The significance of aligned magnetic flux on free convective radiative nanofluid along a stretching surface with thermal energy storage is investigated in this paper. The problem has been modelled mathematically under Newtonian slip effect. The Prandtl boundary-layer expressions are framed using Lie group analysis and treated numerically. By employing the shooting method and the Runge–Kutta fourth-order technique, a solution to the dimensionless equations is obtained. The influence of pertinent dimensionless variables on the velocity, temperature, shear stress and heat transfer rate are scrutinized via graphical plots. The results of this study show that the velocity of the nanofluid is lower and wall shear flux is higher for greater aligned magnetic flux. More energy is transferred from the fluid system when multi-walled carbon nanotubes are immersed in the base liquid. The velocity of the nanofluid is decreased with increased slip parameter. Also, the temperature rises and heat flux is reduced with enhanced thermal energy storage/generation. The numerical solutions obtained in the present work are compared to existing literature, and they are found to be in a good agreement. © 2020, Springer Nature Switzerland AG.