Practical Jointed Approach to Thermal Performance of Functionally Graded Material Annular Fin

Abstract

Using the complementary functions method, a general solution for the one-dimensional steady-state heat conduction equation for the fin together with the boundary conditions made of functionally graded material is presented. Two cases for the variation of the functionally graded material wall thermal conductivity were considered. These are 1) power and 2) exponential types of variation of the thermal conductivity varying with the radial coordinate. In the present paper, a semi-analytical iterative technique, one of the most efficient unified methods, is employed to solve the heat conduction equation. For different values of the inhomogeneity constant, distributions of temperature, heat transfer rate, fin efficiency, and fin effectiveness, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases, and virtually exact results are obtained. © 2019 by the American Institute of Aeronautics and Astronautics, Inc.