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.

总体而言，块方法已被证明是整体上求解常微分方程数值近似的有效方法。因此，研究在求解传热模型时采用具有较高导数的块方法的适用性非常重要。在求解这些模型时，该方法中较高导数的存在为提高精度提供了空间。本文采用的分块方法是使用新型线性分块方法开发的两步三阶导数分块方法。块方法的结果方案被组合为微分方程模型求解的同时积分器。可以看出，该方法可以在各种物理参数的影响下为双曲轮廓的环形翅片问题提供充分的解决方案。