Abstract
Block methods in general have proven to be an efficient approach for the numerical approximation of ordinary differential equations as a whole. Therefore, it is important to investigate the suitability of adopting block methods with the presence of higher derivatives in solving heat transfer models. The presence of the higher derivative in the method gives room for improved accuracy when solving these models. The block method adopted in this article is the two step third derivative block method which is developed using a novel linear block approach. The resultant schemes for the block method were combined as simultaneous integrators for the solution of the differential equation model. The method is seen to adequately provide solutions to the problem of annular fins with hyperbolic profile under the influence of various physical parameters.