In the present study, unsteady heat and mass nanofluid flow past a stretching sheet with the effect of thermal radiation and magnetic field was carried out. To obtain non-similar equation, the boundary layer governing equations including continuity, momentum, energy and concentration balance were non-dimensionaised by usual transformation. The non-similar approach was employed, which depends on the dimensionless parameters such as Magnetic parameter (M), Radiation parameter (R), Prandtl number (Pr), Eckert number (Ec) Lewis number (Le), Brownian motion parameter (Nb), Thermophoresis parameter (Nt), Local Reynolds number (Re) and velocity parameter (b/a). The temperature and concentration distributions are found affected by these dimensionless parameters. The obtained equations have been solved by explicit finite difference method (EFDM). A theoretical model of the stability and convergence to describe the aspects of the finite difference scheme was developed in this study. This analysis makes the EFDM approach more accurate and able to provide the convergence criteria of the method (Pr ≥ 0.375 and Le ≥ 0.25). The temperature and concentration profiles are discussed for the different values of the dimensionless parameters by considering different time steps. The present computational investigation finds applications in the area of magnetic nanomaterials processing.