A note on the heat transfer in convective fins

Abstract

In this paper a generalized approach to the problem of heat transfer through convective fins is given. The proper dimensionless variables, which specify the general problem are identified, and upper bounds of the values of the dimensionless number Nr defined as “the ratio of the heat transferred by the fin to that of the corresponding bare surface” are derived. It was shwon that these limiting values of the Nr are 1/√B1 and √2/B1 for longitudinal fins and spines respectively, where B1 is the Biot number hb/k, while for annular fins of constant thickness and hyperbolic profile, Nr⩽ K(β)/√Bi, where K(β) is a number determined by the profile of the fin and the ratio β=x2/x1 of the outside to the inside radii. It was also shown that for longitudinal fins and spinces the possible adverse insulating effect by the use of the fin is avoided, if one selects the value of √hA/KC < 1, which is a rather stricter criterion than the one reported in the literature, namely that of hA/kC < 1 [2–5]. An example is given to show how one may utilize the appropriate value of Nr and the fin effectiveness e, to obtain the dimensions of the fin.