This paper discusses unsteady/steady radiating magnetohydrodynamic (MHD) nanofluid flow over a slippery stretching sheet. Introducing similarity variables reduces partial differential equations (PDEs) into a new set of partial differential equations (PDEs) where a solution is a function of two independent variables. For the time integration, we perform first order explicit Euler method and spatial derivatives are approximated by the finite differences. The steady flow solution is computed by MATLAB built-in solver bvp4c. The flow regime is controlled by a number of thermophysical parameters such as thermal Grashof number (Gr), Lewis number (Le), Eckert number (Ec), Brownian motion (Nb) and thermophoresis (Nt) and heat source or sink (S), Prandtl number (Pr), magnetic field parameter (M), and Darcy number (Da). The findings are analyzed by validation through graphs and tables for velocity, temperature and concentration profiles and the skin friction coefficient, the local Nusselt and the local Sherwood numbers, respectively. The results converge in accordance with the grid convergence test. For an unsteady flow, the temperature of the nanofluid is higher near the surface without thermophoresis parameter Nt and reduced significantly when Nt is present. Moreover, concentration boundary layer thickness decreases with an increase of Darcy number Da.