In this article, we have investigated the influence of magneto-hydro-dynamic (MHD) Powell–Eyring fluid flow in the presence of non-linear radiation, space dependent internal heat source and variable thermal conductivity over a permeable cylinder with suction/injection effects. We have considered Soret, Dufour and non-linear chemical reaction effect on heat and concentration equations. Using similarly transformation, the governing PDEs are changed into non-linear coupled ODEs and solved by R-K forth order with shooting method. The impact of various parameters such as Powell- Eyring fluid parameters (K), Dufour parameter (Du), radiation parameter (R), small scale parameter (ε), Prandtl number (Pr), curvature parameter (γ), Schmidt number (Sc), chemical reaction parameter (Kn), Eckert number (Ec), relative temperature ratio parameter (θw), Soret parameter (Su), magnetic field parameter (M) and (A*) and (B*) are specific and temperature heat source on axial momentum, heat and concentration profiles have been analyzed graphically and skin friction coefficient, local Nusselt number and local Sherwood number can be discussed tabulated.
non-linear radiation, non-linear heat source, variable thermal conductivity, Powell–Eyring fluid
 Khan MI, Kiyani MZ, Malik MY, Yasmeen T, Khan MWA, Abbas T. (2016). Numerical investigation of magneto hydrodynamic stagnation point flow with variable properties. Alexandria Engineering Journal 55(3): 2367-2373.
 Krishna PM, Sandeep N, Reddy JVR, Sugunamma V. (2016). Dual solutions for unsteady flow of powell-eyring fluid past an inclined stretching sheet. J. of Naval Arch. and Marine Engg. https:// doi.org/ 10.3329/jname. v13i1.25338.
 Mahanthesh B, Gireesha BJ, Gorla RSR. (2017). Unsteady three-dimensional MHD flow of a nano Eyring-Powell fluid past a convectively heated stretching sheet in the presence of thermal radiation, viscous dissipation and Joule heating. J. of the Association of Arab Universities for Basic and Applied Sciences 23: 75-84.
 Akbar NS, Ebaid A. (2015) Numerical analysis of magnetic field on eyring-powell fluid flow towards a stretching sheet. Journal of Magnetism and Magnetic Materials 382: 355-358.
 Javed T, Ali N, Abbas Z, Sajid M. (2013). Flow of an Eyring Powell non-Newtonian fluid over a stretching sheet. Chem. Eng. Comm. 200 (3): 327–336.
 Hayat T, Gull N, Farooq M, Alsaedi A. (2016) Thermal radiation effect in MHD flow of Powell-Eyring nanofluid induced by a stretching cylinder J Aerosp. Eng. 29 (1): 04015011-13.
 Hayat T, Ashraf MB, Shehzad SA, Abouelmagd E. (2015). Three-dimensional flow of Eyring Powell nanofluid over an exponentially stretching sheet. Int. J. Numer. Methods Heat Fluid Flow 25(3): 593–616.
 Hayat T, Pakdemirli M, Aksoy T. (2013). Similarity solutions for boundary layer equations of a Powel-Eyring fluid. Mathematical and Computational Applications 18(1): 62-70.
 Hayat T, Waqas M, Shehzad SA, Alsaedi A. (2016). Mixed convection stagnation-point flow of Powell Eyring fluid with Newtonian heating, Thermal Radiation, and Heat Generation/Absorption. https:// doi.org/ 10.1061/(ASCE)AS.1943-5525.0000674.
 Hayat T, Makhdoom S, Awais M, Saleem S, Rashidi M M (2016). Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis. Appl. Math. Mech. -Engl. Ed. https:// doi.org/ 10.1007/s10483-016-2093-9.
 Gaffar SA, Prasad VR, Reddy EK. (2016). MHD free convection flow of Eyring–Powell fluid from vertical surface in porous media with Hall/ionslip currents and ohmic dissipation. Alexandria Engineering Journal 55(2): 875-905.
 Madhu M, Kishan N. (2016). Finite element analysis of heat and mass transfer by MHD mixed convection stagnation-point flow of a non-Newtonian power-law nano fluid towards a stretching surface with radiation. J. of the Egyptian Mathematical Society 24: 458–470.
 Makinde OD. (2012). Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation. Meccanica 47: 1173–84.
 Jain S, Kumar V, Bohra S. (2017). Entropy generation for MHD radiative compressible fluid flow in a channel partially filled with porous medium, Global and Stochastic Analysis, SI., 13-31.
 Jain S, Choudhary R. (2017). Soret and Dufour effects on MHD fluid flow due to moving permeable cylinder with radiation. Global and Stochastic Analysis, SI, pp. 75-84.
 Jain S. (2006) Temperature distribution in a viscous fluid flow through a channel bounded by a porous medium and a stretching sheet, J. Rajasthan Acad. Phy. Sci. 4: 477-482.
 Jain S, Choudhary R. (2015) Effects of MHD on boundary layer flow in porous medium due to exponentially shrinking sheet with Slip, Procedia Engg. 127: 1203–1210.
 Jain S, Parmar A. (2017). Comparative study of flow and heat transfer behavior of Newtonian and non-Newtonian fluids over a permeable stretching surface. Global and Stochastic Analysis SI: 41-50.
 Das K, Sharma RP, Sarkar A. (2016). Heat and mass transfer of a second-grade magneto-hydrodynamic fluid over a convectively heated stretching sheet. J. of Computational Design and Engg. 3(4): 330-336.
 Chauhan DS, Rastogi P. (2011). Heat transfer and entropy generation in MHD flow through a porous medium past a stretching sheet. Inter. J. of Energy & Tech. 3(15): 1-13.
 Chauhan DS, Rastogi P. (2012). Unsteady MHD flow and heat transfer through a porous medium past a non-isothermal stretching sheet with slip conditions. International Journal of Energy and Technology 4(17): 1-11.
 Chauhan DS, Kumar V. (2012). Radiation effects on unsteady flow through a porous medium channel with velocity and temperature slip boundary conditions, Applied Mathematical Sciences 6(36): 1759-1769.
 Ska Md T, Das K, Kundu PK, (2016). Effect of magnetic field on slip flow of nanofluid induced by a non-linear permeable stretching surface. Applied Thermal Engineering 104: 758–766.
 Animasaun IL, Adebile EA, Fagbade AI. (2016). Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method, J. of the Nigerian Math. Society 35: 1–17.
 Andersson HI, Hansen OR, Holmedal B. (1994). Diffusion of a chem-ically reactive species from a stretching sheet. Int J Heat Mass Transfer 37: 659–64.
 Prasad KV, Sujatha A, Vajravelu K, Pop I. (2012). MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermos-physical properties. Meccanica 47: 1425–39.
 Mukhopadhyay S, Golam AM, Wazed AP. (2013). Effects of transpiration on unsteady MHD flow of an UCM fluid passing through a stretching surface in the presence of a first order chemical reaction. Chin Phys B 22: 124701.
 Palani S, Kumar BR, Kameswaran PK. (2016) Unsteady MHD flow of an UCM fluid over a stretching surface with higher order chemical reaction, Ain Shams Engg. J. 7: 399–408.
 Narayana KL, Gangadhar K, Subhakar MJ. (2015). Effect of viscous dissipation on heat transfer of magneto-Williamson Nano fluid, IOSR-JM 11(4): 25-37.
 Nadeem S, Hussain ST. (2013). Flow and heat transfer analysis of Williamson Nanofluid, Appl Nanosci. Einstein, Ann. Phys. 19: 286.
 Khan WA, Pop I. (2010). Boundary-layer flow of a Nanofluid past a stretching sheet, Int. J. Heat Mass Transf. 53: 2477-2483.
 Gorla RSR, Sidawi I. (1994). Free convection on a vertical stretching surface with suction and blowing, Appl. Sci Res. 52: 247-257.
 Wang Y. (1989). Free convection on a vertical stretching surface, J Appl. Math Mech. 69: 418-420.