A numerical analysis for unsteady magnetohydrodynamic (MHD) flow of Cross nanofluid subject to non-linear thermal radiation is carried out. The Buongiorno's nanofluid model involving Brownian motion and thermophoresis is adopted. Two more realistic conditions namely convective condition and zero nanoparticles mass flux condition are implemented on the boundary. Mathematical problem is modelled with the aid of momentum, temperature as well as nanoparticles concentration equations adopting suitable transforming variables. The resulting highly nonlinear differential systems are solved numerically with the help of shooting Runge-Kutta-Fehlberg method. Numerical computations for Nusselt number as well as skin friction coefficient are performed. Variations of velocity, temperature as well as nanoparticles concentration profiles are examined by varying the involved parameters. A comparative analysis is conducted between existing study and present investigation in limiting case and found to be in excellent agreement. It is interesting to note that thermal as well as nanoparticles concentration boundary layer thicknesses are the upgrading functions of unsteadiness parameter. Additionally, rate of heat transfer is depreciated by upgrading the values of radiation parameter as well as thermophoresis parameter. Furthermore, the magnitude of wall shear stress is an enhancing function of the magnetic parameter. It is also noted that rate of heat transfer enhance with the enhancement of temperature ratio parameter as well as Biot number. (C) 2018 Elsevier Ltd. All rights reserved.