This article presents the transient temperature response of a convective-radiative rectangular profile annular fin under a step temperature change occurring in its base. A convection-radiation fin rip is considered. The nonlinear transient heat transfer and boundary conditions are soh ed by using the hybrid method of Taylor transformation and finite-difference approximation. Also. time domain is controlled by Taylor transformation, and the spatial coordinates are handled by finite-difference approximation. Te,Temperature distribution is implemented by employing natural cubic spline fitting.