This study conducts an analysis for the heat diffusion of an annular fin considering con-vection phenomena at the fin edge as well as along the fin perimeter. When the temperature of the fin base is given with an increasing exponential function, the exact series solutions of tem-perature distribution are obtained by laplace transformation in terms of dimensionless para-meters. From these solutions heat flux and fin efficiency can be obtained. These exact solu-tions converge rapidly for large values of dimensionless time, but slowly for small ones. To avoid this convergence difficulty, approximate solutions of the temperature distribution and heat flux for small values of dimensionless time are also presented. Substituting the variations of dimensionless parameters into the these exact solutions, the characteristics of these response are investigated.