The steady two-dimensional MHD flow of a Jeffery nanofluid over a stretching sheet in the presence of thermal radiation and heat source has been examined numerically. The Brownian motion and thermophoresis effects have been fused in the nanofluid. Applying similarity transformations, the governing partial differential equations are reduced into a set of non-linear ordinary differential equations and then are solved numerically by using the fourth order Runge-Kutta method along with shooting technique (MATLAB package). The influence of various flow parameters on the velocity, temperature, nanoparticles concentration as well as the skin friction coefficient, Nusselt and Sherwood numbers has been presented and discussed through graphs and tables. It is observed that the thermophoresis parameter Nt shows the increasing nature of temperature for both Newtonian and non-Newtonian nanofluids. Whereas the Deborah number β and ratio of relaxation and retardation times λ show opposite effect on the velocity, temperature and concentration distributions. © 2019 by American Scientific Publishers All rights reserved.