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The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

An investigation of hydromagnetic two dimensional boundary layer flow with heat transfer of a viscous, incompressible, electrically conducting, heat absorbing and optically thick heat radiating fluid over a permeable exponentially stretching sheet considering the effects of viscous and Joule dissipations in the presence of velocity and thermal slip is carried out.

Using similarity transform, governing differential equations representing mathematical model of the problem are solved with the help of fourth-order Runge-Kutta method along with shooting technique. Numerical solutions of fluid velocity and fluid temperature are depicted graphically for various values of pertinent flow parameters whereas numerical values of wall velocity gradient and wall temperature gradient are displayed graphically for various values of pertinent flow parameters.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Magnetic field and suction tend to enhance the wall velocity gradient whereas dimensionless co-ordinate, injection and velocity slip factor have reverse effect on it. Suction and heat absorption tend to enhance wall temperature gradient whereas magnetic field, velocity slip factor, injection, thermal radiation, thermal slip factor and viscous dissipation have reverse effect on it.

The investigation of this problem may have bearing in several engineering processes such as extrusion of plastic sheet, annealing and tinning of copper wire, paper production, crystal growing and glass blowing, continuous casting of metals and spinning of fibers.