An Efficient Unified Approach for Performance Analysis of Functionally Graded Annular Fin with Multiple Variable Parameters

Abstract

The present work investigates the performance of an annular fin of constant thickness, made up of a functionally graded material (FGM). The fin surfaces are exposed in an environment where the heat loss occurs through convection and radiation. The various parameters, describing the fin performances, are considered to be varying with the local temperature and fin radius. An efficient and unified approach, homotopy perturbation method (HPM), is applied for obtaining the closed form solution from the non-linear heat transfer equation of equilibrium. The effects of key thermal parameters, i.e. thermo-geometric, conduction— radiation, thermal conductivity variation, heat generation, exponent of heat transfer co-efficient and the parameter of surface emissivity are explored on the temperature field leading to an overall investigation of thermal performance. And, the effects of such parameters on heat transfer rate, efficiency, effectiveness and temperature distributions are found to be significant. The accuracy of the present closed form solution is measured when its results are verified with the results of FEM and FDM solutions. The present results agree very well with those of FDM results and FEM results which is obtained using COMSOL software.