Recursive formulation on thermal analysis of an annular fin with variable thermal properties

This study introduces a discrete model which is pertinent for calculating thermal performance of singular annular fin with variable thermal properties. The singular annular fin can be divided into several circular sections, and each section can take its variable thermal properties, such as heat transfer coefficient and thermal conductivity, into account. The result from each section can be combined and calculated together by a recursive formula. Then, the solutions of temperature distribution and heat transfer rate on singular annular fin can be quickly obtained. For this model, the recursive formulae for both conditions with and without heat transfer on fin tip are demonstrated. Finally, some examples including composite materials for an annular fin have been successfully simulated through the present approach.