This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton's linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number. (C) 2017 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.