A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

An extension of a series solution of the non-linear fin problem with temperature-dependent thermal conductivity [Kim and Huang 2006 J. Phys. D: Appl. Phys. 39 4894 - 901] is done to include a temperature-dependent heat transfer coefficient as well. It is assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. The algorithm is based on the Taylor series solution. The proposed approximate solution is successfully compared with the solutions for the Adomian decomposition method (ADM) and numerical algorithm. Also, it has been shown that the Adomian decomposition solution is just an approximation of the series solution given in this work, and therefore the present algorithm is better than ADM.