Heat Transfer in an Annular Fin With Coordinate Dependent Thermal Conductivity

Some new exact analytical solutions are reported for heat transfer in an annular fin of rectangular profile with coordinate dependent thermal conductivity. A power law type of dependence on radial coordinate is assumed. The analysis assumes a constant base temperature and an insulated tip. Solutions are developed for the temperature distribution, the heat transfer rate, the fin efficiency, and the fin effectiveness. These solutions appear in terms of Airy wave functions or modified Bessel functions or hyperbolic functions or power functions depending on the exponent of the power law variation. Numerical results are presented to illustrate the effect of coordinate dependent thermal conductivity on the thermal performance of the fin. Comparison of exact and results based on the average thermal conductivity model reveals that the latter is in error by as much as 56 percent in a specific situation. The fin model used here is applicable to some contemporary engineering applications where fins made of heterogeneous materials are used. The analysis can be extended to other profile shapes and different thermal boundary conditions.