Approximate analytic temperature distribution and efficiency for annular fins of uniform thickness

Abstract

The salient feature in the quasi one-dimensional differential equation for annular fins of uniform thickness is without question the presence of the variable coefficient 1 / r multiplying the first order derivative, d T / d r . A good-natured manipulation of the variable coefficient 1 / r is the principal objective of the present work. Specifically, the manipulation applies the mean value theorem for integration to 1 / r in the proper fin domain extending from the inner radius r 1 to the outer radius r 2 . It is demonstrated that approximate analytic temperature profiles and heat transfer rates of good quality are easily obtainable without resorting to the exact analytic temperature distribution and heat transfer rate embodying modified Bessel functions. For enhanced visualization, the computed temperature profiles, tip temperatures and fin efficiencies of approximate nature are graphed and tabulated for realistic combinations of the normalized radii ratio c and the thermo-geometric fin parameter ξ of interest in thermal engineering applications.