The modified differential transform method for investigating nano boundary-layers over stretching surfaces

Purpose – The purpose of this paper is to investigate the nano boundary-layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two-dimensional stretching surface; and viscous flows over an axisymmetric stretching surface. Design/methodology/approach – The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)-Pade´ technique that is a combination of the DTM and the Pade´ approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. Findings – Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM-Pade´ can have wide application in engineering problems especially for boundary-layer problems. Originality/value – The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM-Pade´ technique that is a combination of the DTM and the Pade´ approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Differential transform method (DTM), Nanofluids, Pade´ approximants, Stretching sheet, Navier boundary condition, Flow, Boundary layers