In the current study, an efficient, reliable and relatively novel analytical method is applied to describe the temperature behavior of an unsteady nanofluid flow containing water as the base fluid and graphene oxide particles as the nanoparticles between moving parallel plates. The first phase of this investigation involves turning the governing equations including partial differential equations (PDE) into ordinary differential equations (ODE) using similarity solution. Subsequently, a system of differential equations is solved applying Akbari-Ganji method (AGM) and reliable functions are obtained for temperature and velocity distributions. The effect of viscous dissipation in the derived equations is considered and comprehensively discussed. In order to examine the accuracy and precision of the current analytical results, the equations are also solved by using appropriate numerical solution. By comparing the results, a proper agreement with low error rate is observed between the analytical and numerical results. Finally, by definition of a viscous dissipation ratio parameter, the amount of heat due to shear stress is calculated for several nanoparticles and Eckert numbers. According to the results, viscous dissipation ratio of titanium oxide nanoparticles is greater than that of the other considered nanoparticles.