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 for solving approximately, but analytically, the one-dimensional heat equation for circumferential fins of uniform thickness with constant properties. This differential equation with variable coefficients, called the modified Bessel equation of zero order, is subject to a prescribed temperature at the base and zero heat rejection at the tip. Approximate temperature distributions and companion heat transfer rates of excellent quality have been obtained 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 using the exact solution by modified Bessel functions as the baseline case. The calculations of analytic character were carried out with a symbolic algebra software, Maple V, on a personal computer.
KeywordsHeat Transfer Rate Successive Approximation Modify Bessel Function Constant Property Heat Rejection
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