Application of the finite-element method to the solution of nonsimilar boundary layer-derived infinite series equations

•Application of the finite-element method to treat infinite ODEs.•A robust error analysis of the method.•Validation of the method with results in the literature showing good agreement. One of the most prolific areas of fluid mechanics applications in general and nanofluid applications in particular, is boundary layer flows. In the recent past, a great many of these applications, have been limited to one-term similarity approximations. This work however, was concerned with numerically approximating nonsimilar fluid boundary layer transfer. Nonsimilar fluid boundary layer problems are more generally valid and are more prevalent industrially. In this research, the objective was to establish and advance numerically the first application of the finite-element method (FEM) to the solution of a set of nonsimilar boundary layer-derived infinite series ordinary differential equations (ODEs). Thus, this work emphasizes an FEM technique devised and used for a class of nonsimilar boundary layer-derived ODEs. The motivation is to improve and complement the numerical heat transfer literature regarding an FEM technique that may be applied to solve a coupled system of nonsimilar boundary layer-derived infinite series ODEs. The analysis obtained results that correlate very well with highly accurate benchmarked results for heat transfer and universal velocity functions. An examination of the convergence of the FEM is also shown and discussed. The results indicate that the FEM is a very robust technique for nonsimilar boundary layer infinite series differential equations.