Soret and Dufour effects on MHD convective–radiative heat and mass transfer of nanofluids over a vertical non-linear stretching/shrinking sheet

A numerical investigation is applied to study the influence of the Soret and Dufour effect on mixed convection heat and mass transfer of nanofluids in the boundary layer region over a non-linear stretching and shrinking sheets in the presence of thermal radiation. The governing differential equations are solved numerically using a fifth-order Runge–Kutta–Fehlberg integration scheme with a shooting technique. The influence of mixed convection parameter, Soret and Dufour number, magnetic field and thermal radiation parameters on velocity, temperature and concentration fields as well as on the skin-friction coefficient, local Nusselt number and local Sherwood number are illustrated graphically for three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) in the base fluid water in order to show some interesting phenomena. The obtained results show appreciable effects of Soret and Dufour numbers i.e. the effects of increase in Soret number (or decrease in Dufour number) decrease the skin-friction coefficient and Nusselt number for shrinking sheet, whereas the reverse effects are found for stretching sheet.