Analytical solutions of the 1-D heat conduction problem for a single fin with temperature dependent heat transfer coefficient – II. Recurrent direct solution

• Published in: International journal of heat and mass transfer Vol. 45; no. 9; pp. 1905 - 1914
• Main Authors: Dul'kin, I.N, Garas'ko, G.I
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-04-2002
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/S0017-9310(01)00285-X

The recurrent direct solution of the 1-D heat conduction problem for a single straight fin and spine with power-law-type temperature dependent heat transfer coefficient has been derived using inversion of the closed-form solution obtained in the first part of the study. The expression with improving convergence to calculate accurately the dimensionless temperature excess
T
e at the fin tip for a given values of the fin parameter
N and exponent
n in heat transfer equation has been obtained by a linearization method. Equation for the temperature excess distribution throughout the fin has also been derived. The obtained formula for
T
e allows to calculate the fin base thermal conductance and augmentation factor. Obtained expressions are seen to be simple and convenient for the engineering design of the fins and finned surfaces.