Uma visão crítica do comprimento corrigido de aletas.

Abstract

This work examines the real meaning of the corrected length of fins. As we know, such a concept started with Harper and Brown [8], and won some notoriety after the physical interpretation given by Schneider [9]. It seems that the sole goal of Harper and Brown [8], when they took a simpler equation instead of the one valid for a fin losing heat by convection at its tip, was to reduce laborious computation. Schneider's [9] considerations, however, raised a series of controversies, such as: after adding just half of the fin thickness to the original fin length. In order to do this, Schneider [9] took into account a physical model in which the temperature of the modified fin, should be at the room temperature, just after the increment of such a small fraction. To be more realistic, a series of experiments was carried out. From these experiments, we could see, as it was expected, that even when we "add" a length larger than the fin thickness at the fin tip, it is impossible for the fin's terminal to reach the room temperature. Some other remarks came out from our analysis: 1. Considering Fig. 2-1, due to Schneider [9], it is shown that y = 2, is not the best value for equations (1-16) and (1-18) to give close results. 2. Examining some real situations, it is possible to see that there is no practical meaning in dealing with fins of length rate, L, over thickness, 8, i.e. s = L/5, smaller than 3. Looking at Fig. 2-1, from where Schneider [9] concluded that only for VNu < 0.5, the curves obtained from equations (1-16) and (1-18) could be superposed, it is evident that in Fig. 2-1, s < 3. On the other hand, we have seen that for s > 3, the superposition occurs no matter the Nusselt number is. Thus, from an engineering viewpoint, the mentioned equations may give the same results. 3. It is not necessary to have any additional extension to the original fin length to get identical results from both equations (1-16) and (1- 18), no matter the Nu number is. Thus even when TL » Tr o, the heat flux at the fin tip is negligible. 4. The fin tip's area, is, in general, so small, that the flux through it may be disregarded compared to the heat exchanged by the whole fin. Thus, in terms of the heat flux at the tip of a fin, be it thermal insulated, or not, does not, pragmatically, offer any physical distinction. This fact is enough to transform the fin corrected length concept in a mere and formal sterile abstraction.