The main target of the present model is to find the idea of magneto-hydrodynamics incompressible nanofluid flow past over an infinite rotating disk. The effect of the magnetic field is existed to check the nanofluid flow. The single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) engine oil can be utilized despite carrier fluid for an unsteady rotating disk. Here, we transform the nonlinear system of differential equations to the dimensionless ordinary differential equation by using similarity transformation. Then, we use the numerical method of lines to solve the nonlinear ODE via the Runge–Kutta technique. The resultant of the velocity, Nusselt number and Skin friction is demonstrated under the effect of several factors. We note that when we increase the velocity of the rotating disk, fluid velocity and temperature are safely increased. Finally, we note that the outcomes obtained demonstrate that the SWCNTs nanofluids improved the heat transfer more than the MWCNTs.