Simple Correlation to Evaluate Efficiency of Annular Elliptical Fin Circumscribing Circular Tube

Efficiency of annular elliptical fin has been studied numerically. Results show that constant temperature lines do not remain circular in lower aspect ratio fins. So, it is expected that some common methods such as equivalent fin area or sector method do not have enough accuracy. For this reason, at first, a new simple correlation has been proposed to approximate annular circular fin efficiency based on longitudinal fin efficiency and then, comparing to the numerical results, it has been shown that the proposed formula is still applicable if one uses arithmetic mean of elliptical fin lengths and geometric mean of elliptical fin radiuses.