We report on the magnetohydrodynamic impact on the axisymmetric flow of Al2O3/Cu nanoparticles suspended in H2O past a stretched/shrinked sheet. With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles, the physical flow process is illustrated. The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations. The transformed differential equations are solved analytically. Impacts of the magnetic parameter, solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically. The skin friction and Nusselt number were also evaluated. In addition, existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one. Further, Al2O3/H2O nanofluid flow has better thermal conductivity on comparing with Cu/H2O nanofluid. Furthermore, it was found that the first solutions of the stream are stable and physically realizable, whereas those of the second ones are unstable.