The current study explores the transient magnetohydrodynamic (MHD) flow with the interaction of quadratic convection, slip of second-order momentum, viscous dissipation, and Newtonian heating. In this setup, the governing equations become highly nonlinear. The numerical solutions are attained by utilizing an implicit type of the Crank–Nicolson technique. The primary aim of the exploration is to figure out the consequence of MHD nonlinear convection and momentum slip of second-order on the overall behavior of the system. The robust agreement is evinced by numerical computations verified against existing research. Skin friction and Nusselt number decreases for second-order slips,