An ease of analysis for optimum design of an annular step fin

Abstract

In the present study, exact and approximate analytical techniques are developed to determine the optimum design of a rectangular stepped annular fin with constant base temperature. An algebraic expression based on the mean value theorem is used as the vehicle for an approximation tool. The corresponding temperature distribution and heat transfer characteristics in the fin are determined using exponential functions. The standard modified Bessel function formulation is employed for the exact analysis. Error analysis has been carried out to compare between the exact and approximate results. It is found that the integral approach of calculating the rate of heat transfer is more accurate than the differential approach while applying the approximate analytic technique. The errors associated with the approximate analytic methods falls well within acceptable accuracy levels for engineering analysis and design. (C) 2015 Elsevier Ltd. All rights reserved.