Approximate analytic temperature solution for uniform annular fins by adapting the power series method

Abstract

The primary specification faced by thermal engineers when designing annular fins is the amount of heat transfer from a finned tube to a fluid. The temperature along annular fins of uniform thickness is governed by an ordinary differential equation of second order with variable coefficients, called the modified Bessel equation of zero order. Approximate temperature distributions and fin efficiencies, both of good quality, have been obtained by adapting a power series method for solving this Bessel equation with symbolic algebra software such as Maple or Mathematica. Students of heat transfer courses can benefit from this simple computational procedure that circumvents the use of Bessel functions and still produces approximate analytic results of good caliber.