The unsteady flow of nanoliquid film over a flexible surface has been inspected. Water and ethylene glycol are used as the base liquids for the graphene oxide platelets. The comparison of two sorts of nanoliquids has been used for heat transfer enhancement applications. The thickness of the nanoliquid film is kept as a variable. The governing equations for the flow problem have been altered into the set of nonlinear differential equations. The BVP 2.0 package has been used for the solution of the problem. The sum of the square residual error has been calculated up to the 10th order approximations. It has been observed that the graphene oxide ethylene glycol based nanofluid (GO-EG) is more efficient for heat transfer enhancement as compared to the graphene oxide water based nanofluid (GO-W). The impact of the physical parameters has been plotted and discussed.