The effects of the amplified velocity of the plate on nanoparticle migration and heat transfer characteristics in unsteady free convection flow have been studied with the uniform heat flux boundary condition. The governing set of partial differential equations for the non-homogeneous nanofluid model is employed. A numerically stable second-order accurate method is applied to solve the dimensionless governing equations. The numerical solutions are obtained for nanofluid velocity and temperature fields, nanoparticles displacement, skin-friction, and Nusselt number for different values of amplified velocity parameter, and shown in graphs. The results show that the amplified plate velocity decreases the nanoparticle migration slightly while it increases the average Nusselt number and skin-friction. Also, a good comparison is found between the present numerical results and available correlation results of steady-state local Nusselt number for the limiting case. © Published under licence by IOP Publishing Ltd.