Extended surface heat transfer—the dovetail fin

A generalised equation is developed for the temperature profile along a fin of various profiles: tapered, trapezoidal and inverted trapezoidal (so-called dovetail fin). The inhomogeneous second order ordinary differential equation is converted into a homogeneous equation by introducing a number of dimensionless parameters. The analytical solution of this equation is used to produce performance and design charts. The design and performance charts are presented in terms of the performance ratio (PR=Q˙f/Q˙f,max) for the four parameters of the problem: the maximum fin effectiveness (ζmax=λf/αδf), the fin aspect ratio (l/δf), the ratio of the film heat transfer coefficient at the tip to that along the length of the fin, (αe/α) and the fin tip length factor (a). The length of the fin is l, the thickness of the fin at its base is 2 × δf and a is the ratio of the thickness at the tip of the fin to that at the base. For a tapered fin, the value of a is zero, for the trapezoidal the values for a are in the range 0 < a < 1 and for the dovetail fin, the values of a are greater than unity. The design charts cover the following ranges 0.1 < PR < 0.99, 1 < ζmax < 10000,0.01 < l/δf < 1000. Various values of ratios αe/α and a can be used in an Excel spreadsheet to generate the charts and for illustrative purposes a chart is included for αe/α = 1 and a = 2. The heat flows through the fins having the same base thickness increase as the values of a become larger, so that the tapered fin has the lowest heat flow and the dovetail fin the largest. The dovetail fin profile is recommended as an improvement over the longitudinal rectangular fin currently used in double pipe heat exchanger applications.