Introduction

Concentration gradient often lead to mass diffusion in a mixture of two more species (gases, liquids, plasma or solids) in an isothermal system where species are not evenly distributed. Temperature gradient is also another factor that can be responsible for mass diffusion as a result of Soret effect (thermo-diffusion). Thermo-diffusion has several industrial applications such as the optimum oil recovery from hydrocarbon reservoirs, fabrication of semiconductor devices in molten metal and semiconductor mixtures, separation of species such as polymers, manipulation of macromolecules such as DNA, and engineering processed like wire drawing, glass fibre and paper production and crystal growth\(\mathbf{[1]}\). Dufour effect is the reverse of the Soret effect arising in a system where concentration gradient results in a temperature change. Dufour effect may be insignificant in liquid-liquid mixture but not when gases are involved. Blasius boundary layer equations \(\mathbf{[2]}\) describe a steady flow of viscous incompressible fluids about a two-dimensional flat-plate and these equations were later generalized by Falkner and Skan to wedge flow. Sakiadis obtained the boundary layer equations for a flow of a quiescent ambient fluid over a moving flat surface similar to the Blasius equations except that the boundary conditions differ\(\mathbf{[3,4]}\).
Rafael \(\mathbf{[5]}\) showed that there exist discrepancies when both the Blasius and Sakiadis flows are compared. Olanrewaju et al . \(\mathbf{[6]}\) reported the effects thermal radiation, Eckert number, Prandtl number and convective parameter on both Blasius and Sakiadis flows with a convective surface boundary condition. Gangadhar \(\mathbf{[7]}\) extended the work of \(\mathbf{[6]}\) by adding the effects of buoyancy and magnetohydrodynamic on radiation and viscous dissipation for the Blasius and Sakiadis flows with a convective surface boundary condition. Hady et al . \(\mathbf{[8]}\) studied the effect of porosity on the flow dynamics of both Blasius and Sakiadis flows of nanofluid in the presence of thermal radiation under a convective boundary condition. Mustafa et al . \(\mathbf{[9]}\)examined the effect of magnetic field parameter on Sakiadis flow of MHD Maxwell fluid. Anjani and Suriyakumar \(\mathbf{[10]}\)furthered the work of \(\mathbf{[9]}\) by comparing both cases of Blasius and Sakiadis MHD nanofluids flows on an inclined plate. Krishina et al . \(\mathbf{[11]}\) investigated the magnetohydrodynamic Blasius and Sakiadis flows with variable properties, thermal and diffusion slip.
In all these studies, Soret–Dufour effects were not considered. However, Makinde et al. \(\mathbf{[12]}\) examined the hydrodynamic flow and mass diffusion of chemical species with first and higher-order reactions of an electrically conducting fluid over a moving vertical plate with Dufor and Soret. Animasaun and Oyem\(\mathbf{[13]}\) considered the effects of variable fluid viscosity and thermal conductivity, Dufour and Soret on a non-Darcian free convective heat and mass transfer fluid flow past a porous flat surface. The influences of partial slips, Soret and Dufour on unsteady boundary layer flow, heat and mass transfer over shrinking sheet in copper-water nanofluid was looked into by Dzulkifli et al .\(\mathbf{[14]}\). Swamy et al .\(\left[\mathbf{15}\right]\) studies the onset of convection, heat and mass transports in anisotropic densely packed porous layer filled with chemically reactive binary liquid heated at the bottom in presence of Soret and Dufour effects. Similarly, Hayatet al . \(\left[\mathbf{16}\right]\) addressed the convective heat and mass transfer conditions in the radiative flow of Powell-Eyring fluid past an inclined exponentially stretching surface taking Soret and Dufour effects into account. Kafayati\(\left[\mathbf{17}\right]\) looked into entropy generation of associated with double diffusive natural convection of non-Newtonian power-fluids in an inclined porous cavity. Shojaeiet al . \(\left[\mathbf{18}\right]\) examined the analytical approach of a second grade fluid flow along a stretching cylinder and the Soret and Dufour effects. Hayat et al .\(\left[\mathbf{19}\right]\) investigated Soret and Dufour effects on the peristaltic flow of magnetohydrodynamic (MHD) psuedoplastic nanofluid in a tapered asymmetric channel.
In all the above mentioned studies, the interaction between Blasius-Sakiadis flows and Soret-Dufour effects about a flat plate was not investigated adequately. Gangadhar\(\left[\mathbf{7}\right]\) neither considered Soret-Dufour effects and convective heat transfer but neglected the viscous dissipation and thermal radiation parameter. In view of this, the presented paper have extended the work of\(\mathbf{[7]}\) to include Soret (thermal-diffusion) and Dufour (thermo-diffusion) effects as the Blasius and Sakiadis flows are considered about a flat plate with variability properties. A similarity transformation has been adopted to convert the governing partial differential equations into a system of nonlinear ordinary differential equations and the resulting boundary value problem has been solved numerically with Runge-Kutta-Gills method with shooting technique. Results are obtained for different values of the governing dimensionless properties and discussed extensively.