Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins

This study addresses a distinct, unsophisticated computational procedure fo r solving approximately, but analytically, the one-dimensional heat equatio n for circumferential fins of uniform thickness with constant properties. T his differential equation with variable coefficients, called the modified B essel equation of zero order, is subject to a prescribed temperature at the base and zero heat rejection at the tip. Approximate temperature distribut ions and companion heat transfer rates of excellent quality have been obtai ned by adequately blending a polynomial curve fit, the method of successive approximations and the method of undetermined coefficients. Detailed error distributions are also presented for real uniform circumferential fins usi ng the exact solution by modified Bessel functions as the baseline case. Th e calculations of analytic character were carried out with a symbolic algeb ra software, Maple V, on a personal computer.