Numerical research has been done on the movement of a Magnetohydrodynamics (MHD) viscous nanofluid together with thermal radiation over a nonlinearly stretching sheet. Variable magnetic and variable permeability are used in this study instead of the more frequent constant magnetic and permeability, which makes it distinctive and the results more realistic and practically helpful. The flow, heat, and mass transfer equations have been generated as coupled second order nonlinear partial differential equations using a mathematical model that resembles the physical flow problem. First, a similarity transformation is employed to modify PDEs into a system of nonlinear ODEs. By using a shooting method and a Runge-Kutta-Fehlberg’s (RKF-45) scheme, the boundary value problem is solved. The role of mass-transfer characteristics, heat-transfer characteristics and dimensionless temperature, as well as flow parameters of the problem like magnetic parameter, the radiation parameter, nonlinearly stretching sheet parameter, and the viscous parameter etc. are drawn and tabulated. The numerical findings in the current analysis are very well validated and are shown in both tabular and graphical form.