JAGUARIBE, D. C. A.; http://lattes.cnpq.br/5182923745438960; JAGUARIBE, Danielle Christine Almeida.
Resumen:
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.