Indian Journal of Pure & Applied Physics Vol. 55, August 2017, pp. 551-563 Soret and Dufour effects on MHD flow with heat and mass transfer past a permeable stretching sheet in presence of thermal radiation G Sreedevi a *, D R V Prasada Rao b , O D Makinde c & G Venkata Ramana Reddy a a Department of Mathematics, K L University, Green Fields, Vaddeswaram, Guntur 522 502, India b Department of Mathematics, S K University, Anantapur 515 003, India c Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa Received 14 June 2016; accepted 3 January 2017 An analysis has been carried out to study the combined effects of the magnetic field, Joule heating, thermal radiation absorption, viscous dissipation, Buoyancy forces, thermal-diffusion and diffusion-thermion the convective heat and mass transfer flow of an electrically conducting fluid over a permeable vertically stretching sheet. The boundary layer equations for the fluid flow, heat and mass flux under consideration have been obtained and reduced into a system of non-linear ordinary differential equations by using appropriate similarity transformation. Using shooting method coupled with the fourth order Runge-Kutta integration scheme, the numerically solutions have been obtained and presented graphically. The effects of various embedded thermo-physical parameters on the fluid velocity, temperature, skin friction, Nusselt number and Sherwood number have been determined and discussed quantitatively. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement. An increase in values of thermal radiation, viscous dissipation, suction/injection coefficient and chemical reaction results in the increase of velocity, temperature and heat-mass transfer rates. It is further noted that the velocity, temperature and heat-mass transfer rates reduces on the boundary layer of a permeable vertical stretching sheet due to increase in the values of Soret or decrease in values of Dufour. Further, this work leads to study different flows of electrically conducting fluid over a permeable vertical stretching sheet problem that includes the two dimensional non-linear boundary equations. Keywords: Joule heating, MHD, Thermal radiation, Buoyancy forces, Soret effect, Dufour effect 1 Introduction Natural convection permeates, either be it a study of natural phenomenon like the structure of stars and planets or be it in an engineering application study say cooling of nuclear reactors. On the other hand, an increase in the temperature of a conductor by the result of resistance to the electrical current flowing through it is referred to as Joule heating. However, at an atomic level, Joule heating is the resultant of moving electrons colliding with atoms in a conductor, whereupon momentum is transferred to the atom, increasing its kinetic energy. Electro migration is when similar collisions results in a permanent structural change, rather than just an elastic response. The rise in the temperature of the conductor is due to the increase in the kinetic energy of the ions which manifests itself as heat. Accordingly, the energy is transferred from electrical power supply to the conductor and any other material that comes in thermal contact. The study of magneto-hydrodynamic (MHD) radiative viscous flows has gained much importance in geothermal and industrial applications such as high-temperature plasmas, cooling of nuclear reactors, liquid metal fluids, MHD accelerators and power generation systems. Advanced studies went into MHD free convective flow analyzing the effect of viscous dissipation and Joule heating with variable plate temperature 1-3 . Makinde and Chinyoka 4 examined the MHD transient flow and heat transfer in a channel with radiative heat and convective cooling. Das et al. 5 analyzed the effects of Joule heating and viscous dissipation on MHD mixed convective slip flow over an inclined porous plate. Makinde et al. 6 analyzed nanofluid in a porous medium of a convectively heated plate and studied the combined effects of variable viscosity, thermophoresis and thermal radiation on MHD boundary layer flow. The study of heat and mass transfer flow over a moving vertical plate with convective surface boundary conditions on MHD was studied by Makinde 7 . Hossain and Alim 8 examined the problem of natural convection-radiation —————— *Corresponding author (E-mail: sreedevihari2007@gmail.com)