A closed form solution for periodic heat transfer in annular fins

Abstract

A closed form solution is presented for an annular fin of a constant cross-sectional area subjected to a periodic base heat flux. The solution involves Bessel functions with complex arguments. Closed form expressions for real and imaginary parts of Bessel functions K0, I0 and I1 are developed. The solution of the temperature distribution, instantaneous and time-average efficiencies depends on the amplitude A and frequency B, of the base heat flux as well as on the fin parameter m. The effect of these parameters on the amplitude and phase angle of the temperature as well as on the efficiency are discussed. A qualitative analysis of fins of similar and different geometries subjected to different periodic boundary conditions is presented.