Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials

Abstract

This paper studies a radial fin of uniform thickness with convective heating at the base and convective–radiative cooling at the tip. The fin is assumed to experience uniform internal heat generation. The exposed surfaces of the fin lose heat by simultaneous convection and radiation to the surroundings. Two types of fin materials are investigated: homogeneous material and functionally graded material (FGM). For the homogeneous material, the thermal conductivity is assumed to be a linear function of temperature, while for the FGM fin the thermal conductivity is modeled as a linear function of the dimensionless radial coordinate. The analysis is conducted using the differential transformation method (DTM). The accuracy of DTM is verified by comparing the results for the simplified versions of the present model with an exact analytical solution derived here. Once the accuracy of DTM is authenticated, the method is used to generate results for the general problem formulated here. These results illustrate the effects of various dimensionless parameters on the thermal performance of homogeneous material fins and FGM fins.