximizing heat transfer. For "supercritical" situations (h > h_crit), however, the heat transfer rate decreases with length, asymptotically approaching that for an infinitely long fin. Here, short fins will suffice to provide near-maximum heat duty. Compared to the unfinned base exposed to the tip coefficient, subcritical fins will enhance heat transfer; under supercritical situations, they will insulate the surface. However, compared to the finless base exposed to the surface coefficient, fins will always increase heat transfer. If the fin tip is employed to accurately measure the fluid temperature, the dimensionless fin length L must be no less than L_min, which is a function only of Bi and h/h_crit . An analytical expression for L_min necessary to keep the relative error within one percent has been developed. Whether the fin is used to enhance heat transfer or measure fluid temperature, the fin cross section should have as high surface area-to-volume ratio as possible.