In this work, natural convection in a non-Newtonian fluid/nanofluid between two vertical plates is investigated. The study was carried out on three types of nanofluids, namely Silver/Water, Oxide Copper-Water and Titanium oxide/Water. The mathematical formulation gives a set of strongly coupled nonlinear ordinary differential equations of the second order. These equations, characterizing velocity and temperature distributions, were solved numerically by the Runge-Kutta fourth order method, and analytically by a new Adomian of decomposition approach named the Adomian generalized method (GDM). The results show clearly the effectiveness, accuracy and applicability of the used technique (GDM). Using nanoparticles (Ag, CuO and 𝑇𝑖𝑂2) in water as a base fluid substantially increases the coefficient of friction and characteristics of heat transfer. Compared to other works, the generalized Adomian decomposition technique (GDM) offers the advantages of precision and velocity of convergence.