Differential Transformation Method for Newtonian and non-Newtonian nanofluids flow analysis: Compared to numerical solution

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 on two different cases, natural convection of a non-Newtonian nanofluid between two vertical plates and Newtonian nanofluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by a numerical solution (Fourth-order Runge-Kutta) to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient which can achieve more reliable results compared to other analytical methods in solving some engineering and sciences problems.