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

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 Te 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 Te 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.