New analytical method for the study of natural convection flow of a non-Newtonian fluid

Purpose – The purpose of this paper is to discuss the natural convection flow of an incompressible third grade fluid between two parallel plates. The basic equations governing the flow are reduced to a nonlinear ordinary differential equation. Design/methodology/approach – The resulting nonlinear ordinary differential equation is solved by multi-step differential transform method (MDTM). Findings – The obtained solutions in comparison with the numerical solutions (fourth-order Runge-Kutta) admit a remarkable accuracy. Originality/value – The analysis illustrates the validity and the great potential of the MDTM in solving nonlinear differential equations.

Differential equations, Convection, Fluids, Flow, Natural convection, Non-Newtonian fluid, Multi-step differential transform method