A decomposition solution for fins with temperature dependent surface heat flux

In this study, the Adomian decomposition method is used to analyze the thermal characteristics of a straight rectangular fin for all possible types of heat transfer. The local heat transfer coefficient is assumed to vary with a power-law function of temperature. Instead of a traditionally implicit form of solution, the decomposition solution gives an explicit expression of temperature distribution as a function of position along the fin. The obtained decomposed analytic solution is in the form of an infinite power series and the series can be truncated in a practical way to obtain numerical results. Thus, the fin tip temperature, fin base heat transfer rate, and fin efficiency can be calculated directly without the need of iteration. Results indicate that the series converges rapidly with high accuracy and seems to be convenient for the engineering application.