The Significance of Fin Profile and Convective-Radiative Fin Tip on Temperature Distribution in a Longitudinal Fin

Abstract

In this article, the one dimensional nonlinear transient heat transfer through fins of rectangular, convex parabolic and concave parabolic is studied using the two dimensional Differential Transform Method (2D DTM). The thermal conductivity and heat transfer coefficient are modeled as linear and power law functions of temperature respectively. The fin tip dissipate heat to the ambient temperature by convection and radiation. A comparison is made between the proposed convectiveradiative fin tip boundary condition and the adiabatic (insulated) fin tip boundary condition which is widely used in literature. It is found that the fin with a convective-radiative tip dissipates heat to the ambient fluid at a faster rate when compared to a fin with an insulated tip. The results further show that the longitudinal fins of parabolic profiles dissipate more heat when compared to the conventional rectangular fin profile. The accuracy of the analytical method is demonstrated by comparing its results with those generated by an inbuilt numerical solver in MATLAB. Furthermore, a wide range of thermo-physical parameters are studied and their impact on the temperature distribution are illustrated and explained.