Differential transformation method for Newtonian and Non-Newtonian fluids flow analysis: comparison with HPM and numerical solution

Abstract

In this study, a simple and high accurate series-based method called differential transformation method (DTM) is used for solving the coupled nonlinear differential equations in fluids’ mechanic problems. The concept of the DTM is briefly introduced, and its application for two different cases, natural convection of a non-Newtonian fluid between two vertical plates and Newtonian fluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by another series-based analytical technique namely homotopy perturbation method (HPM) and a numerical solution (Fourth-order Runge–Kutta) to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient and can achieve more suitable results compared to HPM in some areas of equations in engineering and science problems.