Recent days, graphene is emanating as one of the most encouraging nanomaterials due to its continuous electrical conducting behaviour even at zero carrier concentrations. Heat transfer in non-Newtonian fluids plays a major role in technology and in nature due to its stress relaxation, shear thinning and thickening properties. With this incentive, we investigate the flow and heat transfer characteristics of electrically conducting liquid film flow of water based non-Newtonian nanofluids dispensed with graphene nanoparticles. For this investigation, we proposed a mathematical model for the flow of Jeffrey, Maxwell and Oldroyd-B nanofluids past a stretching surface in the presence of transverse magnetic field and non-uniform heat source/sink. Numerical results are carried out by employing Runge-Kutta-Felhberg integration scheme. The influence of pertinent parameters on reduced Nusselt number, friction factor, flow and heat transfer is discussed with the assistance of graphs. Embedding the graphene nanoparticles effectively enhances the thermal conductivity of Jeffrey nanofluid when compared with the Oldroyd-B and Maxwell nanofluids. Deborah number in terms of relaxation time plays a major role in convective heat transfer. (C) 2016 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.